context stringlengths 250 5.97k | A stringlengths 250 5.02k | B stringlengths 250 3.37k | C stringlengths 250 3.6k | D stringlengths 250 8.2k | label stringclasses 4
values |
|---|---|---|---|---|---|
+x\left[D-1-(D+1)x^{2}\right]\frac{d}{dx}R_{n}^{m}(x).start_ROW start_CELL italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 1 ) divide start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 2 e... | x2(x2−1)d2dx2Rnm(x)=[nx2(n+D)−m(D−2+m)]Rnm(x)+x[D−1−(D+1)x2]ddxRnm(x).superscript𝑥2superscript𝑥21superscript𝑑2𝑑superscript𝑥2superscriptsubscript𝑅𝑛𝑚𝑥delimited-[]𝑛superscript𝑥2𝑛𝐷𝑚𝐷2𝑚superscriptsubscript𝑅𝑛𝑚𝑥𝑥delimited-[]𝐷1𝐷1superscript𝑥2𝑑𝑑𝑥superscriptsubscript𝑅𝑛𝑚𝑥x^{2}(x^{2}-... | Rnm(x)=(−1)(n−m)/2(D+m+n2−1n−m2)xmF(−(n−m)/2,(D+n+m)/2m+D/2∣x2),superscriptsubscript𝑅𝑛𝑚𝑥superscript1𝑛𝑚2binomial𝐷𝑚𝑛21𝑛𝑚2superscript𝑥𝑚𝐹conditional𝑛𝑚2𝐷𝑛𝑚2𝑚𝐷2superscript𝑥2R_{n}^{m}(x)=(-1)^{(n-m)/2}\binom{\frac{D+m+n}{2}-1}{\frac{n-m}{2}}x^{m}{}F%
\left(\begin{array}[]{c}-(n-m)/2,(D+n+m)/2\\ |
−(1+n−m2)(1−n−D2)n+m+D2Rn+2m(x)=n−m2(1+n+D2)(1−n+m+D2)Rn−2m(x)+(n+D2)[(1+n+D2)(1−n−D2)(1−x2)+12(n−m)2+(m+D2)(n−m)+m+D2−1]Rnm(x).1𝑛𝑚21𝑛𝐷2𝑛𝑚𝐷2superscriptsubscript𝑅𝑛2𝑚𝑥𝑛𝑚21𝑛𝐷21𝑛𝑚𝐷2superscriptsubscript𝑅𝑛2𝑚𝑥𝑛𝐷2delimited-[]1𝑛𝐷21𝑛𝐷21superscript𝑥212superscript𝑛𝑚2𝑚𝐷2𝑛𝑚𝑚𝐷21sup... |
x3(x2−1)2d3dx3Rnm(x)={−n(3+D)(n+D)x4+[(n+m)D2+(n2+m2−n+3m)D−10m+5m2−n2]x2−m(D+1)(D−2+m)}Rnm(x)+x{[D2+(3+n)D+n2+2]x4+[−2D2−(2+n+m)D+6+2m−n2−m2]x2+D2+D(m−1)−2m+m2}ddxRnm(x).superscript𝑥3superscriptsuperscript𝑥212superscript𝑑3𝑑superscript𝑥3superscriptsubscript𝑅𝑛𝑚𝑥𝑛3𝐷𝑛𝐷superscript𝑥4delimited-[]𝑛𝑚supe... | D |
\ldots,d.italic_T start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT := { italic_t start_POSTSUBSCRIPT italic_i ( italic_i - 1 ) end_POSTSUBSCRIPT ( italic_ω start_POSTSUPERSCRIPT roman_ℓ end_POSTSUPERSCRIPT ) ∣ roman_ℓ = 0 , … , italic_f - 1 } for italic_i = 2 , … , italic_d .
| The cost of the subroutines is determined with this in mind; that is, for each subroutine we determine the maximum length and memory requirement for an MSLP that returns the required output when evaluated with an initial memory containing the appropriate input.
| This adds only one extra MSLP instruction, in order to form and store the element xv−1𝑥superscript𝑣1xv^{-1}italic_x italic_v start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT needed in the conjugate on the right-hand side of (2) (this element can later be overwritten and so does not add to the overall maximum memory quo... | A total of four MSLP instructions (group multiplications or inversions) are required, and only one memory slot is needed in addition to the two memory slots used to permanently store the input elements g,h𝑔ℎg,hitalic_g , italic_h.
In other words, there exists an MSLP S𝑆Sitalic_S with memory quota b=3𝑏3b=3italic_b = ... |
The first step of the algorithm is the one-off computation of T2subscript𝑇2T_{2}italic_T start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT from the LGO standard generators of SL(d,q)SL𝑑𝑞\textnormal{SL}(d,q)SL ( italic_d , italic_q ). The length and memory requirement of an MSLP for this step is as follows. | A |
As in many multiscale methods previously considered, our starting point is the decomposition of the solution space into fine and coarse spaces that are adapted to the problem of interest. The exact definition of some basis functions requires solving global problems, but, based on decaying properties, only local comput... | The idea of using exponential decay to localize global problems was already considered by the interesting approach developed under the name of Localized Orthogonal Decomposition (LOD) [MR2831590, MR3591945, MR3246801, MR3552482] which are
related to ideas of Variational Multiscale Methods [MR1660141, MR2300286]. In the... | One difficulty that hinders the development of efficient methods is the presence of high-contrast coefficients [MR3800035, MR2684351, MR2753343, MR3704855, MR3225627, MR2861254]. When LOD or VMS methods are considered, high-contrast coefficients might slow down the exponential decay of the solutions, making the method ... |
As in many multiscale methods previously considered, our starting point is the decomposition of the solution space into fine and coarse spaces that are adapted to the problem of interest. The exact definition of some basis functions requires solving global problems, but, based on decaying properties, only local comput... |
It is essential for the performing method that the static condensation is done efficiently. The solutions of (22) decay exponentially fast if w𝑤witalic_w has local support, so instead of solving the problems in the whole domain it would be reasonable to solve it locally using patches of elements. We note that the ide... | A |
Alg-A computes at most n𝑛nitalic_n candidate triangles (proof is trivial and omitted) whereas Alg-CM computes at most 5n5𝑛5n5 italic_n triangles (proved in [8]) and so as Alg-K.
(by experiment, Alg-CM and Alg-K have to compute roughly 4.66n4.66𝑛4.66n4.66 italic_n candidate triangles.) |
Alg-A has simpler primitives because (1) the candidate triangles considered in it have all corners lying on P𝑃Pitalic_P’s vertices and (2) searching the next candidate from a given one is much easier – the code length for this is 1:7 in Alg-A and in Alg-CM. |
Our experiment shows that the running time of Alg-A is roughly one eighth of the running time of Alg-K, or one tenth of the running time of Alg-CM. (Moreover, the number of iterations required by Alg-CM and Alg-K is roughly 4.67 times that of Alg-A.) | Comparing the description of the main part of Alg-A (the 7 lines in Algorithm 1) with that of Alg-CM (pages 9–10 of [8]),
Alg-A is conceptually simpler. Alg-CM is claimed “involved” by its authors as it contains complicated subroutines for handling many subcases. | Alg-A computes at most n𝑛nitalic_n candidate triangles (proof is trivial and omitted) whereas Alg-CM computes at most 5n5𝑛5n5 italic_n triangles (proved in [8]) and so as Alg-K.
(by experiment, Alg-CM and Alg-K have to compute roughly 4.66n4.66𝑛4.66n4.66 italic_n candidate triangles.) | A |
𝖫(x(i),y(i))=1{y(i)=yrumor}log(y~rumor(i))+1{y(i)=ynews}log(y~news(i))𝖫superscript𝑥𝑖superscript𝑦𝑖1superscript𝑦𝑖subscript𝑦𝑟𝑢𝑚𝑜𝑟𝑙𝑜𝑔superscriptsubscript~𝑦𝑟𝑢𝑚𝑜𝑟𝑖1superscript𝑦𝑖subscript𝑦𝑛𝑒𝑤𝑠𝑙𝑜𝑔superscriptsubscript~𝑦𝑛𝑒𝑤𝑠𝑖\mathsf{L}(x^{(i)},y^{(i)})=1\{y^{(i)}=y... | Based on the credibility model we develop a novel and effective cascaded model for rumor classification. The model uses time-series structure of features to capture their temporal dynamics. Our model clearly
outperforms strong baselines, especially for the targeted early stage of the diffusion. It already | In the lower part of the pipeline, we extract features from tweets and combine them with the creditscore to construct the feature vector in a time series structure called Dynamic Series Time Model. These feature vectors are used to train the classifier for rumor vs. (non-rumor) news classification.
|
As observed in [19, 20], rumor features are very prone to change during an event’s development. In order to capture these temporal variabilities, we build upon the Dynamic Series-Time Structure (DSTS) model (time series for short) for feature vector representation proposed in [20]. We base our credibility feature on t... |
Most relevant for our work is the work presented in [20], where a time series model to capture the time-based variation of social-content features is used. We build upon the idea of their Series-Time Structure, when building our approach for early rumor detection with our extended dataset, and we provide a deep analys... | C |
\left(\sqrt{\frac{\log\log t}{\log t}}\right)∥ divide start_ARG bold_w ( italic_t ) end_ARG start_ARG ∥ bold_w ( italic_t ) ∥ end_ARG - divide start_ARG over^ start_ARG bold_w end_ARG end_ARG start_ARG ∥ over^ start_ARG bold_w end_ARG ∥ end_ARG ∥ = italic_O ( square-root start_ARG divide start_ARG roman_log roman_log i... | In some non-degenerate cases, we can further characterize the asymptotic behavior of 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ). To do so, we need to refer to the KKT conditions (eq. 6)
of the SVM problem (eq. 4) and the associated |
where the residual 𝝆k(t)subscript𝝆𝑘𝑡\boldsymbol{\rho}_{k}(t)bold_italic_ρ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_t ) is bounded and 𝐰^ksubscript^𝐰𝑘\hat{\mathbf{w}}_{k}over^ start_ARG bold_w end_ARG start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT is the solution of the K-class SVM: | where 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) has a bounded norm for almost all datasets, while in zero measure case 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) contains additional O(loglog(t))𝑂𝑡O(\log\log(t))italic_O ( roman_log roman_log ( italic_t ) ) componen... | The follow-up paper (Gunasekar et al., 2018) studied this same problem with exponential loss instead of squared loss. Under additional assumptions on the asymptotic convergence of update directions and gradient directions, they were able to relate the direction of gradient descent iterates on the factorized parameteriz... | A |
Text feature set contains totally 16 features. The feature ranking are shown in Table 7. The best one is NumOfChar which is the average number of different characters in tweets. PolarityScores is the best feature when we tested the single tweets model, but its performance in time series model is not ideal. It is true ... | The performance of user features is similar with the Twitter features, they are both quite stable from the first hour to the last hour. As shown in Table 9, the best feature over 48 hours of the user feature group is UserTweetsPerDays and it is the best feature overall in the first 4 hours, but its rank decreases with ... | The performance of Twitter features are stable over time from the beginning to the end. The 3 best of Twitter Features are all based on contained URLs in tweets: ContainNEWS, UrlRankIn5000, WotScore, as shown in Table 8. It is quite reasonable that the news event would have higher probability to be reported by news or ... | As we can see in Figure 9 the best result on average over 48 hours is the BestSet. Second one is All features. Except those two, the best group feature is Text features. One reason is the text feature set has the largest group of feature with totally 16 features. But if look into each feature in text feature group, we ... |
Text feature set contains totally 16 features. The feature ranking are shown in Table 7. The best one is NumOfChar which is the average number of different characters in tweets. PolarityScores is the best feature when we tested the single tweets model, but its performance in time series model is not ideal. It is true ... | B |
Results. The baseline and the best results of our 1stsuperscript1𝑠𝑡1^{st}1 start_POSTSUPERSCRIPT italic_s italic_t end_POSTSUPERSCRIPT stage event-type classification is shown in Table 3-top. The accuracy for basic majority vote is high for imbalanced classes, yet it is lower at weighted F1. Our learned model achie... | For this part, we first focus on evaluating the performance of single L2R models that are learned from the pre-selected time (before, during and after) and types (Breaking and Anticipate) set of entity-bearing queries. This allows us to evaluate the feature performance i.e., salience and timeliness, with time and type ... | Multi-Criteria Learning. Our task is to minimize the global relevance loss function, which evaluates the overall training error, instead of assuming the independent loss function, that does not consider the correlation and overlap between models. We adapted the L2R RankSVM [12]. The goal of RankSVM is learning a linear... | RQ3. We demonstrate the results of single models and our ensemble model in Table 4. As also witnessed in RQ2, SVMall𝑆𝑉subscript𝑀𝑎𝑙𝑙SVM_{all}italic_S italic_V italic_M start_POSTSUBSCRIPT italic_a italic_l italic_l end_POSTSUBSCRIPT, will all features, gives a rather stable performance for both NDCG and Recall... | We further investigate the identification of event time, that is learned on top of the event-type classification. For the gold labels, we gather from the studied times with regards to the event times that is previously mentioned. We compare the result of the cascaded model with non-cascaded logistic regression. The res... | D |
The special case of piecewise-stationary, or abruptly changing environments, has attracted a lot of interest in general [Yu and Mannor, 2009; Luo et al., 2018],
and for UCB [Garivier and Moulines, 2011] and Thompson sampling [Mellor and Shapiro, 2013] algorithms, in particular. | with Bernoulli and contextual linear Gaussian reward functions [Kaufmann et al., 2012; Garivier and Cappé, 2011; Korda et al., 2013; Agrawal and Goyal, 2013b],
as well as for context-dependent binary rewards modeled with the logistic reward function Chapelle and Li [2011]; Scott [2015] —Appendix A.3. | The use of SMC in the context of bandit problems was previously considered for probit [Cherkassky and Bornn, 2013] and softmax [Urteaga and Wiggins, 2018c] reward models,
and to update latent feature posteriors in a probabilistic matrix factorization model [Kawale et al., 2015]. | The special case of piecewise-stationary, or abruptly changing environments, has attracted a lot of interest in general [Yu and Mannor, 2009; Luo et al., 2018],
and for UCB [Garivier and Moulines, 2011] and Thompson sampling [Mellor and Shapiro, 2013] algorithms, in particular. | RL [Sutton and Barto, 1998] has been successfully applied to a variety of domains,
from Monte Carlo tree search [Bai et al., 2013] and hyperparameter tuning for complex optimization in science, engineering and machine learning problems [Kandasamy et al., 2018; Urteaga et al., 2023], | B |
Table 1 shows basic patient information. Half of the patients are female and ages range from 17 to 66, with a mean age of 41.8 years. Body weight, according to BMI, is normal for half of the patients, four are overweight and one is obese. The mean BMI value is 26.9. Only one of the patients suffers from diabetes type ... | Likewise, the daily number of measurements taken for carbohydrate intake, blood glucose level and insulin units vary across the patients.
The median number of carbohydrate log entries vary between 2 per day for patient 10 and 5 per day for patient 14. | Table 2 gives an overview of the number of different measurements that are available for each patient.111For patient 9, no data is available.
The study duration varies among the patients, ranging from 18 days, for patient 8, to 33 days, for patient 14. | Overall, the distribution of all three kinds of values throughout the day roughly correspond to each other.
In particular, for most patients the number of glucose measurements roughly matches or exceeds the number of rapid insulin applications throughout the days. | Patient 17 has more rapid insulin applications than glucose measurements in the morning and particularly in the late evening.
For patient 15, rapid insulin again slightly exceeds the number of glucose measurements in the morning. Curiously, the number of glucose measurements match the number carbohydrate entries – it i... | B |
Later attempts addressed that shortcoming by taking advantage of classification architectures pre-trained on the ImageNet database Deng et al. (2009). This choice was motivated by the finding that features extracted from CNNs generalize well to other visual tasks Donahue et al. (2014). Consequently, DeepGaze I Kümmerer... | We propose a new CNN architecture with modules adapted from the semantic segmentation literature to predict fixation density maps of the same image resolution as the input. Our approach is based on a large body of research regarding saliency models that leverage object-specific features and functionally replicate human... | The spatial allocation of attention when viewing natural images is commonly represented in the form of topographic saliency maps that depict which parts of a scene attract fixations reliably. Identifying the underlying properties of these regions would allow us to predict human fixation patterns and gain a deeper under... | Table 2 demonstrates that we obtained state-of-the-art scores for the CAT2000 test dataset regarding the AUC-J, sAUC, and KLD evaluation metrics, and competitive results on the remaining measures. The cumulative rank (as computed above) suggests that our model outperformed all previous approaches, including the ones ba... |
With the large-scale acquisition of eye tracking measurements under natural viewing conditions, data-driven machine learning techniques became more practicable. Judd et al. (2009) introduced a model based on support vector machines to estimate fixation densities from a set of low-, mid-, and high-level visual features... | A |
In this work, we have answered several open questions about the string parameter of the locality number. Our main tool was to relate the locality number to the graph parameters cutwidth and pathwidth via suitable reductions. As an additional result, our reductions also pointed out an interesting relationship between th... |
While our focus is on theoretical results in form of lower and upper complexity bounds, we stress here that the reductions may also be of practical interest, since they allow to transform any practical pathwidth or cutwidth algorithm into a practical algorithm for computing the locality number (or to transform a pract... | The main results are presented in Sections 4, 5 and 6. First, in Section 4, we present the reductions from Loc to Cutwidth and vice versa, and we discuss the consequences of these reductions. Then, in Section 5, we show how Loc can be reduced to Pathwidth, which yields an approximation algorithm for computing the local... |
In this section, we introduce polynomial-time reductions from the problem of computing the locality number of a word to the problem of computing the cutwidth of a graph, and vice versa. This establishes a close relationship between these two problems (and their corresponding parameters), which lets us derive several u... | Many existing algorithms constructing path decompositions are of theoretical interest only, and this disadvantage carries over to the possible algorithms computing the locality number or cutwidth (see Section 6) based on them. However, the reduction of 5.7 is also applicable in a purely practical scenario, since any ki... | A |
Additionally, convolutional layers create feature maps using shared weights that have a fixed number of parameters in contrast with fully connected layers, making them much faster.
VGG[17] is a simple CNN architecture that utilizes small convolutional filters (3×3333\times 33 × 3) and performance is increased by increa... | Convolutional Neural Networks (CNNs), as shown in Fig. 2, consist of a convolutional part where hierarchical feature extraction takes place (low-level features such as edges and corners and high-level features such as parts of objects) and a fully connected part for classification or regression, depending on the nature... | GoogleNet[18] is another CNN-like architecture that makes use of the inception module.
The inception module uses multiple convolutional layers in parallel from which the result is the concatenated, thus allowing the network to learn multiple level features. | In[159] the authors detect the area, position and shape of the MI using a model that consists of three layers; first, the heart localization layer is a Fast R-CNN[166] which crops the ROI sequences including the LV; second, the motion statistical layers, which build a time-series architecture to capture the local motio... | A common AE architecture is Stacked Denoised AE (SDAE) that has an objective to reconstruct the clean input from an artificially corrupted version of the input[20] which prevents the model from learning trivial solutions.
Another AE-like architecture is u-net[4], which is of special interest to the biomedical community... | B |
We will now describe the details of SimPLe, outlined in Algorithm 1. In step 6 we use the proximal policy optimization (PPO) algorithm (Schulman et al., 2017) with γ=0.95𝛾0.95\gamma=0.95italic_γ = 0.95. The algorithm generates rollouts in the simulated environment env′𝑒𝑛superscript𝑣′env^{\prime}italic_e italic_n ... |
Given the stochasticity of the proposed model, SimPLe can be used with truly stochastic environments. To demonstrate this, we ran an experiment where the full pipeline (both the world model and the policy) was trained in the presence of sticky actions, as recommended in (Machado et al., 2018, Section 5). Our world mod... | The iterative process of training the model, training the policy, and collecting data is crucial for non-trivial tasks where random data collection is insufficient. In a game-by-game analysis, we quantified the number of games where the best results were obtained in later iterations of training. In some games, good pol... |
The main loop in Algorithm 1 is iterated 15151515 times (cf. Section 6.4). The world model is trained for 45454545K steps in the first iteration and for 15151515K steps in each of the following ones. Shorter training in later iterations does not degrade the performance because the world model after first iteration cap... | Figure 1: Main loop of SimPLe. 1) the agent starts interacting with the real environment following the latest policy (initialized to random). 2) the collected observations will be used to train (update) the current world model. 3) the agent updates the policy by acting inside the world model. The new policy will be eva... | C |
Zhang et al. [11] trained an ensemble of CNNs containing two to ten layers using STFT features extracted from EEG band frequencies for mental workload classification.
Giri et al. [12] extracted statistical and information measures from frequency domain to train an 1D CNN with two layers to identify ischemic stroke. | The spectrogram S2I results are in contrary with the expectation that the interpretable time-frequency representation would help in finding good features for classification.
We hypothesize that the spectrogram S2I was hindered by its lack of non-trainable parameters. | The names of the classes are depicted at the right along with the predictions for this example signal.
The image between m𝑚mitalic_m and bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT depicts the output of the one layer CNN Signal2Image module, while the ‘signal as image’ and spectrogram h... | Figure 1: High level overview of a feed-forward pass of the combined methods.
xisubscript𝑥𝑖x_{i}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is the input, m𝑚mitalic_m is the Signal2Image module, bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT is the 1D or 2D architecture ‘base ... | For the purposes of this paper and for easier future reference we define the term Signal2Image module (S2I) as any module placed after the raw signal input and before a ‘base model’ which is usually an established architecture for imaging problems.
An important property of a S2I is whether it consists of trainable para... | D |
This section describes the primary locomotion modes, rolling and walking locomotion of our hybrid track-legged robot named Cricket shown in Fig. 2. It also introduces two proposed gaits designed specifically for step negotiation in quadrupedal wheel/track-legged robots.
| In this section, we explore the autonomous locomotion mode transition of the Cricket robot. We present our hierarchical control design, which is simulated in a hybrid environment comprising MATLAB and CoppeliaSim. This design facilitates the decision-making process when transitioning between the robot’s rolling and wal... | The Cricket robot, as referenced in [20], forms the basis of this study, being a fully autonomous track-legged quadruped robot. Its design specificity lies in embodying fully autonomous behaviors, and its locomotion system showcases a unique combination of four rotational joints in each leg, which can be seen in Fig. 3... | Similarly, when the robot encountered a step with a height of 3h (as shown in Fig. 12), the mode transition was activated when the energy consumption of the rear track negotiation in rolling mode surpassed the threshold value derived from the previously assessed energy results of the rear body climbing gait. The result... | Figure 2: The Cricket robot (left) and its leg joints layout (right). The Cricket robot [20] is a hybrid locomotion system that utilizes four revolute joints on each leg. The outermost leg segment is equipped with a drivable track that encircles it, enabling the robot to move like traditional skid-steer tank robots.
| B |
(1.5,4.5)1.54.5(1.5,4.5)( 1.5 , 4.5 )-competitive; otherwise, we set α𝛼\alphaitalic_α to a smaller value. For α=0.9𝛼0.9\alpha=0.9italic_α = 0.9 for example, the algorithm is asymptotically
(1.5625,3.75)1.56253.75(1.5625,3.75)( 1.5625 , 3.75 )-competitive. Similarly, for α=0.868𝛼0.868\alpha=0.868italic_α = 0.868, we ... | Johnson [18] proved that the competitive ratio of First-Fit and Best-Fit
is 1.7. Many other algorithms with improved competitive ratios have been studied. The best known algorithm was introduced by Balogh et al. [6] and has a competitive ratio of at most 1.5783. Moreover, it is known that no online algorithm can achiev... |
Our solution uses an algorithm introduced by Boyar et al. [12] which achieves a competitive ratio of 1.5 using O(logn)𝑂𝑛O(\log n)italic_O ( roman_log italic_n ) bits of advice. We refer to this algorithm as Reserve-Critical in this paper and describe it briefly. See Figure 2 for an illustration. |
To address this issue, we introduce an algorithm named Toggle (Tog) that has a parameter β∈[0,1/2]𝛽012\beta\in[0,1/2]italic_β ∈ [ 0 , 1 / 2 ], and uses 2 advice bits to select one of the algorithms Timestamp, Mtfe or Mtfo, see Figure 3. This algorithm achieves a competitive ratio of rTog=5/3+5β6+3βsubscript𝑟Tog535... | This can be accomplished with a binary search in the interval [1,⌈logu⌉]1𝑢[1,\lceil\log u\rceil][ 1 , ⌈ roman_log italic_u ⌉ ] , since we know that the doubling strategy in
which the i𝑖iitalic_i-th bid equals 2isuperscript2𝑖2^{i}2 start_POSTSUPERSCRIPT italic_i end_POSTSUPERSCRIPT is w𝑤witalic_w-competitive for al... | B |
Thus, all these other models were also implemented in Python 2.7, using the sklearn library181818https://scikit-learn.org/, version 0.17. Vectorization was done with the TfidfVectorizer class, with the standard English stop words list. Additionally, terms having a document frequency lower than 20 were ignored. Finally,... | In this pilot task, classifiers must decide, as early as possible, whether each user is depressed or not based on his/her writings.
In order to accomplish this, during the test stage and in accordance with the pilot task definition, the subject’s writings were divided into 10 chunks —thus each chunk contained 10% of th... | In the context of online environments such as social media, an ADD scenario that is gaining interest, as we will see in Subsection 2.2, is the one known as early depression detection (EDD). In EDD the task is, given users’ data stream, to detect possible depressive people as soon and accurate as possible.
| In the first one, we performed experiments in accordance with the original eRisk pilot task definition, using the described chunks.
However, since this definition assumes, by using chunks, that the total number of user’s writings is known in advance191919Which is not true when working with a dynamic environment, such a... | As said earlier, each chunk contained 10% of the subject’s writing history, a value that for some subjects could be just a single post while for others hundreds or even thousands of them. Furthermore, the use of chunks assumes we know in advance all subject’s posts, which is not the case in real life scenarios, in whic... | C |
With the rapid growth of data, distributed SGD (DSGD) and its variant distributed MSGD (DMSGD) have garnered much attention. They distribute the stochastic gradient computation across multiple workers to expedite the model training.
These methods can be implemented on distributed frameworks like parameter server and al... | We use the CIFAR10 and CIFAR100 datasets under both IID and non-IID data distribution. For the IID scenario, the training data is randomly assigned to each worker. For the non-IID scenario, we use Dirichlet distribution with parameter 0.1 to partition the training data as in (Hsu et al., 2019; Lin et al., 2021).
We ado... | Each worker computes stochastic gradients locally and communicates with the server or other workers to obtain the aggregated stochastic gradients for updating the model parameter. Recently, more and more large-scale deep learning models, such as large language models (Devlin et al., 2019; Brown et al., 2020; Touvron et... | Researchers have proposed two main categories of communication compression methods for reducing communication cost: quantization (Wen et al., 2017; Alistarh et al., 2017; Jiang and Agrawal, 2018) and sparsification (Aji and Heafield, 2017; Alistarh et al., 2018; Stich et al., 2018; Karimireddy et al., 2019; Tang et al.... | In existing error feedback based sparse communication methods, most are for vanilla DSGD (Aji and Heafield, 2017; Alistarh et al., 2018; Stich et al., 2018; Karimireddy et al., 2019; Tang et al., 2019).
There has appeared one error feedback based sparse communication method for DMSGD, called Deep Gradient Compression (... | B |
A limitation of SANs is the use of varying amplitude-only kernels, which are not sufficient for more complex data and also do not fully utilize the compressibility of the data.
A possible solution would be using a grid sampler [45] on the kernel allowing it to learn more general transformations (such as scale) than sim... | From the point of view of Sparse Dictionary Learning, SANs kernels could be seen as the atoms of a learned dictionary specializing in interpretable pattern matching (e.g. for Electrocardiogram (ECG) input the kernels of SANs are ECG beats) and the sparse activation map as the representation.
The fact that SANs are wide... | We then defined SANs which have minimal structure and with the use of sparse activation functions learn to compress data without losing important information.
Using Physionet datasets and MNIST we demonstrated that SANs are able to create high quality representations with interpretable kernels. | Comparing the differences of φ¯¯𝜑\bar{\varphi}over¯ start_ARG italic_φ end_ARG between the Identity, the ReLU and the rest sparse activation functions in Fig. 4LABEL:sub@subfig:flithos_m we notice that the latter produce a minimum region in which we observe interpretable kernels.
|
In Section II we define the φ𝜑\varphiitalic_φ metric, then in Section III we define the five tested activation functions along with the architecture and training procedure of SANs, in Section IV we experiment SANs on the Physionet [32], UCI-epilepsy [33], MNIST [34] and FMNIST [35] databases and provide visualization... | B |
We establish a multi-factor system model based on large-scale UAV networks in highly dynamic post-disaster scenarios. Considering the limitations in existing algorithms, we devise a novel algorithm which is capable of updating strategies simultaneously to fit the highly dynamic environments. The main contributions of ... | Since the UAV ad-hoc network game is a special type of potential game, we can apply the properties of the potential game in the later analysis. Some algorithms that have been applied in the potential game can also be employed in the UAV ad-hoc network game. In the next section, we investigate the existing algorithm wit... |
Game theory provides an efficient tool for the cooperation through resource allocation and sharing [20][21]. A computation offloading game has been designed in order to balance the UAV’s tradeoff between execution time and energy consumption [25]. A sub-modular game is adopted in the scheduling of beaconing periods fo... |
We establish a multi-factor system model based on large-scale UAV networks in highly dynamic post-disaster scenarios. Considering the limitations in existing algorithms, we devise a novel algorithm which is capable of updating strategies simultaneously to fit the highly dynamic environments. The main contributions of ... | We propose a novel UAV ad-hoc network model with the aggregative game which is compatible with the large-scale highly dynamic environments, in which several influences are coupled together. In the aggregative game, the interference from other UAVs can be regarded as the integral influence, which makes the model more pr... | D |
With boundary conditions 𝐯¯⟂|Γ=𝟎evaluated-atsubscript¯𝐯perpendicular-toΓ0\overline{\mathbf{v}}_{\perp}|_{\Gamma}=\mathbf{0}over¯ start_ARG bold_v end_ARG start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = bold_0, | impose the natural boundary conditions (∇⟂ω)|Γ=0evaluated-atsubscript∇perpendicular-to𝜔Γ0\left(\nabla_{\perp}\,\omega\,\right)|_{\Gamma}=0( ∇ start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT italic_ω ) | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0,
and the third term in equation 3.21 will vanish due to | of the electric field at the boundary. The boundary condition (∇⟂ψ)|Γ=0evaluated-atsubscript∇perpendicular-to𝜓Γ0(\nabla_{\perp}\psi)|_{\Gamma}=0( ∇ start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT italic_ψ ) | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0
or (Δ∗ψ)|Γ=0evaluated-atsuperscriptΔ𝜓Γ0(\Delta^{*}\psi)|_{\Gamma}=... | to density, n¯¯𝑛\overline{n}over¯ start_ARG italic_n end_ARG will automatically evolve to satisfy the
natural boundary condition (ζ∇⟂n)|Γ=0evaluated-at𝜁subscript∇perpendicular-to𝑛Γ0\left(\zeta\,\nabla_{\perp}n\right)|_{\Gamma}=0( italic_ζ ∇ start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT italic_n ) | start_POSTSUBSCRIPT ro... | and ψ|Γ=0evaluated-at𝜓Γ0\psi|_{\Gamma}=0italic_ψ | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0 automatically leads to the boundary condition
(Δ∗ψ)|Γ=0evaluated-atsuperscriptΔ𝜓Γ0(\Delta^{*}\psi)|_{\Gamma}=0( roman_Δ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT italic_ψ ) | start_POSTSUBSCRIPT roman_Γ end_POSTSUB... | C |
Let r𝑟ritalic_r be the relation on 𝒞Rsubscript𝒞𝑅\mathcal{C}_{R}caligraphic_C start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT given to the left of Figure 12.
Its abstract lattice ℒrsubscriptℒ𝑟\mathcal{L}_{r}caligraphic_L start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT is represented to the right. | First, remark that both A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B and B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A are possible.
Indeed, if we set g=⟨b,a⟩𝑔𝑏𝑎g=\langle b,a\rangleitalic_g = ⟨ italic_b , italic_a ⟩ or g=⟨a,1⟩𝑔𝑎1g=\langle a,1\rangleitalic_g = ⟨ italic_a , 1 ⟩, then r⊧gA→... | The tuples t1subscript𝑡1t_{1}italic_t start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, t4subscript𝑡4t_{4}italic_t start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT represent a counter-example to BC→A𝐵𝐶→𝐴BC\operatorname{\rightarrow}Aitalic_B italic_C → italic_A for g1subscript𝑔1g_{1}italic_g start_POSTSUBSCRIPT 1 end_POSTSUBSCRI... | For convenience we give in Table 7 the list of all possible realities
along with the abstract tuples which will be interpreted as counter-examples to A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B or B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A. | If no confusion is possible, the subscript R𝑅Ritalic_R will be omitted, i.e., we will use
≤,∧,∨\leq,\operatorname{\land},\operatorname{\lor}≤ , ∧ , ∨ instead of ≤R,∧R,∨Rsubscript𝑅subscript𝑅subscript𝑅\leq_{R},\operatorname{\land}_{R},\operatorname{\lor}_{R}≤ start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT , ∧ start_P... | C |
Figure 6 shows the loss metrics of the three algorithms in CARTPOLE environment, this implies that using Dropout-DQN methods introduce more accurate gradient estimation of policies through iterations of different learning trails than DQN. The rate of convergence of one of Dropout-DQN methods has done more iterations t... |
The results in Figure 3 show that using DQN with different Dropout methods result in better-preforming policies and less variability as the reduced standard deviation between the variants indicate to. In table 1, Wilcoxon Sign-Ranked test was used to analyze the effect of Variance before applying Dropout (DQN) and aft... | In this study, we proposed and experimentally analyzed the benefits of incorporating the Dropout technique into the DQN algorithm to stabilize training, enhance performance, and reduce variance. Our findings indicate that the Dropout-DQN method is effective in decreasing both variance and overestimation. However, our e... | In this paper, we introduce and conduct an empirical analysis of an alternative approach to mitigate variance and overestimation phenomena using Dropout techniques. Our main contribution is an extension to the DQN algorithm that incorporates Dropout methods to stabilize training and enhance performance. The effectivene... | To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... | B |
In medical image segmentation works, researchers have converged toward using classical cross-entropy loss functions along with a second distance or overlap based functions. Incorporating domain/prior knowledge (such as coding the location of different organs explicitly in a deep model) is more sensible in the medical d... |
Going beyond pixel intensity-based scene understanding by incorporating prior knowledge, which have been an active area of research for the past several decades (Nosrati and Hamarneh, 2016; Xie et al., 2020). Encoding prior knowledge in medical image analysis models is generally more possible as compared to natural im... | Deep learning has had a tremendous impact on various fields in science. The focus of the current study is on one of the most critical areas of computer vision: medical image analysis (or medical computer vision), particularly deep learning-based approaches for medical image segmentation. Segmentation is an important pr... |
Exploring reinforcement learning approaches similar to Song et al. (2018) and Wang et al. (2018c) for semantic (medical) image segmentation to mimic the way humans delineate objects of interest. Deep CNNs are successful in extracting features of different classes of objects, but they lose the local spatial information... |
For image segmentation, sequenced models can be used to segment temporal data such as videos. These models have also been applied to 3D medical datasets, however the advantage of processing volumetric data using 3D convolutions versus the processing the volume slice by slice using 2D sequenced models. Ideally, seeing ... | A |
Note that we interchangeably refer with 𝐀(0)superscript𝐀0{\mathbf{A}}^{(0)}bold_A start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT or 𝐀𝐀{\mathbf{A}}bold_A to the original adjacency matrix.
The adjacency matrices in 𝒜𝒜\mathcal{A}caligraphic_A are used to implement hierarchical pooling in deep GNN architectures. |
We conclude by noticing that, due to the smoothing effect of MP operations, the nodes belonging to densely connected graph components are likely to have very similar representations computed by the GNN; it is, therefore, not important which of these nodes are dropped by a random cut. | The red line indicates the number of edges that remain in 𝐀¯¯𝐀\bar{{\mathbf{A}}}over¯ start_ARG bold_A end_ARG after sparsification.
It is possible to see that for small increments of ϵitalic-ϵ\epsilonitalic_ϵ the spectral distance increases linearly, while the number of edges in the graph drops exponentially. |
Generating hierarchical representations across the layers of a neural network is key to deep learning methods. This hierarchical representation is usually achieved through pooling operations, which progressively reduce the dimensionality of the inputs encouraging the network to learn high-level data descriptors. | Due to the connectivity preservation property, by repeatedly applying Kron reduction the graph eventually becomes fully-connected.
This implies a high computational burden in deeper layers of the network, since the complexity of MP operations scales with the number of edges. | D |
Fernández-Delgado et al. (2014) conduct extensive experiments comparing 179 classifiers on 121 UCI datasets (Dua & Graff, 2017). The authors show that random forests perform best, followed by support vector machines with a radial basis function kernel. Therefore, random forests are often considered as a reference for n... | The generalization performance has been widely studied. Zhang et al. (2017) demonstrate that deep neural networks are capable of fitting random labels and memorizing the training data. Bornschein et al. (2020) analyze the performance across different dataset sizes.
Olson et al. (2018) evaluate the performance of modern... | Mapping random forests into neural networks is already used in many applications such as network initialization (Humbird et al., 2019), camera localization (Massiceti et al., 2017), object detection (Reinders et al., 2018, 2019), or semantic segmentation (Richmond et al., 2016).
State-of-the-art methods (Massiceti et a... | Neural networks have become very popular in many areas, such as computer vision (Krizhevsky et al., 2012; Reinders et al., 2022; Ren et al., 2015; Simonyan & Zisserman, 2015; Zhao et al., 2017; Qiao et al., 2021; Rudolph et al., 2022; Sun et al., 2021), speech recognition (Graves et al., 2013; Park et al., 2019; Sun et... | Random forests are trained with 500500500500 decision trees, which are commonly used in practice (Fernández-Delgado et al., 2014; Olson et al., 2018).
The decision trees are constructed up to a maximum depth of ten. For splitting, the Gini Impurity is used and N𝑁\sqrt{N}square-root start_ARG italic_N end_ARG features ... | A |
Theoretically, we establish the sample efficiency of OPPO in an episodic setting of Markov decision processes (MDPs) with full-information feedback, where the transition dynamics are linear in features (Yang and Wang, 2019b, a; Jin et al., 2019; Ayoub et al., 2020; Zhou et al., 2020). In particular, we allow the trans... | Moreover, we prove that, even when the reward functions are adversarially chosen across the episodes, OPPO attains the same regret in terms of competing with the globally optimal policy in hindsight (Cesa-Bianchi and Lugosi, 2006; Bubeck and Cesa-Bianchi, 2012). In comparison, existing algorithms based on value iterati... | Our work is based on the aforementioned line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) on the computational efficiency of policy optimization, which covers PG, NPG, TRPO, PPO, and AC. In p... |
We study the sample efficiency of policy-based reinforcement learning in the episodic setting of linear MDPs with full-information feedback. We proposed an optimistic variant of the proximal policy optimization algorithm, dubbed as OPPO, which incorporates the principle of “optimism in the face of uncertainty” into po... |
Broadly speaking, our work is related to a vast body of work on value-based reinforcement learning in tabular (Jaksch et al., 2010; Osband et al., 2014; Osband and Van Roy, 2016; Azar et al., 2017; Dann et al., 2017; Strehl et al., 2006; Jin et al., 2018) and linear settings (Yang and Wang, 2019b, a; Jin et al., 2019;... | A |
The newly emerging NAS approaches are promising candidates to automate the design of application-specific architectures with little user interaction.
However, it appears unlikely that current NAS approaches will discover new fundamental design principles as the resulting architectures highly depend on a-priori knowledg... | The computational cost of performing inference should match the (usually limited) resources in deployed systems and exploit the available hardware optimally in terms of time and energy.
Computational efficiency, in particular, also includes mapping the representational efficiency to available hardware structures. | In experiments, we demonstrated on two benchmark data sets the difficulty of finding a good trade-off among prediction quality, representational efficiency and computational efficiency.
Considering three embedded hardware platforms, we showed that massive parallelism is required for inference efficiency and that quanti... | In this section, we provide a comprehensive overview of methods that enhance the efficiency of DNNs regarding memory footprint, computation time, and energy requirements.
We have identified three different major approaches that aim to reduce the computational complexity of DNNs, i.e., (i) weight and activation quantiza... | In this regard, resource-efficient neural networks for embedded systems are concerned with the trade-off between prediction quality and resource efficiency (i.e., representational efficiency and computational efficiency). This is highlighted in Figure 1.
Note that this requires observing overall constraints such as pre... | B |
A metric space (X,dX)𝑋subscript𝑑𝑋(X,d_{X})( italic_X , italic_d start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT ) is said to be ANR (Absolute Neighborhood Retract) if, whenever X𝑋Xitalic_X is a subspace of another metric space Y𝑌Yitalic_Y, there exists an open set X⊂U⊆Y𝑋𝑈𝑌X\subset U\subseteq Yitalic_X ⊂ italic_U... | are all metric homotopy pairings, since the second element in each pair is an injective metric space (see [61, Section 3]) into which X𝑋Xitalic_X isometrically embeds via the map κ:x↦dX(x,⋅):𝜅maps-to𝑥subscript𝑑𝑋𝑥⋅\kappa:x\mapsto d_{X}(x,\cdot)italic_κ : italic_x ↦ italic_d start_POSTSUBSCRIPT italic_X end_POSTSU... | It is known that every topological manifold with compatible metric (so, a metric manifold) is an ANR. Not only that, every locally Euclidean metric space is an ANR (see [51, Theorem III.8.1]). Also, every compact, (topologically) finite dimensional, and locally contractible metric space is ANR (see [34, Section 1]). Th... | X:=𝒢∨M1∨⋯∨Mnassign𝑋𝒢subscript𝑀1⋯subscript𝑀𝑛X:=\mathcal{G}\vee M_{1}\vee\cdots\vee M_{n}italic_X := caligraphic_G ∨ italic_M start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ∨ ⋯ ∨ italic_M start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT
arising from metric gluings via v1∼p1,…,vn∼pnformulae-sequencesimilar-tosubscript𝑣1subs... |
For a compact metric space (X,dX)𝑋subscript𝑑𝑋(X,d_{X})( italic_X , italic_d start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT ), the map κ:X→L∞(X):𝜅→𝑋superscript𝐿𝑋\kappa:X\to L^{\infty}(X)italic_κ : italic_X → italic_L start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT ( italic_X ), x↦dX(x,⋅)maps-to𝑥subscript𝑑𝑋𝑥⋅x\... | B |
Although our main design goal was to support the investigation of t-SNE projections, most of our views and interaction techniques are not strictly confined to the t-SNE algorithm. For example, the Dimension Correlation view could, in theory, be applied to any projection generated by any other algorithm. Its motivation,... | In this paper, we introduced t-viSNE, an interactive tool for the visual investigation of t-SNE projections. By partly opening the black box of the t-SNE algorithm, we managed to give power to users allowing them to test the quality of the projections and understand the rationale behind the choices of the algorithm whe... | The main goal of the study was to test if t-viSNE improved the usability and effectiveness of the exploration of high-dimensional data with t-SNE when compared to another state-of-the-art tool.
Table I in Section 2 was used as the basis for an Analysis of Competing Hypotheses (ACH) [64], a methodology for the fair comp... | Tasks
Six tasks were provided to the participants, without any specific mentions to the tool’s features. In consequence, the participants themselves were responsible for performing them to the best of their abilities. The six tasks were designed to match the six main pitfalls of the exploration of high-dimensional da... | The goals of the comparative study presented in this paper were to provide initial evidence of the acceptance of t-viSNE by analysts, the consistency of their results when exploring a t-SNE projection using our tool, and the improvement over another state-of-the-art tool.
The tasks of the study were designed to test ho... | D |
As mentioned previously, the global set of Swarm Intelligence algorithms can be divided as a function of the type of animals. Between the possible categories stemming from this criteria, we have grouped them according to the environmental medium inhibited by the inspiring animal (aquatic, terrestrial or aerial). This c... | Reviewed algorithms that fall under the Swarm Intelligence umbrella are shown in Tables 3, 4, 5, 6, 7 and 8. This is the most populated category of all our study, characterized by a first category that relates to the type of animal that has inspired each algorithm: as such, we find i) flying animals, namely, algorithms... |
Terrestrial animals: Meta-heuristics in this category are inspired by foraging or movements in terrestrial animals. The most renowned approach within this category is the classical ACO meta-heuristic [115], which replicates the stigmergic mechanism used by ants to locate food sources and inform of the existence of the... |
Flying animals: This category comprises meta-heuristics based on the concept of Swarm Intelligence in which the trajectory of agents is inspired by flying movements, as those observed in birds, bats, or other flying insects. The most well-known algorithms in this subcategory are PSO [80] and ABC [116]. | Movement: We have considered that an algorithm belongs to the movement inspiration subcategory if the biological inspiration resides mainly in the way the animal inspiring the algorithm regularly moves around its environment. As such, the differential aspect of the movement could hinge on the dynamics of the movement i... | C |
where φ(⋅)𝜑⋅\varphi(\cdot)italic_φ ( ⋅ ) is certain activation function, A^=D~−12A~D~−12^𝐴superscript~𝐷12~𝐴superscript~𝐷12\hat{A}=\widetilde{D}^{-\frac{1}{2}}\widetilde{A}\widetilde{D}^{-\frac{1}{2}}over^ start_ARG italic_A end_ARG = over~ start_ARG italic_D end_ARG start_POSTSUPERSCRIPT - divide start_ARG 1 e... | To apply graph convolution on unsupervised learning, GAE is proposed [20].
GAE firstly transforms each node into latent representation (i.e., embedding) via GCN, and then aims to reconstruct some part of the input. GAEs proposed in [20, 29, 22] intend to reconstruct the adjacency via decoder while GAEs developed in [21... | Network embedding is a fundamental task for graph type data such as recommendation systems, social networks, etc.
The goal is to map nodes of a given graph into latent features (namely embedding) such that the learned embedding can be utilized on node classification, node clustering, and link prediction. | (1) Via extending the generative graph models into general type data, GAE is naturally employed as the basic representation learning model and weighted graphs can be further applied to GAE as well. The connectivity distributions given by the generative perspective also inspires us to devise a novel architecture for dec... |
Figure 1: Framework of AdaGAE. k0subscript𝑘0k_{0}italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the initial sparsity. First, we construct a sparse graph via the generative model defined in Eq. (7). The learned graph is employed to apply the GAE designed for the weighted graphs. After training the GAE, we update ... | A |
In a recent longitudinal data analysis by the Spoofer Project (Luckie et al., 2019) the authors observed that despite increase in the coverage of ASes that do not perform ingress filtering in the Internet, the test coverage across networks and geo-locations is still non-uniform.
|
Closely related to volunteers is the vantage points measurements with faulty or misconfigured servers. (Mauch, 2013) noticed that some DNS resolvers do not change the source IP addresses of the DNS requests that they forward to upstream resolvers and return the DNS responses using the IP addresses of the upstream reso... |
Identifying DNS resolvers. The main challenge here is to locate the DNS resolvers within a domain/network and to trigger a DNS request to our Name servers. We use Email service in the target networks (retrieved via the MX type request in the target domain) to find the DNS resolvers. We send an email to target domain’s... |
∙∙\bullet∙ Limited coverage. Previous studies infer spoofability based on measurements of a limited set of networks, e.g., those that operate servers with faulty network stack (Kührer et al., 2014) or networks with volunteers that execute the measurement software (Beverly and Bauer, 2005; Beverly et al., 2009; Mauch, ... | The most significant aspect of our methodologies is that they do not require coordination with the scanned networks. SMap can measure spoofability in any TCP/IP network with standard and widely supported services, such as Email and web. We integrated into SMap three techniques for testing ingress filtering: DNS-based, ... | A |
The current design of the context-based network relies on labeled data because the odor samples for a given class are presented as ordered input to the context layer. However, the model can be modified to be trained on unlabeled data, simply by allowing arbitrary data samples as input to the context layer. This design... | An alternative approach is to emulate adaptation in natural sensor systems. The system expects and automatically adapts to sensor drift, and is thus able to maintain its accuracy for a long time. In this manner, the lifetime of sensor systems can be extended without recalibration.
| While natural systems cope with changing environments and embodiments well, they form a serious challenge for artificial systems. For instance, to stay reliable over time, gas sensing systems must be continuously recalibrated to stay accurate in a changing physical environment. Drawing motivation from nature, this pape... |
The purpose of this study was to demonstrate that explicit representation of context can allow a classification system to adapt to sensor drift. Several gas classifier models were placed in a setting with progressive sensor drift and were evaluated on samples from future contexts. This task reflects the practical goal... | This paper builds upon previous work with this dataset [7], which used support vector machine (SVM) ensembles. First, their approach is extended to a modern version of feedforward artificial neural networks (NNs) [8]. Context-based learning is then introduced to utilize sequential structure across batches of data. The ... | B |
Third, we gave a 2O(δ1−1/d)nsuperscript2𝑂superscript𝛿11𝑑𝑛2^{O(\delta^{1-1/d})}n2 start_POSTSUPERSCRIPT italic_O ( italic_δ start_POSTSUPERSCRIPT 1 - 1 / italic_d end_POSTSUPERSCRIPT ) end_POSTSUPERSCRIPT italic_n expected time algorithm for random point sets. | Random point sets.
In the third scenario the points in P𝑃Pitalic_P are drawn independently and uniformly at random from the hypercylinder [0,n]×Balld−1(δ/2)0𝑛superscriptBall𝑑1𝛿2[0,n]\times\mathrm{Ball}^{d-1}(\delta/2)[ 0 , italic_n ] × roman_Ball start_POSTSUPERSCRIPT italic_d - 1 end_POSTSUPERSCRIPT ( italic_δ / ... |
Let Xnsubscript𝑋𝑛X_{n}italic_X start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT be a random point set of n𝑛nitalic_n points in ℝdsuperscriptℝ𝑑\mathbb{R}^{d}blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT, where the x𝑥xitalic_x-coordinates of the points are taken independently uniformly at random fro... | The proof also gives a way to relate the expected running times of algorithms for any problem on two different kinds of random point sets:
a version where the x𝑥xitalic_x-coordinates of the points are taken uniformly at random from [0,n]0𝑛[0,n][ 0 , italic_n ], and a version where the differences between two consecut... | Let Ynsubscript𝑌𝑛Y_{n}italic_Y start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT be a random point set of n𝑛nitalic_n points in ℝdsuperscriptℝ𝑑\mathbb{R}^{d}blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT, where the spacings Δi=xi+1−xisubscriptΔ𝑖subscript𝑥𝑖1subscript𝑥𝑖\Delta_{i}=x_{i+1}-x_{i}roman... | C |
The free product of two semigroups R=⟨P∣ℛ⟩𝑅inner-product𝑃ℛR=\langle P\mid\mathcal{R}\rangleitalic_R = ⟨ italic_P ∣ caligraphic_R ⟩ and S=⟨Q∣𝒮⟩𝑆inner-product𝑄𝒮S=\langle Q\mid\mathcal{S}\rangleitalic_S = ⟨ italic_Q ∣ caligraphic_S ⟩
(with P∩Q=∅𝑃𝑄P\cap Q=\emptysetitalic_P ∩ italic_Q = ∅) is the semigroup with pres... |
There is a quite interesting evolution of constructions to present free groups in a self-similar way or even as automaton groups (see [15] for an overview). This culminated in constructions to present free groups of arbitrary rank as automaton groups where the number of states coincides with the rank [18, 17]. While t... | While our main result significantly relaxes the hypothesis for showing that the free product of self-similar semigroups (or automaton semigroups) is self-similar (an automaton semigroup), it does not settle the underlying question whether these semigroup classes are closed under free product. It is possible that there ... | While the question which free groups and semigroups can be generated using automata is settled, there is a related natural question, which is still open: is the free product of two automaton/self-similar (semi)groups again an automaton/self-similar (semi)group? The free product of two groups or semigroups X=⟨P∣ℛ⟩𝑋inne... | Note that there is a difference between the free product in the category of semigroups and the free product in the category of monoids or groups.
In particular, in the semigroup free product (which we are exclusively concerned with in this paper) there is no amalgamation over the identity element of two monoids. Thus, ... | D |
It is also interesting to note that the drop in training accuracy is lower with this regularization scheme as compared to the state-of-the-art methods. Of course, if any model was actually visually grounded, then we would expect it to improve performances on both train and test sets. We do not observe such behavior in ... |
As expected of any real world dataset, VQA datasets also contain dataset biases Goyal et al. (2017). The VQA-CP dataset Agrawal et al. (2018) was introduced to study the robustness of VQA methods against linguistic biases. Since it contains different answer distributions in the train and test sets, VQA-CP makes it nea... | Some recent approaches employ a question-only branch as a control model to discover the questions most affected by linguistic correlations. The question-only model is either used to perform adversarial regularization Grand and Belinkov (2019); Ramakrishnan et al. (2018) or to re-scale the loss based on the difficulty o... | While our results indicate that current visual grounding based bias mitigation approaches do not suffice, we believe this is still a good research direction. However, future methods must seek to verify that performance gains are not stemming from spurious sources by using an experimental setup similar to that presented... |
The VQA-CP dataset Agrawal et al. (2018) showcases this phenomenon by incorporating different question type/answer distributions in the train and test sets. Since the linguistic priors in the train and test sets differ, models that exploit these priors fail on the test set. To tackle this issue, recent works have ende... | C |
The corpus contains policies from over 800 different top level domains (TLDs). .com, .org, and .net make up a major share of the corpus covering 63%, 5% and 3% respectively. Country-level domains like .uk, .au, .ca and .du show the geographic variety of the sources of the corpus covering 12%, 4%, and 2% respectively. T... | Readability. Readability of a text can be defined as the ease of understanding or comprehension due to the style of writing (Klare et al., 1963). Along with length, readability plays a role in internet users’ decisions to either read or ignore a privacy policy (Ermakova et al., 2015). While prior studies on readability... | To train the RoBERTa model on the privacy policy classification task, we used the sequence classification head of the pretrained language model from HuggingFace (Wolf et al., 2019). We used the pretrained RoBERTa tokenizer to tokenize text extracted from the documents. Since Roberta accepts a maximum of 512 tokens as i... | Table 2 shows the results for the data practice classification task comparing the performance between RoBERTa, PrivBERT and Polisis (Harkous et al., 2018), a CNN based classification model. We report reproduced results for Polisis since the original paper takes into account both the presence and absence of a label whil... |
Prior research on the readability based on small corpora of privacy policies had found that they were generally hard to understand for the average internet user. Our large scale analysis using the Flesch-Kincaid readability metric was consistent with prior findings. We found that on average about 14.87 years or roughl... | A |
To illustrate how to choose different metrics (and with which weights), we start our exploration by selecting the heart disease data set in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(a). Knowing that the data set is balanced, we pick accuracy (weight... |
To illustrate how to choose different metrics (and with which weights), we start our exploration by selecting the heart disease data set in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(a). Knowing that the data set is balanced, we pick accuracy (weight... | Pressing the Execute Stacking Ensemble button leads to the stacking ensemble shown in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(b, \raisebox{-.0pt} {\tiny\bfS1}⃝) with the performances shown at the end of the circular barcharts (in %) and in StackGen... | We normalize the importance from 0 to 1 and use a two-hue color encoding from dark red to dark green to highlight the least to the most important features for our current stored stack, see Figure 4(b). The panel in Figure 4(c) uses a table heatmap view where data features are mapped to the y-axis (13 attributes, only 7... | Weighted-average calculates the metrics for each label and finds their average weighted by support (the number of true instances for each label). The data set is a binary classification problem and contains 165 diseased and 138 healthy patients.
Hence, we choose micro-average to weight the importance of the largest cla... | D |
By using the pairwise adjacency of (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), (v,[003])𝑣delimited-[]003(v,[003])( italic_v , [ 003 ] ), and
(v,[113])𝑣delimited-[]113(v,[113])( italic_v , [ 113 ] ), we can confirm that in the 3333 cases, these | Then, by using the adjacency of (v,[013])𝑣delimited-[]013(v,[013])( italic_v , [ 013 ] ) with each of
(v,[010])𝑣delimited-[]010(v,[010])( italic_v , [ 010 ] ), (v,[323])𝑣delimited-[]323(v,[323])( italic_v , [ 323 ] ), and (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), we can confirm that | cannot be adjacent to 2¯¯2\overline{2}over¯ start_ARG 2 end_ARG nor 3¯¯3\overline{3}over¯ start_ARG 3 end_ARG,
and so f′superscript𝑓′f^{\prime}italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT is [013]delimited-[]013[013][ 013 ] or [010]delimited-[]010[010][ 010 ]. | By using the pairwise adjacency of (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), (v,[003])𝑣delimited-[]003(v,[003])( italic_v , [ 003 ] ), and
(v,[113])𝑣delimited-[]113(v,[113])( italic_v , [ 113 ] ), we can confirm that in the 3333 cases, these | (E𝐂,(2¯,(u2,[013])))superscript𝐸𝐂¯2subscript𝑢2delimited-[]013(E^{\mathbf{C}},(\overline{2},(u_{2},[013])))( italic_E start_POSTSUPERSCRIPT bold_C end_POSTSUPERSCRIPT , ( over¯ start_ARG 2 end_ARG , ( italic_u start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , [ 013 ] ) ) ),
(E𝐂,((u1,[112]),(u2,[010])))superscript𝐸𝐂subscr... | A |
To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... | In text classification experiment, we use accuracy (Acc) to evaluate the classification performance.
In dialogue generation experiment, we evaluate the performance of MAML in terms of quality and personality. We use PPL and BLEU [Papineni et al., 2002] to measure the similarity between the reference and the generated r... | In this paper, we take an empirical approach to systematically investigating these impacting factors and finding when MAML works the best. We conduct extensive experiments over 4 datasets. We first study the effects of data quantity and distribution on the training strategy:
RQ1. Since the parameter initialization lear... |
To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... | The finding suggests that parameter initialization at the late training stage has strong general language generation ability, but performs comparative poorly in task-specific adaptation.
Although in the early training stage, the performance improves benefiting from the pre-trained general language model, if the languag... | D |
Although the GP-based UAV’s position and attitude prediction results fit well with the position and attitude data, the prediction performance is effected by UAV’s mobility. When the UAV has higher mobility such as the more random trajectory and high velocity, the prediction error may influence the beam tracking. The c... | In this subsection, two beam tracking schemes with different types of antenna array are illustrated by simulation results. One is the proposed DRE-covered CCA scheme where all the t-UAVs are equipped with the CCA of the size Nt=64subscript𝑁𝑡64N_{t}=64italic_N start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT = 64, Mt=16... | Without loss of generality, let us focus on the TE-aware codeword
selection for the k𝑘kitalic_k-th t-UAV at the r-UAV side. The beam gain is selected as the optimization objective, and the problem of beamwidth control is translated to choose the appropriate subarray size, which corresponds to the appropriate layer in ... | The SEs of two array schemes against the transmit power with K=2𝐾2K=2italic_K = 2 t-UAVs are illustrated in Fig. 13. The TE-aware codeword selection uses the proposed Algorithm 2 and Algorithm 3. Serving as a reference, the minimum-beamwidth scheme always select the minimum beamwidth, i.e., the maximum number of anten... | As shown in Fig. 11, the SE of the CCA codebook scheme and the traditional codebook scheme is compared. The proposed DRE-covered CCA codebook is used in the CCA codebook scheme. In the traditional codebook scheme, the codebook without subarray partition is used. The CCA on the r-UAV is equally partitioned into K𝐾Kital... | C |
Thus,
a¯|b¯conditional¯𝑎¯𝑏\bar{a}|\bar{b}over¯ start_ARG italic_a end_ARG | over¯ start_ARG italic_b end_ARG-regular digraphs with size M¯¯𝑀\bar{M}over¯ start_ARG italic_M end_ARG can be characterized as a¯|b¯conditional¯𝑎¯𝑏\bar{a}|\bar{b}over¯ start_ARG italic_a end_ARG | over¯ start_ARG italic_b end_ARG-biregula... | To conclude this section, we stress that although the 1111-color case contains many of the key ideas, the multi-color case requires a finer
analysis to deal with the “big enough” case, and also may benefit from a reduction that allows one to restrict | This will be bootstrapped to the multi-color case in later sections. Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on
the left must be connected, via the unique edge relation, to every node on the ri... | We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | The case of fixed degree and multiple colors is done via an induction, using merging and then swapping to eliminate parallel edges.
The case of unfixed degree is handled using a case analysis depending on whether sizes are “big enough”, but the approach is different from | A |
To address such an issue of divergence, nonlinear gradient TD (Bhatnagar et al., 2009) explicitly linearizes the value function approximator locally at each iteration, that is, using its gradient with respect to the parameter as an evolving feature representation. Although nonlinear gradient TD converges, it is unclear... |
Contribution. Going beyond the NTK regime, we prove that, when the value function approximator is an overparameterized two-layer neural network, TD and Q-learning globally minimize the mean-squared projected Bellman error (MSPBE) at a sublinear rate. Moreover, in contrast to the NTK regime, the induced feature represe... | In this section, we extend our analysis of TD to Q-learning and policy gradient. In §6.1, we introduce Q-learning and its mean-field limit. In §6.2, we establish the global optimality and convergence of Q-learning. In §6.3, we further extend our analysis to soft Q-learning, which is equivalent to policy gradient.
| Szepesvári, 2018; Dalal et al., 2018; Srikant and Ying, 2019) settings. See Dann et al. (2014) for a detailed survey. Also, when the value function approximator is linear, Melo et al. (2008); Zou et al. (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is nonlinear, T... | To address such an issue of divergence, nonlinear gradient TD (Bhatnagar et al., 2009) explicitly linearizes the value function approximator locally at each iteration, that is, using its gradient with respect to the parameter as an evolving feature representation. Although nonlinear gradient TD converges, it is unclear... | A |
We explore the use of LSTMs to connect layers in stacked deep architectures for Transformers: we show how residual connections can be replaced by LSTMs connecting self-, cross- and masked self-attention layers. In contrast to standard LSTMs that process token sequences, we refer to the use of LSTMs in connecting stacke... | We suggest that selectively aggregating different layer representations of the Transformer may improve the performance, and propose to use depth-wise LSTMs to connect stacked (sub-) layers of Transformers. We show how Transformer layer normalization and feed-forward sub-layers can be absorbed by depth-wise LSTMs, while... | We explore the use of LSTMs to connect layers in stacked deep architectures for Transformers: we show how residual connections can be replaced by LSTMs connecting self-, cross- and masked self-attention layers. In contrast to standard LSTMs that process token sequences, we refer to the use of LSTMs in connecting stacke... | The computation of depth-wise LSTM is the same as the conventional LSTM except that depth-wise LSTM connects stacked Transformer layers instead of tokens in a token sequence as in conventional LSTMs. The gate mechanisms in the original LSTM are to enhance its ability in capturing long-distance relations and to address ... |
In this paper, we replace residual connections of the Transformer with depth-wise LSTMs, to selectively manage the representation aggregation of layers benefiting performance while ensuring convergence of the Transformer. Specifically, we show how to integrate the computation of multi-head attention networks and feed-... | A |
Finally, consider a compact open set U𝑈Uitalic_U of
Ynsubscript𝑌𝑛{Y_{n}}italic_Y start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT. By Lemma 7.3, U𝑈Uitalic_U is open in Xρ(n)subscript𝑋𝜌𝑛X_{\rho(n)}italic_X start_POSTSUBSCRIPT italic_ρ ( italic_n ) end_POSTSUBSCRIPT | \circ}\!\left(X_{\rho(n)}\right)\subseteq\mathcal{K}^{\circ}\!\left(X\right)∀ italic_n ≥ 1 , caligraphic_K start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT ( italic_Y start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) ⊆ caligraphic_K start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT ( italic_X start_POSTSUBSCRIPT italic_ρ ( italic_... | homomorphisms, A⊧φmodels𝐴𝜑A\models\varphiitalic_A ⊧ italic_φ, and A→ρ(n)Csubscript→𝜌𝑛𝐴𝐶A\to_{\rho(n)}Citalic_A → start_POSTSUBSCRIPT italic_ρ ( italic_n ) end_POSTSUBSCRIPT italic_C. Let us define B≜Coreρ(n)(A)≜𝐵superscriptCore𝜌𝑛𝐴B\triangleq\operatorname{Core}^{\rho(n)}(A)italic_B ≜ roman_Core start_POSTSU... | as well. Furthermore, U𝑈Uitalic_U is compact in Xρ(n)subscript𝑋𝜌𝑛X_{\rho(n)}italic_X start_POSTSUBSCRIPT italic_ρ ( italic_n ) end_POSTSUBSCRIPT since
Xρ(n)subscript𝑋𝜌𝑛X_{\rho(n)}italic_X start_POSTSUBSCRIPT italic_ρ ( italic_n ) end_POSTSUBSCRIPT is Noetherian. | Finally, consider a compact open set U𝑈Uitalic_U of
Ynsubscript𝑌𝑛{Y_{n}}italic_Y start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT. By Lemma 7.3, U𝑈Uitalic_U is open in Xρ(n)subscript𝑋𝜌𝑛X_{\rho(n)}italic_X start_POSTSUBSCRIPT italic_ρ ( italic_n ) end_POSTSUBSCRIPT | C |
The comparison results of the real distorted image are shown in Fig. 13. We collect the real distorted images from the videos on YouTube, captured by popular fisheye lenses, such as the SAMSUNG 10mm F3, Rokinon 8mm Cine Lens, Opteka 6.5mm Lens, and GoPro. As illustrated in Fig. 13, our approach generates the best rect... |
In contrast to the long history of traditional distortion rectification, learning methods began to study distortion rectification in the last few years. Rong et al. [8] quantized the values of the distortion parameter to 401 categories based on the one-parameter camera model [22] and then trained a network to classify... |
As listed in Table II, our approach significantly outperforms the compared approaches in all metrics, including the highest metrics on PSNR and SSIM, as well as the lowest metric on MDLD. Specifically, compared with the traditional methods [23, 24] based on the hand-crafted features, our approach overcomes the scene l... |
In this work, we presented a new learning representation for the deep distortion rectification and implemented a standard and widely-used camera model to validate its effectiveness. The rectification results on the synthesized and real-world scenarios also demonstrated our approach’s superiority compared with the stat... | In this section, we first state the details of the synthetic distorted image dataset and the training process of our learning model. Subsequently, we analyze the learning representation for distortion estimation. To demonstrate the effectiveness of each module in our framework, we conduct an ablation study to show the ... | C |
The momentum coefficient is set as 0.9 and the weight decay is set as 0.001. The initial learning rate is selected from {0.001,0.01,0.1}0.0010.010.1\{0.001,0.01,0.1\}{ 0.001 , 0.01 , 0.1 } according to the performance on the validation set. We do not adopt any learning rate decay or warm-up strategies.
The model is tra... | showed that existing SGD methods with a large batch size will lead to a drop in the generalization accuracy of deep learning models. Figure 1
shows a comparison of training loss and test accuracy between MSGD with a small batch size and MSGD with a large batch size. We can find that large-batch training indeed | Table 6 shows the test perplexity of the three methods with different batch sizes. We can observe that for small batch size, SNGM achieves test perplexity comparable to that of MSGD, and for large batch size, SNGM is better than MSGD. Similar to the results of image classification, SNGM outperforms LARS for different b... | Figure 2 shows the learning curves of the five methods. We can observe that in the small-batch training, SNGM and other large-batch training methods achieve similar performance in terms of training loss and test accuracy as MSGD.
In large-batch training, SNGM achieves better training loss and test accuracy than the fou... | Hence, with the same number of gradient computations, SNGM can adopt a larger batch size than MSGD to converge to the ϵitalic-ϵ\epsilonitalic_ϵ-stationary point.
Empirical results on deep learning further verify that SNGM can achieve better test accuracy than MSGD and other state-of-the-art large-batch training methods... | D |
Our main goal is to develop algorithms for the black-box setting. As usual in two-stage stochastic problems, this has three steps. First, we develop algorithms for the simpler polynomial-scenarios model. Second, we sample a small number of scenarios from the black-box oracle and use our polynomial-scenarios algorithms ... |
We remark that if we make an additional assumption that the stage-II cost is at most some polynomial value ΔΔ\Deltaroman_Δ, we can use standard SAA techniques without discarding scenarios; see Theorem 2.6 for full details. However, this assumption is stronger than is usually used in the literature for two-stage stocha... |
Unfortunately, standard SAA approaches [26, 7] do not directly apply to radius minimization problems. On a high level, the obstacle is that radius-minimization requires estimating the cost of each approximate solution; counter-intuitively, this may be harder than optimizing the cost (which is what is done in previous ... | Clustering is a fundamental task in unsupervised and self-supervised learning. The stochastic setting models situations in which decisions must be made in the presence of uncertainty and are of particular interest in learning and data science. The black-box model is motivated by data-driven applications where specific ... | An outbreak is an instance from 𝒟𝒟\mathcal{D}caligraphic_D, and after it actually happened, additional testing and vaccination locations were deployed or altered based on the new requirements, e.g., [20], which corresponds to stage-II decisions.
To continue this example, there may be further constraints on FIsubscrip... | B |
Besides, the network graphs may change randomly with spatial and temporal dependency (i.e. Both the weights of different edges in the network graphs at the same time instant and the network graphs at different time instants may be mutually dependent.) rather than i.i.d. graph sequences as in [12]-[15],
and additive and... | We have studied the distributed stochastic subgradient algorithm for the stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions.
We have proved that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditio... |
II. The structure of the networks among optimizers is modeled by a more general sequence of random digraphs. The sequence of random digraphs is conditionally balanced, and the weighted adjacency matrices are not required to have special statistical properties such as independency with identical distribution, Markovian... | I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... |
Motivated by distributed statistical learning over uncertain communication networks, we study the distributed stochastic convex optimization by networked local optimizers to cooperatively minimize a sum of local convex cost functions. The network is modeled by a sequence of time-varying random digraphs which may be sp... | D |
WHERE pred𝑝𝑟𝑒𝑑preditalic_p italic_r italic_e italic_d(A1QIsuperscriptsubscript𝐴1𝑄𝐼A_{1}^{QI}italic_A start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_Q italic_I end_POSTSUPERSCRIPT) AND pred𝑝𝑟𝑒𝑑preditalic_p italic_r italic_e italic_d(A2QIsuperscriptsubscript𝐴2𝑄𝐼A_{2}^{QI}italic... |
This experiment measures the information loss of MuCo. Note that, the mechanism of MuCo is much more different from that of generalization. Thus, for the sake of fairness, we compare the information loss of MuCo and Mondrian when they provide the same level of protections. Then, the experiment measures the effectivene... | The advantages of MuCo are summarized as follows. First, MuCo can maintain the distributions of original QI values as much as possible. For instance, the sum of each column in Figure 3 is shown by the blue polyline in Figure 2, and the blue polyline almost coincides with the red polyline representing the distribution i... |
We observe that the results of MuCo are much better than that of Mondrian and Anatomy. The primary reason is that MuCo retains the most distributions of the original QI values and the results of queries are specific records rather than groups. Consequently, the accuracy of query answering of MuCo is much better and mo... |
Observing from Figure 7(a), the information loss of MuCo increases with the decrease of parameter δ𝛿\deltaitalic_δ. According to Corollary 3.2, each QI value in the released table corresponds to more records with the reduction of δ𝛿\deltaitalic_δ, causing that more records have to be involved for covering on the QI ... | C |
We implement PointRend using MMDetection Chen et al. (2019b) and adopt the modifications and tricks mentioned in Section 3.3. Both X101-64x4d and Res2Net101 Gao et al. (2019) are used as our backbones, pretrained on ImageNet only. SGD with momentum 0.9 and weight decay 1e-4 is adopted. The initial learning rate is set... | As shown in Table 3, all PointRend models achieve promising performance. Even without ensemble, our PointRend baseline, which yields 77.38 mAP, has already achieved 1st place on the test leaderboard. Note that several attempts, like BFP Pang et al. (2019) and EnrichFeat, give no improvements against PointRend baseline,... | Deep learning has achieved great success in recent years Fan et al. (2019); Zhu et al. (2019); Luo et al. (2021, 2023); Chen et al. (2021). Recently, many modern instance segmentation approaches demonstrate outstanding performance on COCO and LVIS, such as HTC Chen et al. (2019a), SOLOv2 Wang et al. (2020), and PointRe... | Bells and Whistles. MaskRCNN-ResNet50 is used as baseline and it achieves 53.2 mAP. For PointRend, we follow the same setting as Kirillov et al. (2020) except for extracting both coarse and fine-grained features from the P2-P5 levels of FPN, rather than only P2 described in the paper. Surprisingly, PointRend yields 62.... | Table 3: PointRend’s performance on testing set (trackB). “EnrichFeat” means enhance the feature representation of coarse mask head and point head by increasing the number of fully-connected layers or its hidden sizes. “BFP” means Balanced Feature Pyramid. Note that BFP and EnrichFeat gain little improvements, we guess... | A |
For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
|
In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails. This solves a question raised by Gady Kozma s... |
Here we give an embarrassingly simple presentation of an example of such a function (although it can be shown to be a version of the example in the previous version of this note). As was written in the previous version, an anonymous referee of version 1 wrote that the theorem was known to experts but not published. Ma... | For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| We denote by εi:{−1,1}n→{−1,1}:subscript𝜀𝑖→superscript11𝑛11\varepsilon_{i}:\{-1,1\}^{n}\to\{-1,1\}italic_ε start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : { - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT → { - 1 , 1 } the projection onto the i𝑖iitalic_i-s coordinate: εi(δ1,…,δn)=δisubscript𝜀𝑖subsc... | A |
Compared to OPT-WLSVI and MASTER, our proposed algorithms achieve comparable empirical performance. More specifically, MASTER outperforms our proposed algorithm which agrees with its dynamic regret upper bound. However, the variance of MASTER is larger due to the random scheduling of multiple base algorithms. Our algo... | For the case when the environment changes abruptly L𝐿Litalic_L times, our algorithm enjoys an O~(L1/3T2/3)~𝑂superscript𝐿13superscript𝑇23\tilde{O}(L^{1/3}T^{2/3})over~ start_ARG italic_O end_ARG ( italic_L start_POSTSUPERSCRIPT 1 / 3 end_POSTSUPERSCRIPT italic_T start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ) dy... | \mathcal{S})+\frac{k-100i}{100}\bm{\mu}_{h}^{(i+1)\mod 5}(\mathcal{S}),bold_italic_μ start_POSTSUBSCRIPT italic_h , italic_k end_POSTSUBSCRIPT ( caligraphic_S ) = ( 1 - divide start_ARG italic_k - 100 italic_i end_ARG start_ARG 100 end_ARG ) bold_italic_μ start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT start_POSTSUPERSC... | From Figure 1, we find that the restart strategy works better under abrupt changes than under gradual changes, since the gap between our algorithms and the baseline algorithms designed for stationary environments is larger in this setting. The reason is that the algorithms designed to explore in stationary MDPs are gen... |
Figure 1: Comparisons of different methods on cumulative reward under two different environments. The results are averaged over 10 trials and the error bars show the standard deviations. The environment changes abruptly in the left subfigure, whereas the environment changes gradually in the right subfigure. | D |
There is a very strong, negative correlation between the media sources of fake news and the level of trust in them (ref. Figures 1 and 2) which is statistically significant (r(9)=−0.81𝑟90.81r(9)=-0.81italic_r ( 9 ) = - 0.81, p<.005𝑝.005p<.005italic_p < .005). Trust is built on transparency and truthfulness, and t... | While fake news is not a new phenomenon, the 2016 US presidential election brought the issue to immediate global attention with the discovery that fake news campaigns on social media had been made to influence the election (Allcott and Gentzkow, 2017). The creation and dissemination of fake news is motivated by politic... |
There is a very strong, negative correlation between the media sources of fake news and the level of trust in them (ref. Figures 1 and 2) which is statistically significant (r(9)=−0.81𝑟90.81r(9)=-0.81italic_r ( 9 ) = - 0.81, p<.005𝑝.005p<.005italic_p < .005). Trust is built on transparency and truthfulness, and t... |
In general, respondents possess a competent level of digital literacy skills with a majority exercising good news sharing practices. They actively verify news before sharing by checking with multiple sources found through the search engine and with authoritative information found in government communication platforms,... | Singapore is a city-state with an open economy and diverse population that shapes it to be an attractive and vulnerable target for fake news campaigns (Lim, 2019). As a measure against fake news, the Protection from Online Falsehoods and Manipulation Act (POFMA) was passed on May 8, 2019, to empower the Singapore Gover... | C |
6: 𝐠i,𝐞i←ℳ(ei,Ni)←subscript𝐠𝑖subscript𝐞𝑖ℳsubscript𝑒𝑖subscript𝑁𝑖{\mathbf{g}}_{i},{\mathbf{e}}_{i}\leftarrow{\mathcal{M}}(e_{i},N_{i})bold_g start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT , bold_e start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ← caligraphic_M ( italic_e start_POSTSUBSCRIPT italic_i end... |
We present the training procedure of decentRL for entity alignment in Algorithm 1. It is worth noting that decentRL does not rely on additional data such as pretrained KG embeddings or word embeddings. The algorithm first randomly initializes the DAN model, entity embeddings, and relation embeddings. The training proc... |
Table 6 and Table 7 present the results for conventional entity prediction. decentRL demonstrates competitive or even superior performance when compared to state-of-the-art methods on the FB15K and WN18 benchmarks, showcasing its efficacy in entity prediction. While on the FB15K-237 and WN18RR datasets, the performanc... | The existing methods for KG embedding and word embedding exhibit even more similarities. As shown in Figure 1, the KG comprises three triplets conveying similar information to the example sentence. Triplet-based KG embedding models like TransE [11] transform the embedding of each subject entity and its relation into a ... |
The results in Table 10 demonstrate that all variants of decentRL achieves state-of-the-art performance on Hits@1, empirically proving the superiority of using neighbor context as the query vector for aggregating neighbor embeddings. The proposed decentRL outperforms both decentRL w/ infoNCE and decentRL w/ L2, provid... | A |
The related exploration methods aim to remove the stochasticity of the dynamics rather than modeling it. For example, Inverse Dynamics [10], Random Features [11], and EMI [30] learn a feature space to remove the task-irrelevant information in feature space such as white-noise. Curiosity-Bottleneck [31] and Dynamic Bot... | We analyze the possible reasons in the following. (i) The probabilistic-ensemble model proposed in [48] is used in continuous control tasks, where the state is low-dimensional and unstructured. However, Noisy-Mnist has high-dimensional image-based observations. The probabilistic ensemble may not suitable for this setti... |
In this paper, we propose the Variational Dynamic Model (VDM), which models the multimodality and stochasticity of the dynamics explicitly based on conditional variational inference. VDM considers the environmental state-action transition as a conditional generative process by generating the next-state prediction unde... |
The related exploration methods aim to remove the stochasticity of the dynamics rather than modeling it. For example, Inverse Dynamics [10], Random Features [11], and EMI [30] learn a feature space to remove the task-irrelevant information in feature space such as white-noise. Curiosity-Bottleneck [31] and Dynamic Bot... |
Variational inference posits a set of densities and then finds the member in the set that is close to the target [14, 34]. Combining RL and variational inference requires formalizing RL as a probabilistic inference problem [35, 36, 37]. Several RL methods propose to use pseudo-likelihood inference framework [38, 39] a... | D |
This allowed us to extend the classic 1D Newton and Lagrange interpolation methods to multivariate
schemes in a numerically stable and efficient way, resulting in a practically implemented algorithm with 𝒪(|A|2)𝒪superscript𝐴2\mathcal{O}(|A|^{2})caligraphic_O ( | italic_A | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIP... | The observations made in 2D remain valid. However, Floater-Hormann becomes indistinguishable from 5thsuperscript5𝑡ℎ5^{th}5 start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT-order splines.
Further, when considering the amount of coefficients/nodes required to determine the interpolant, plotted in the right p... | convergence rates for the Runge function, as a prominet example of a Trefethen function. We show that the number of nodes required scales sub-exponentially with space dimension. We therefore believe that the present generalization of unisolvent nodes to non-tensorial grids is key to lifting the curse of dimensionality.... | If one only requires the nodes PAsubscript𝑃𝐴P_{A}italic_P start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT to be unisolvent, then they do not have to be given by a (sub) grid at all. The nodes used for the present m𝑚mitalic_mD Newton interpolation are given by a sub-grid,
but that sub-grid is neither symmetric nor ten... | In contrast to previous approaches, such as Chebfun [32], multivariate splines [26], and Floater-Hormann interpolation [38], the present
MIP algorithm achieves exponential approximation rates for the Runge function using only sub-exponentially many interpolation nodes. | D |
For instance, in anomaly detection [1, 2, 3], the abnormal observations follow a different distribution from the typical distribution.
Similarly, in change-point detection [4, 5, 6], the post-change observations follow a different distribution from the pre-change one. | Several data-efficient two-sample tests [20, 21, 22] are constructed based on Maximum Mean Discrepancy (MMD), which quantifies the distance between two distributions by introducing test functions in a Reproducing Kernel Hilbert Space (RKHS).
However, it is pointed out in [23] that when the bandwidth is chosen based on ... | However, the two-sample tests based on concentration inequalities in Section III give conservative results in practice. We examine the two-sample tests using the projected Wasserstein distance via the permutation approach.
Specifically, we permute the collected data points for Np=100subscript𝑁𝑝100N_{p}=100italic_N st... | In this paper, we consider non-parametric two-sample testing, in which no prior information about the unknown distribution is available.
Two-sample tests for non-parametric settings are usually constructed based on some metrics quantifying the distance between two distributions. | Classical tests (see, e.g., [12]) mainly follow the parametric approaches, which are designed based on prior information about the distributions under each class.
Examples in classical tests include the Hotelling’s two-sample test [13] and the Student’s t-test [14]. | D |
Learning disentangled factors h∼qϕ(H|x)similar-toℎsubscript𝑞italic-ϕconditional𝐻𝑥h\sim q_{\phi}(H|x)italic_h ∼ italic_q start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( italic_H | italic_x ) that are semantically meaningful representations of the observation x𝑥xitalic_x is highly desirable because such interpreta... | Specifically, we apply a DGM to learn the nuisance variables Z𝑍Zitalic_Z, conditioned on the output image of the first part, and use Z𝑍Zitalic_Z in the normalization layers of the decoder network to shift and scale the features extracted from the input image. This process adds the details information captured in Z𝑍Z... | Prior work in unsupervised DR learning suggests the objective of learning statistically independent factors of the latent space as means to obtain DR. The underlying assumption is that the latent variables H𝐻Hitalic_H can be partitioned into independent components C𝐶Citalic_C (i.e. the disentangled factors) and corre... | While the aforementioned models made significant progress on the problem, they suffer from an inherent trade-off between learning DR and reconstruction quality. If the latent space is heavily regularized, not allowing enough capacity for the nuisance variables, reconstruction quality is diminished. On the other hand, i... |
The model has two parts. First, we apply a DGM to learn only the disentangled part, C𝐶Citalic_C, of the latent space. We do that by applying any of the above mentioned VAEs111In this exposition we use unspervised trained VAEs as our base models but the framework also works with GAN-based or FLOW-based DGMs, supervise... | B |
As shown in the above method, logical aggregates can be constructed with structural wiring if digital signals are computed in pairs of inverted signals. Especially for the NOT gate, you can twist the α𝛼\alphaitalic_α line and the β𝛽\betaitalic_β line once, making it much simpler to operate than a semiconductor-based ... | The structure-based computer mentioned in this paper are based on Boolean Algebra, a system commonly applied to digital computers. Boolean algebra is a concept created by George Boole (1815-1854) of the United Kingdom that expresses the True and False of logic 1 and 0, and mathematically describes digital electrical si... | If a pair of lines of the same color is connected, 1, if broken, the sequence pair of states of the red line (α𝛼\alphaitalic_α) and blue line (β𝛽\betaitalic_β) determines the transmitted digital signal. Thus, signal cables require one transistor for switching action at the end. When introducing the concept of an inve... |
The structural computer used an inverted signal pair to implement the reversal of a signal (NOT operation) as a structural transformation, i.e. a twist, and four pins were used for AND and OR operations as a series and parallel connection were required. However, one can think about whether the four pin designs are the... | As shown in the above method, logical aggregates can be constructed with structural wiring if digital signals are computed in pairs of inverted signals. Especially for the NOT gate, you can twist the α𝛼\alphaitalic_α line and the β𝛽\betaitalic_β line once, making it much simpler to operate than a semiconductor-based ... | B |
Hence any function xnsuperscript𝑥𝑛x^{n}italic_x start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT with gcd(n,q−1)≠1𝑔𝑐𝑑𝑛𝑞11gcd(n,q-1)\neq 1italic_g italic_c italic_d ( italic_n , italic_q - 1 ) ≠ 1, under the action of 𝐊𝐊\mathbf{K}bold_K settles down to the function xq−1superscript𝑥𝑞1x^{q-1}italic_x start... |
In this section, we provide examples of estimating the possible orbit lengths of permutation polynomials in the form of Dickson polynomials Dn(x,α)subscript𝐷𝑛𝑥𝛼D_{n}(x,\alpha)italic_D start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ( italic_x , italic_α ) [10] of degree n𝑛nitalic_n through the linear representati... |
In this section, we aim to compute the possible cycle lengths of the PP through the linear representation defined in (10). As discussed in Section 1.3, given a polynomial f(x)𝑓𝑥f(x)italic_f ( italic_x ), we associate a dynamical system through a difference equation of the form | The work [19] also provides a computational framework to compute the cycle structure of the permutation polynomial f𝑓fitalic_f by constructing a matrix A(f)𝐴𝑓A(f)italic_A ( italic_f ), of dimension q×q𝑞𝑞q\times qitalic_q × italic_q through the coefficients of the (algebraic) powers of fksuperscript𝑓𝑘f^{k}italic... | The paper is organized as follows. Section 2 focuses on linear representation for maps over finite fields 𝔽𝔽\mathbb{F}blackboard_F, develops conditions for invertibility, computes the compositional inverse of such maps and estimates the cycle structure of permutation polynomials. In Section 3, this linear representat... | B |
In order to evaluate the relative merits of different feature selection algorithms in non-asymptotic settings, empirical comparisons are typically performed. Recent work on this topic includes Wah \BOthers. (\APACyear2018) comparing different filter and wrapper methods for feature selection using both simulations and r... |
with tuning parameters λ≥0𝜆0\lambda\geq 0italic_λ ≥ 0 and α∈[0,1]𝛼01\alpha\in[0,1]italic_α ∈ [ 0 , 1 ]. Ridge regression (α=0𝛼0\alpha=0italic_α = 0) and the lasso (α=1𝛼1\alpha=1italic_α = 1) are both special cases of the elastic net. Choosing any other value of α𝛼\alphaitalic_α leads to a mixture of L1subscript𝐿... |
In this article we investigate how the choice of meta-learner affects the view selection and classification performance of MVS. We compare the following meta-learners: (1) the interpolating predictor of Breiman (\APACyear1996), (2) nonnegative ridge regression (Hoerl \BBA Kennard, \APACyear1970; Le Cessie \BBA Van Hou... |
In MVS, different meta-learners may behave differently with respect to the trade-offs between accuracy, sparsity, and interpretability. For example, in a general feature selection setting with correlated features, the lasso is known to select only a small subset, while the so-called elastic net (Zou \BBA Hastie, \APAC... | In high-dimensional biomedical studies, a common goal is to create an accurate classification model using only a subset of the features (Y. Li \BOthers., \APACyear2018). A popular approach to this type of joint classification and feature selection problem is to apply penalized methods such as the lasso (Tibshirani, \AP... | C |
Table 6 presents the reduction rates achieved by each of the five techniques. The reduction rate is computed as 1 minus the ratio of the number of relevant variables selected to the total number of variables in a dataset. The results reveal substantial variations in reduction rates among the different techniques for t... | Compared to other methods, IEPC exhibits a notably lower reduction rate, which, we believe, contributes to its unstable performance. The experimental results in Figure 3 indicate that when considering only linear prediction models, IEPC performs better with regularization techniques such as LASSO and Ridge, as opposed ... |
Table 6 presents the reduction rates achieved by each of the five techniques. The reduction rate is computed as 1 minus the ratio of the number of relevant variables selected to the total number of variables in a dataset. The results reveal substantial variations in reduction rates among the different techniques for t... | Conversely, algorithms that contain combinations of DC with Lasso or Ridge demonstrate the worst performance. Additionally, algorithms using MI as the relevant variable selection technique generally show inferior results, regardless of the techniques used in the other two phases. When using IEPC for relevant variable s... | Conversely, the results from the combination of IEPC with Ridge exhibit much lower performance compared to other combinations. Methods using Max as the scoring technique yield the worst results. Additionally, the results with MI as the relevant variable selection technique are generally inferior, regardless of the tech... | A |
Figure 1: Illustration of the impact of the κ𝜅\kappaitalic_κ parameter (logistic case, multinomial logit case closely follows): A representative plot of the derivative of the reward function. The x-axis represents the linear function x⊤θsuperscript𝑥top𝜃x^{\top}\thetaitalic_x start_POSTSUPERSCRIPT ⊤ end_POSTSUPERSC... |
Motivated by these issues, we consider the dynamic assortment optimization problem. In every round, the retailer offers a subset (assortment) of products to a consumer and observes the consumer response. Consumers purchase (at most one product from each assortment) products that maximize their utility, and the retaile... | In this paper, we build on recent developments for generalized linear bandits (Faury et al. [2020]) to propose a new optimistic algorithm, CB-MNL for the problem of contextual multinomial logit bandits. CB-MNL follows the standard template of optimistic parameter search strategies (also known as optimism in the face of... | In this work, we proposed an optimistic algorithm for learning under the MNL contextual bandit framework. Using techniques from Faury et al. [2020], we developed an improved technical analysis to deal with the non-linear nature of the MNL reward function. As a result, the leading term in our regret bound does not suffe... | We note that Ou et al. [2018] also consider a similar problem of developing an online algorithm for the MNL model with linear utility parameters. Though they establish a regret bound that does not depend on the aforementioned parameter κ𝜅\kappaitalic_κ, they work with an inaccurate version of the MNL model. More speci... | D |
Though many methods (e.g., [1, 3, 9, 20, 21, 24, 42, 43, 44, 46]) in recent years have been continuously breaking the record of TAL performance, a major challenge hinders its substantial improvement – large variation in action duration. An action can last from a fraction of a second to minutes in the real-world scenari... |
Recent temporal action localization methods can be generally classified into two categories based on the way they deal with the input sequence. In the first category, the works such as BSN [21], BMN [20], G-TAD [44], BC-GNN [3] re-scale each video to a fixed temporal length (usually a small length such as 100 snippets... | Specifically, we propose a Video self-Stitching Graph Network (VSGN) for improving performance of short actions in the TAL problem. Our VSGN is a multi-level cross-scale framework that contains two major components: video self-stitching (VSS); cross-scale graph pyramid network (xGPN). In VSS, we focus on a short period... |
In this paper, to tackle the challenging problem of large action scale variation in the temporal action localization (TAL) problem, we target short actions and propose a multi-level cross-scale solution called video self-stitching graph network (VSGN). It contains a video self-stitching (VSS) component that generates ... |
Why are short actions hard to localize? Short actions have small temporal scales with fewer frames, and therefore, their information is prone to loss or distortion throughout a deep neural network. Most methods in the literature process videos regardless of action duration, which as a consequence sacrifices the perfor... | D |
(b.1) indicates that \raisebox{0.15pt}{\resizebox{!}{0.8ex}{\textbf{\textsf{C1}}}}⃝ contains well-performing RF models, in contrast to (b.2), in which \raisebox{0.15pt}{\resizebox{!}{0.8ex}{\textbf{\textsf{C3}}}}⃝ includes more diverse RF models and a GradB model.
For the accuracy, recall, and f1-score metrics, \raiseb... | However, \raisebox{0.15pt}{\resizebox{!}{0.8ex}{\textbf{\textsf{C3}}}}⃝ achieves better results for the precision metric.
In the grid-based view (d.1), LR, RF, and GradB algorithms appear more powerful than other algorithms that are more diverse due to the good predictions of hard-to-classify instances. | (b.1) indicates that \raisebox{0.15pt}{\resizebox{!}{0.8ex}{\textbf{\textsf{C1}}}}⃝ contains well-performing RF models, in contrast to (b.2), in which \raisebox{0.15pt}{\resizebox{!}{0.8ex}{\textbf{\textsf{C3}}}}⃝ includes more diverse RF models and a GradB model.
For the accuracy, recall, and f1-score metrics, \raiseb... | From Figure 2(d.1), we observe that KNN and MLP contain more diverse models (darker green color for instances at the bottom), because they better predict hard-to-classify instances when compared to LR, RF, and GradB (which work better for the easy-to-predict instances). Since we have already found powerful and diverse ... | Similarly-performing models can overlap in this view (due to the y-axis values), so we apply a force-based layout algorithm to make sure they are visible.
However, moving models around introduce uncertainty in this view. Thus, we visualize the mean deviation in pixels for every algorithm (cf. VisEvol: Visual Analytics ... | A |
Unlike the homogeneous Markov chain synthesis algorithms in [4, 7, 5, 6, 8, 9], the Markov matrix, synthesized by our algorithm, approaches the identity matrix as the probability distribution converges to the desired steady-state distribution. Hence the proposed algorithm attempts to minimize the number of state transi... | Furthermore, unlike previous algorithms in [14, 15], the convergence rate of the DSMC algorithm does not rapidly decrease in scenarios where the state space contains sparsely connected regions.
Due to the decentralized nature of the consensus protocol, the Markov chain synthesis relies on local information, similar to ... | Unlike the homogeneous Markov chain synthesis algorithms in [4, 7, 5, 6, 8, 9], the Markov matrix, synthesized by our algorithm, approaches the identity matrix as the probability distribution converges to the desired steady-state distribution. Hence the proposed algorithm attempts to minimize the number of state transi... | Building on this new consensus protocol, the paper introduces a decentralized state-dependent Markov chain (DSMC) synthesis algorithm. It is demonstrated that the synthesized Markov chain, formulated using the proposed consensus algorithm, satisfies the aforementioned mild conditions. This, in turn, ensures the exponen... | In this section, we apply the DSMC algorithm to the probabilistic swarm guidance problem and provide numerical simulations that show the convergence rate of the DSMC algorithm is considerably faster as compared to the previous Markov chain synthesis algorithms in [7] and [14].
| A |
The output of ZoomOut are pairwise correspondences {Pij}subscript𝑃𝑖𝑗\{P_{ij}\}{ italic_P start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT } and pairwise functional maps {𝒞ij}subscript𝒞𝑖𝑗\{\mathcal{C}_{ij}\}{ caligraphic_C start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT } between all pairs of sha... | Most pipelines for partial matching include the full reference shape to resolve some of the complexity. Although our optimisation does not need any information about the complete geometry, we use a partiality-adjusted version of ZoomOut to obtain the shape-to-universe initialisation for IsoMuSh.
In this case, the optim... | We compare our method against several recent state-of-the-art methods, including the pairwise matching approach ZoomOut [47], the two-stage approach ZoomOut+Sync that performs synchronisation to achieve cycle consistency in the results produced by ZoomOut, as well as the multi-matching methods HiPPI [9] and ConsistentZ... | In contrast, HiPPI and our method require shape-to-universe representations. To obtain these, we use synchronisation to extract the shape-to-universe representation from the pairwise transformations. By doing so, we obtain the initial U𝑈Uitalic_U and Q𝑄Qitalic_Q. We refer to this method of synchronising the ZoomOut r... |
We presented a novel formulation for the isometric multi-shape matching problem. Our main idea is to simultaneously solve for shape-to-universe matchings and shape-to-universe functional maps. By doing so, we generalise the popular functional map framework to multi-matching, while guaranteeing cycle consistency, both ... | C |
Directed path graphs are characterized by Gavril [9], in the same article he also gives the first recognition algorithms that has O(n4)𝑂superscript𝑛4O(n^{4})italic_O ( italic_n start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT ) time complexity. In the above cited article, Monma and Wei [18] give the second characterizati... | interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs.interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs\text{interval graphs $\subset$ rooted path graphs $\subset$ directed path %
graphs $\subset$ path graphs $\subset$ chordal graphs}.interva... | A graph is an interval graph if it is the intersection graph of a family of intervals on the real line; or, equivalently, the intersection graph of a family of subpaths of a path. Interval graphs are characterized by Lekkerkerker and Boland [15] as chordal graphs with no asteroidal triples, where an asteroidal triple i... |
A clique is a clique separator if its removal disconnects the graph in at least two connected components. A graph with no clique separator is called atom. For example, every cycle has no clique separator, and the butterfly/hourglass graph has two cliques and it is an atom. In [18] it is proved that an atom is a path g... |
Path graphs and directed path graphs are classes of graphs between interval graphs and chordal graphs. A graph is a chordal graph if it does not contain a hole as an induced subgraph, where a hole is a chordless cycle of length at least four. Gavril [8] proves that a graph is chordal if and only if it is the intersect... | D |
Before comparing these methods, we take some preprocessing to remove nodes that may have mixed memberships for community detection. For the Polbooks data, nodes labeled as “neutral” are removed. The smallest group with only 2 nodes in UKfaculty data is removed. Table 1 presents some basic information about the four dat... | In this section, four real-world network datasets with known label information are analyzed to test the performances of our Mixed-SLIM methods for community detection. The four datasets can be downloaded from
http://www-personal.umich.edu/~mejn/netdata/. For the four datasets, the true labels are suggested by the origi... | In this paper, we extend the symmetric Laplacian inverse matrix (SLIM) method (SLIM, ) to mixed membership networks and call this proposed method as mixed-SLIM. As mentioned in SLIM , the idea of using the symmetric Laplacian inverse matrix to measure the closeness of nodes comes from the first hitting time in a random... | Table 2 records the error rates on the four real-world networks. The numerical results suggest that Mixed-SLIM methods enjoy satisfactory performances compared with SCORE, SLIM, OCCAM, Mixed-SCORE, and GeoNMF when detecting the four empirical datasets. Especially, the number error for Mixed-SLIM on the Polblogs network... |
We report the averaged mixed Hamming error rates for our methods and the other three competitors in Table 4. Mixed-SLIMτapprosubscriptSLIM𝜏𝑎𝑝𝑝𝑟𝑜\mathrm{SLIM}_{\tau appro}roman_SLIM start_POSTSUBSCRIPT italic_τ italic_a italic_p italic_p italic_r italic_o end_POSTSUBSCRIPT outperforms the other three Mixed-S... | C |
For any functional F:ℳ→ℝ:𝐹→ℳℝF\colon\mathcal{M}\rightarrow\mathbb{R}italic_F : caligraphic_M → blackboard_R, we let gradFgrad𝐹\operatorname{{\mathrm{grad}}}Froman_grad italic_F denote the functional gradient of F𝐹Fitalic_F with respect to the Riemannian metric g𝑔gitalic_g.
| Here the statistical error is incurred in estimating the Wasserstein gradient by solving the dual maximization problem using functions in a reproducing kernel Hilbert space (RKHS) with finite data, which converges sublinearly to zero as the number of particles goes to infinity.
Therefore, in this scenario, variational ... | we prove that variational transport constructs a sequence of probability distributions that converges linearly to the global minimizer of the objective functional up to a statistical error due to estimating the Wasserstein gradient with finite particles. Moreover, such a statistical error converges to zero as the numbe... | To study optimization problems on the space of probability measures, we first introduce the background knowledge of the Riemannian manifold and the Wasserstein space. In addition, to analyze the statistical estimation problem that arises in estimating the Wasserstein gradient, we introduce the reproducing kernel Hilber... | Second, when the Wasserstein gradient is approximated using RKHS functions and the objective functional satisfies the PL condition, we prove that the sequence of probability distributions constructed by variational transport converges linearly to the global minimum of the objective functional, up to certain statistical... | C |
Intrinsic motivation methods have been widely studied in the literature, such as handling the difficult-to-learn dilemma in sparse reward environments [51] or trading off the exploration and exploitation in non-sparse reward scenarios [50]. Most of the intrinsic reward approaches can be classified into two classes. The... | For the policy network θ𝜃\thetaitalic_θ, the learning objective is to maximize the cumulative reward as well as the intrinsic reward rtintsubscriptsuperscript𝑟𝑖𝑛𝑡𝑡r^{int}_{t}italic_r start_POSTSUPERSCRIPT italic_i italic_n italic_t end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT in Eq. 12:
|
Besides the above two classes, other intrinsic reward methods are mainly task-oriented and for a specific purpose. For example, the method in [19] uses the discrepancy between the marginal policy and the conditional policy as the intrinsic reward for encouraging agents to have a greater social impact on others. The er... | Secondly, even for a specific task, the received rewards and observations are uncertain to the agent, as illustrated in Fig. 1, which make the policy learning unstable and non-convergent. Even if the agent performs the same action on the same observation at different timesteps, the agent may receive different rewards a... | To make the policy transferable, traffic signal control is also modeled as a meta-learning problem in [14, 49, 36]. Specifically, the method in [14] performs meta-learning on multiple independent MDPs and ignores the influences of neighbor agents. A data augmentation method is proposed in [49] to generates diverse traf... | B |
bounded convex neighborhood Ω1×Σ1subscriptΩ1subscriptΣ1\Omega_{1}\times\Sigma_{1}roman_Ω start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × roman_Σ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT of (𝐱∗,𝐲∗)subscript𝐱subscript𝐲(\mathbf{x}_{*},\mathbf{y}_{*})( bold_x start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT , bold_y start_POSTSUBSCRIP... | of the mapping 𝐱↦𝐟𝐱(𝐱,𝐲~)rank-r†𝐟(𝐱,𝐲~)maps-to𝐱subscript𝐟𝐱superscriptsubscript𝐱~𝐲rank-r†𝐟𝐱~𝐲\mathbf{x}\,\mapsto\,\mathbf{f}_{\mathbf{x}}(\mathbf{x},\tilde{\mathbf{y}})_{%
\mbox{\scriptsize rank-{r}}}^{\dagger}\,\mathbf{f}(\mathbf{x},\tilde{\mathbf{y% | ‖𝐟𝐱(𝐱^,𝐲^)rank-r†‖2(γ‖𝐱^−𝐱ˇ‖2+ζ‖𝐟(𝐱^,𝐲^)‖2)subscriptnormsubscript𝐟𝐱superscriptsubscript^𝐱^𝐲rank-r†2𝛾subscriptnorm^𝐱ˇ𝐱2𝜁subscriptnorm𝐟^𝐱^𝐲2\displaystyle\big{\|}\mathbf{f}_{\mathbf{x}}(\hat{\mathbf{x}},\hat{\mathbf{y}}%
)_{\mbox{\scriptsize rank-$r$}}^{\dagger}\big{\|}_{2}\,\big{(}\gamma\,\|\hat{... |
‖𝐟𝐱(𝐱^,𝐲^)rank-r𝐟𝐱(𝐱^,𝐲^)rank-r†−𝐟𝐱(𝐱ˇ,𝐲^)rank-r𝐟𝐱(𝐱ˇ,𝐲^)rank-r†‖2subscriptnormsubscript𝐟𝐱subscript^𝐱^𝐲rank-rsubscript𝐟𝐱superscriptsubscript^𝐱^𝐲rank-r†subscript𝐟𝐱subscriptˇ𝐱^𝐲rank-rsubscript𝐟𝐱superscriptsubscriptˇ𝐱^𝐲rank-r†2\displaystyle\big{\|}\mathbf{f}_{\mathbf{x}}(\hat{\mathbf... | ‖𝐟𝐱(𝐱^,𝐲^)rank-r†−𝐟𝐱(𝐱^,𝐲ˇ)rank-r†‖2subscriptnormsubscript𝐟𝐱superscriptsubscript^𝐱^𝐲rank-r†subscript𝐟𝐱superscriptsubscript^𝐱ˇ𝐲rank-r†2\displaystyle\big{\|}\mathbf{f}_{\mathbf{x}}(\hat{\mathbf{x}},\hat{\mathbf{y}}%
)_{\mbox{\scriptsize rank-$r$}}^{\dagger}-\mathbf{f}_{\mathbf{x}}(\hat{\mathbf% | C |
Suppose that an item of size x𝑥xitalic_x arrives. If there is an empty placeholder of size x𝑥xitalic_x in a non-empty bin, then the item is assigned to that bin (and to the corresponding placeholder), and declared PP-item. Otherwise, there are two possibilities: If 𝚙𝚙𝚌𝚘𝚞𝚗𝚝(x)𝚙𝚙𝚌𝚘𝚞𝚗𝚝𝑥{\tt ppcount}(x)ty... | Figure 4 depicts the number of bins opened by the algorithms. The experiments show that the parameter m𝑚mitalic_m has little impact on the performance of Hybrid(λ𝜆\lambdaitalic_λ), that is, as long as m𝑚mitalic_m is sufficiently large (e.g., when m≥1000𝑚1000m\geq 1000italic_m ≥ 1000), the performance of Hybrid(λ𝜆\... | Note that in Hybrid(λ𝜆\lambdaitalic_λ), A𝐴Aitalic_A and ProfilePacking maintain their own bin space, so when serving according to one of these algorithms, only the bins opened by the corresponding algorithm are considered. Thus, we can partition the bins used by Hybrid(λ𝜆\lambdaitalic_λ) into PP-bins and A𝐴Aitalic_... | Figure 1: The packing output by ProfilePacking on the input sequence σ=2,3,1,4,10,2,9,4,6,9,2,6,5𝜎23141029469265\sigma=2,3,1,4,10,2,9,4,6,9,2,6,5italic_σ = 2 , 3 , 1 , 4 , 10 , 2 , 9 , 4 , 6 , 9 , 2 , 6 , 5. The predictions and the corresponding profile are as given in Example 1. The optimal packing of the profile con... | standard online model in which there is no prediction.
Specifically, we will define a class of algorithms based on a parameter λ∈[0,1]𝜆01\lambda\in[0,1]italic_λ ∈ [ 0 , 1 ] and the robust algorithm A𝐴Aitalic_A, and which we denote by Hybrid(λ𝜆\lambdaitalic_λ); we will also say that Hybrid(λ𝜆\lambdaitalic_λ) is base... | B |
where Wϕsubscript𝑊italic-ϕW_{\phi}italic_W start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT are weights of ϕitalic-ϕ\phiitalic_ϕ produced by the hypernetwork directly from the point cloud embedding and [⋅,⋅]⋅⋅[\cdot,\cdot][ ⋅ , ⋅ ] is a concatenation operator. | Table 2: Shape auto-encoding on the ShapeNet dataset. The best results are highlighted in bold. CD is multiplied by 104superscript10410^{4}10 start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT, and EMD is multiplied by 102superscript10210^{2}10 start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. (HC) denotes the HyperCloud autoencod... | Table 1: Generation results. MMD-CD scores are multiplied by
103superscript10310^{3}10 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT; MMD-EMD and JSD scores are multiplied by 102superscript10210^{2}10 start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. (HC) denotes the HyperCloud autoencoder in LoCondA, and (HF) - the HyperFlow... |
The results are presented in Table 1. LoCondA-HF obtains comparable results to the reference methods dedicated for the point cloud generation. It can be observed that values of evaluated measures for HyperFlow(P) and LoCondA-HF (uses HyperFlow(P) as a base model in the first part of the training) are on the same level... |
In this experiment, we set N=105𝑁superscript105N=10^{5}italic_N = 10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT. Using more rays had a negligible effect on the output value of WT𝑊𝑇WTitalic_W italic_T but significantly slowed the computation. We compared AtlasNet with LoCondA applied to HyperCloud (HC) and HyperFl... | B |
For non-strongly convex-concave case, distributed SPP with local and global variables were studied in [41], where the authors proposed a subgradient-based algorithm for non-smooth problems with O(1/N)𝑂1𝑁O(1/\sqrt{N})italic_O ( 1 / square-root start_ARG italic_N end_ARG ) convergence guarantee (N𝑁Nitalic_N is the n... | Paper [61] introduced an Extra-gradient algorithm for distributed multi-block SPP with affine constraints. Their method covers the Euclidean case and the algorithm has O(1/N)𝑂1𝑁O(1/N)italic_O ( 1 / italic_N ) convergence rate.
Our paper proposes an algorithm based on adding Lagrangian multipliers to consensus constr... | Now we show the benefits of representing some convex problems as convex-concave problems on the example of the Wasserstein barycenter (WB) problem and solve it by the DMP algorithm. Similarly to Section (3), we consider a SPP in proximal setup and introduce Lagrangian multipliers for the common variables. However, in t... |
For non-strongly convex-concave case, distributed SPP with local and global variables were studied in [41], where the authors proposed a subgradient-based algorithm for non-smooth problems with O(1/N)𝑂1𝑁O(1/\sqrt{N})italic_O ( 1 / square-root start_ARG italic_N end_ARG ) convergence guarantee (N𝑁Nitalic_N is the n... |
We proposed a decentralized method for saddle point problems based on non-Euclidean Mirror-Prox algorithm. Our reformulation is built upon moving the consensus constraints into the problem by adding Lagrangian multipliers. As a result, we get a common saddle point problem that includes both primal and dual variables. ... | A |
And from the bijection we can deduce that
∩(Tw)<∩(Gw∧Ts)subscript𝑇𝑤subscript𝐺𝑤subscript𝑇𝑠\cap(T_{w})<\cap(G_{w}\wedge T_{s})∩ ( italic_T start_POSTSUBSCRIPT italic_w end_POSTSUBSCRIPT ) < ∩ ( italic_G start_POSTSUBSCRIPT italic_w end_POSTSUBSCRIPT ∧ italic_T start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ) for so... | In this section we present some experimental results to reinforce
Conjecture 14. We proceed by trying to find a counterexample based on our previous observations. In the first part, we focus on the complete analysis of small graphs, that is: graphs of at most 9 nodes. In the second part, we analyze larger families of g... | necessarily complete) G=(V,E)𝐺𝑉𝐸G=(V,E)italic_G = ( italic_V , italic_E ) that admits a star spanning tree
Tssubscript𝑇𝑠T_{s}italic_T start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT. In the first part we present a formula to calculate ∩(Ts)subscript𝑇𝑠\cap(T_{s})∩ ( italic_T start_POSTSUBSCRIPT italic_s end_POSTSU... |
The remainder of this section is dedicated to express the problem in the context of the theory of cycle bases, where it has a natural formulation, and to describe an application. Section 2 sets some notation and convenient definitions. In Section 3 the complete graph case is analyzed. Section 4 presents a variety of i... |
The study of cycles of graphs has attracted attention for many years. To mention just three well known results consider Veblen’s theorem [2] that characterizes graphs whose edges can be written as a disjoint union of cycles, Maclane’s planarity criterion [3] which states that planar graphs are the only to admit a 2-ba... | A |
(m+1)𝑚1(m+1)( italic_m + 1 )-tuples of ℱℱ\mathcal{F}caligraphic_F with nonempty intersection. In other words, πm+1(ℱ)subscript𝜋𝑚1ℱ\pi_{m+1}(\mathcal{F})italic_π start_POSTSUBSCRIPT italic_m + 1 end_POSTSUBSCRIPT ( caligraphic_F ) is at least δ′=defρ/(mtm+1)superscriptdefsuperscript𝛿′𝜌binomial𝑚𝑡𝑚1\delta^{\prim... | If we use Lemma 4.8 in place of Lemma 4.6 in the proof of Theorem 2.1, the hypothesis on the m𝑚mitalic_m-colored family ℱℱ\mathcal{F}caligraphic_F can be weakened. This “improved” Theorem 2.1 can in turn be applied in the proof of Theorem 1.2, yielding the following:
| a positive fraction of the m𝑚mitalic_m-tuples to have a nonempty intersection, where for dimK>1dimension𝐾1\dim K>1roman_dim italic_K > 1, m𝑚mitalic_m is some hypergraph Ramsey number depending on b𝑏bitalic_b and K𝐾Kitalic_K.
So in order to prove Corollary 1.3 it suffices to show that if a positive fraction of the ... | The rest of Section 4.1 is devoted to the proof of Lemma 4.2. The proof first handles the case k=m𝑘𝑚k=mitalic_k = italic_m, and then uses it to prove the case k<m𝑘𝑚k<mitalic_k < italic_m. Note that for k>m𝑘𝑚k>mitalic_k > italic_m the lemma is trivial, as the chain group contains only a trivial chain and we can ta... | Lemma 4.6 assumes that the m𝑚mitalic_m-colored family ℱℱ\mathcal{F}caligraphic_F has the property that for 0≤j<dimK0𝑗dimension𝐾0\leq j<\dim K0 ≤ italic_j < roman_dim italic_K and for every colorful subfamily 𝒢𝒢\mathcal{G}caligraphic_G of ℱℱ\mathcal{F}caligraphic_F, the j𝑗jitalic_jth reduced Betti number β~j(⋂F∈�... | A |
G3: Application of alternative feature transformations according to feedback received from statistical measures.
In continuation of the preceding goal, the tool should provide sufficient visual guidance to users to choose between diverse feature transformations (T3). Statistical measures such as target correlation and ... | G4: Generation of new features and comparison with the original features.
With the same statistical evidence as defined in G3, users should get visually informed about strongly correlated features that perform the same for each class. Next, the tool can use automatic feature selection techniques to compare the new feat... |
Figure 1: Selecting important features, transforming them, and generating new features with FeatureEnVi: (a) the horizontal beeswarm plot for manually slicing the data space (which is sorted by predicted probabilities) and continuously checking the migration of data instances throughout the process; (b) the table heat... | Next, as XGBoost [29] is a nonlinear ML algorithm, we also train a linear classifier (a logistic regression [83] model with the default Scikit-learn’s hyperparameters [84]) to compute the coefficients matrix and then use Recursive Feature Elimination (RFE) [40] to rank the features from the best to the worst in terms o... | T4: Combine features to generate new features.
It is common in feature engineering to combine features in many ways by using mathematical operators. Feature generation produces features with higher levels of contribution because they pack additional information. Here, users need means to select a few features and a way... | A |
In machining, positioning systems need to be fast and precise to guarantee high productivity and quality. Such performance can be achieved by model predictive control (MPC) approach tailored for tracking a 2D contour [1, 2], however requiring precise tuning and good computational abilities of the associated hardware. ... | which is an MPC-based contouring approach to generate optimized tracking references. We account for model mismatch by automated tuning of both the MPC-related parameters and the low level cascade controller gains, to achieve precise contour tracking with micrometer tracking accuracy. The MPC-planner is based on a combi... |
In machining, positioning systems need to be fast and precise to guarantee high productivity and quality. Such performance can be achieved by model predictive control (MPC) approach tailored for tracking a 2D contour [1, 2], however requiring precise tuning and good computational abilities of the associated hardware. ... | MPC accounts for the real behavior of the machine and the axis drive dynamics can be excited to compensate for the contour error to a big extent, even without including friction effects in the model [4, 5]. High-precision trajectories or set points can be generated prior to the actual machining process following variou... | This paper demonstrated a hierarchical contour control implementation for the increase of productivity in positioning systems. We use a contouring predictive control approach to optimize the input to a low level controller. This control framework requires tuning of multiple parameters associated with an extensive numbe... | C |
Results. As shown in Table. 1, no method performs universally well across datasets; however, the implicit methods LFF and SD obtain high unbiased accuracies on most datasets. This shows that implicit methods can deal with multiple bias sources without explicit access. Explicit methods work well on CelebA but fail on Bi... | Results.
For CelebA, methods generally show large variance on the minority patterns (blond haired male celebrities), and lower variance on the majority patterns (mean over rest of the groups), whereas for Biased MNISTv1, we find that methods only work for certain set of hyperparameters and show degraded results on both... | We use the GQA visual question answering dataset [33] to highlight the challenges of using bias mitigation methods on real-world tasks. It has multiple sources of biases including imbalances in answer distribution, visual concept co-occurrences, question word correlations, and question type/answer distribution. It is u... | In this set of experiments, we compare the resistance to explicit and implicit biases. We primarily focus on the Biased MNISTv1 dataset, reserving each individual variable as the explicit bias in separate runs of the explicit methods, while treating the remaining variables as implicit biases. To ease analysis, we compu... | Results.
In Fig. 3(a), we present the MMD boxplots for all bias variables, comparing cases when the label of the variable is either explicitly specified (explicit bias), or kept hidden (implicit bias) from the methods. Barring digit position, we observe that the MMD values are higher when the variables are not explicit... | C |
Salvalaio et al. implicitly collect calibration data when users are using computers. They collect data when the user is clicking a mouse, this is based on the assumption that users are gazing at the position of the cursor when clicking the mouse [146]. They use online learning to fine-tune their model with the calibrat... | They build a multi-branch network to extract the features of each view and concatenate them to estimate 2222D gaze position on the screen. Wu et al. collect gaze data using near-eye IR cameras [123]. They use CNN to detect the location of glints, pupil centers and corneas from IR images. Then, they build an eye model u... |
The head-mounted device usually employs near-eye cameras to capture eye images. Tonsen et al. embed millimetre-sized RGB cameras into a normal glasses frame [147]. In order to compensate for the low-resolution captured images, they use multi-cameras to capture multi-view images and use a neural network to regress gaze... |
Tonsen et al. embed multiple millimeter-sized RGB cameras into a normal glasses frame [147]. They use multi-layer perceptrons to process the eye images captured by different cameras, and concatenate the extracted feature to estimate gaze. Lian et al. mount three cameras at the bottom of a screen [121]. | The majority of gaze estimation systems use a single RGB camera to capture eye images, while some studies use different camera settings, e.g., using multiple cameras to capture multi-view images [121, 147, 164], using infrared (IR) cameras to handle low illumination condition [123, 149], and using RGBD cameras to provi... | D |
Table 2 reports the classification rates on the SMFRD dataset. The highest recognition rate is achieved by the ResNet-50 through the quantization of DRF features by 88.9%. This performance is achieved using 70 codewords that feed an MLP classifier. AlexNet model realized good recognition rates comparing to the VGG-16 ... |
The efficiency of each pre-trained model depends on its architecture and the abstraction level of the extracted features. When dealing with real masked faces, VGG-16 has achieved the best recognition rate, while ResNet-50 outperformed both VGG-16 and AlexNet on the simulated masked faces. This behavior can be explaine... |
Covariance-based features have been applied in hariri20163d and achieved high recognition performance on 3D datasets in the presence of occluded regions. We have employed this method using 2D-based features (texture, gray level, LBP) to extract covariance descriptors. The evaluation on the RMFRD and SMFRD datasets co... |
We have tested the face recognizer presented in luttrell2018deep that achieved a good recognition accuracy on two subsets of the FERET database phillips1998feret . This technique is based on transfer learning (TL) which employs pre-trained models and fine-tuning them to recognize masked faces from RMFRD and SMFRD dat... |
Another efficient face recognition method using the same pre-trained models (AlexNet and ResNet-50) is proposed in almabdy2019deep and achieved a high recognition rate on various datasets. Nevertheless, the pre-trained models are employed in a different manner. It consists of applying a TL technique to fine-tune the ... | C |
\leftarrow\operatorname{partition}k\,(p,x)::(y:\exists m,n.\,k=m+n\land\mathrm%
{list}[m]\otimes\mathrm{list}[n])italic_k ; ⋅ ; italic_p : roman_nat , italic_x : roman_list [ italic_k ] ⊢ italic_y ← roman_partition italic_k ( italic_p , italic_x ) : : ( italic_y : ∃ italic_m , italic_n . italic_k = italic_m + italic_n ... |
First, we define head and tail observations on streams of arbitrary depth. Since they are not recursive, we do not bother tracking the size superscript of the typing judgment, since they can be inlined. Moreover, we take the liberty to nest values (boxed and highlighted yellow), which can be expanded into SAX [PP20]. |
In this section, we extend SAX [DPP20] with recursion and arithmetic refinements in the style of Das and Pfenning [DP20b]. SAX is a logic-based formalism and subsuming paradigm [Lev04] for concurrent functional programming that conceives call-by-need and call-by-value strategies as particular concurrent schedules [PP2... |
That is, we assume that we have definitions that (1) append two lists together and (2) partitions one by a pivot. Then, at a high level, quicksort is a size-preserving definition with the input list length as its termination measure. For brevity, we nest patterns (boxed and highlighted yellow), which can be expanded i... |
Our system is closely related to the sequential functional language of Lepigre and Raffalli [LR19], which utilizes circular typing derivations for a sized type system with mixed inductive-coinductive types, also avoiding continuity checking. In particular, their well-foundedness criterion on circular proofs seems to c... | C |
The rest of this paper is outlined below. The next section reviews the related work. Section III describes the system model, threat model, and design goals. Subsequently, Section IV introduces the involved fundamental techniques. The two schemes are constructed in Section V. The performance of the two schemes regardin... | Thirdly, there are also studies that deal with both privacy-protected access control and traitor tracing. Xia et al. [26] introduced the watermarking technique to privacy-protected content-based ciphertext image retrieval in the cloud, which can prevent the user from illegally distributing the retrieved images. However... | To solve Problem 1, cryptosystems implementing privacy-protected access control are required. Attribute-Based Encryption (ABE) [5, 6] is such a cryptosystem, in which a user’s credentials are described by attributes. A ciphertext can be de-crypted by the user when the attributes pass the ciphertext’s access structure. ... | Firstly, this work inherits from the privacy-protected cloud media sharing solutions based on ABE or PRE. Wu et al. [21] came up with an ABE scheme with multi-message ciphertext policy, which was implemented for scalable media sharing and access control based on the user’s attributes.
Polyakov et al. [22] proposed two ... | Liang et al. [23] defined and constructed a deterministic finite automata-based functional PRE scheme for public cloud data sharing without privacy leakage.
After that, Li et al. [24] constructed a fine-grained and accountable access control system in the cloud, which traces suspicious access behaviors while ignores re... | C |
Though based on graph spectral theory Bruna et al. (2013), the learning process of graph convolutional networks (GCN) Kipf and Welling (2017) also can be considered as a mean-pooling neighborhood aggregation.
GraphSAGE Hamilton et al. (2017) concatenates the node features and introduces three | Due to the strength in modeling relations on graph-structured data, GNN has been widely applied to various applications like neural machine translation Beck et al. (2018), semantic segmentation Qi et al. (2017), image classification Marino et al. (2017), situation recognition Li et al. (2017), recommendation Wu et al. ... |
Currently, Graph Neural Networks (GNN) Kipf and Welling (2017); Hamilton et al. (2017); Veličković et al. (2018) have recently emerged as an effective class of models for capturing high-order relationships between nodes in a graph and have achieved state-of-the-art results on a variety of tasks such as computer vision... |
To capture the diversified polysemy of feature interactions in different semantic subspaces Li et al. (2020) and also stabilize the learning process Vaswani et al. (2017); Veličković et al. (2018), we extend our mechanism to employ multi-head attention. | At their core, GNNs learn node embeddings by iteratively aggregating features from the neighboring nodes, layer by layer. This allows them to explicitly encode high-order relationships between nodes in the embeddings. GNNs have shown great potential for modeling high-order feature interactions for click-through rate pr... | A |
This means that Theorems 2.4 and 2.6 effectively bound the number of ZOO, FOO, DO, and LMO oracle calls needed to achieve a target primal gap or Frank-Wolfe gap accuracy ε𝜀\varepsilonitalic_ε as a function of Tνsubscript𝑇𝜈T_{\nu}italic_T start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT and ε𝜀\varepsilonitalic_ε; note... |
Furthermore, with this simple step size we can also prove a convergence rate for the Frank-Wolfe gap, as shown in Theorem 2.6. More specifically, the minimum of the Frank-Wolfe gap over the run of the algorithm converges at a rate of 𝒪(1/t)𝒪1𝑡\mathcal{O}(1/t)caligraphic_O ( 1 / italic_t ). The idea of the proof is... | We note that the LBTFW-GSC algorithm from Dvurechensky et al. [2022] is in essence the Frank-Wolfe algorithm with a modified version of the backtracking line search of Pedregosa et al. [2020]. In the next section, we provide improved convergence guarantees for various cases of interest for this algorithm, which we refe... | In practice, a halving strategy for the step size is preferred for the
implementation of the Monotonic Frank-Wolfe algorithm, as opposed to the step size implementation shown in Algorithm 1. This halving strategy, which is shown in Algorithm 2, helps | The results are shown in Figure 7. On both of these instances, the simple step progress is slowed down or even seems stalled in comparison to the stateless
version because a lot of halving steps were done in the early iterations for the simple step size, which penalizes progress over the whole run. | C |
Storage can also be distributed in a sense that each matched edge and each vertex needs access to poly1/εpoly1𝜀\operatorname{poly}1/\varepsilonroman_poly 1 / italic_ε memory cells, but a vertex/edge does not need a direct access to memory cells of other vertices/edges. |
In this section we describe how to generalize our algorithm to other computation models. We begin by describing what procedures our framework requires the access to. The input contains a graph G𝐺Gitalic_G and an approximation parameter ε𝜀\varepsilonitalic_ε. | The basic building block in the search for augmenting paths is to find semi-matchings between the vertices and their matched neighbors such that each vertex has a small amount of neighbors in the semi-matching.
In the case of bipartite graphs, they show that their method of searching for augmenting paths in a graph def... |
In a distributed/parallel setting, the aforementioned “time” should be understood as the number of rounds. All the times listed above are a function of G𝐺Gitalic_G and ε𝜀\varepsilonitalic_ε, but for the sake of brevity we drop these parameters in the rest of this section. | Table 1: A summary of the running times in several different models, compared to the previous state-of-the-art, for computing a (1+ε)1𝜀(1+\varepsilon)( 1 + italic_ε )-approximate maximum matching. In the distributed setting, “running time” refers to the round complexity, while in the streaming setting it refers to th... | C |
Figure 1: Linear convergence of Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B, CPP, and B-CPP with b𝑏bitalic_b bit quantization (b=2,4,6𝑏246b=2,4,6italic_b = 2 , 4 , 6) and Rand-k (k=5,10,20𝑘51020k=5,10,20italic_k = 5 , 10 , 20) compressors. | Although the additional compression errors slow down the convergence,
our design for CPP guarantees that the impact on the convergence rate is relatively small. Therefore, CPP is much more communication-efficient than the exact Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B method. | To reduce the error from compression, some works [48, 49, 50] increase compression accuracy as the iteration grows to guarantee the convergence. However, they still need high communication costs to get highly accurate solutions. Techniques to remedy this increased communication costs include gradient difference compres... | The existence of compression errors may result in inferior convergence performance compared to uncompressed or centralized algorithms. For example, the methods considered by [41, 42, 43, 44, 45, 46] can only guarantee to reach a neighborhood of the desired solutions when the compression errors exist.
QDGD [47] achieves... | This is reasonable as the compression operator induces additional errors compared to the exact method, and these additional errors could slow down the convergence.
Meanwhile, as the values of b𝑏bitalic_b or k𝑘kitalic_k increases, both CPP and B-CPP speed up since the compression errors decrease. | D |
One can note a branch of recent work devoted to solving non-smooth problems by reformulating them as saddle point problems [8, 9], as well as applying such approaches to image processing
[10, 11]. Recently, significant attention was devoted to saddle problems in machine learning. For example, Generative Adversarial Net... | One can note a branch of recent work devoted to solving non-smooth problems by reformulating them as saddle point problems [8, 9], as well as applying such approaches to image processing
[10, 11]. Recently, significant attention was devoted to saddle problems in machine learning. For example, Generative Adversarial Net... | To the best of our knowledge, this paper is the first to consider decentralized personalized federated saddle point problems, propose optimal algorithms and derives the computational and communication lower bounds for this setting. In the literature, there are works on general (non-personalized) SPPs. We make a detaile... |
Furthermore, there are a lot of personalized federated learning problems utilize saddle point formulation. In particular, Personalized Search Generative Adversarial Networks (PSGANs) [22]. As mentioned in examples above, saddle point problems often arise as an auxiliary tool for the minimization problem. It turns out ... |
In this paper, we present a novel formulation for the Personalized Federated Learning Saddle Point Problem (1). This formulation incorporates a penalty term that accounts for the specific structure of the network and is applicable to both centralized and decentralized network settings. Additionally, we provide the low... | C |
σ∗=b−CATα∗+Cβ∗.superscript𝜎𝑏𝐶superscript𝐴𝑇superscript𝛼𝐶superscript𝛽\sigma^{*}=b-CA^{T}\alpha^{*}+C\beta^{*}.italic_σ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT = italic_b - italic_C italic_A start_POSTSUPERSCRIPT italic_T end_POSTSUPERSCRIPT italic_α start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT + italic_C it... |
The full-support assumption states that all joint probabilities have some positive mass, σ>0𝜎0\sigma>0italic_σ > 0. In this scenario, the dual variable vector corresponding to the non-negative probability constraint is zero, β=0𝛽0\beta=0italic_β = 0. Therefore we can define simplified primal and dual objectives. | The primal objective that we wish to optimize is minσmaxα,β,λL(σ,α,β,λ)=Lσα,β,λsubscript𝜎subscript𝛼𝛽𝜆𝐿𝜎𝛼𝛽𝜆superscriptsubscript𝐿𝜎𝛼𝛽𝜆\min_{\sigma}\max_{\alpha,\beta,\lambda}L(\sigma,\alpha,\beta,\lambda)=L_{%
\sigma}^{\alpha,\beta,\lambda}roman_min start_POSTSUBSCRIPT italic_σ end_POSTSUBSCRIPT roman_max... | There are two important solution concepts in the space of CEs. The first is Maximum Welfare Correlated Equilibrium (MWCE) which is defined as the CE that maximises the sum of all player’s payoffs. An MWCE can be obtained by solving a linear program, however the MWCE may not be unique and therefore does not fully solve ... | MG(C)CE can provide solutions in general-support and, similar to MECE, MG(C)CE permits a scalable representation when the solution is full-support. Under this scenario, the distribution inequality constraint variables, β𝛽\betaitalic_β, are inactive, are equal to zero, can be dropped, and the α𝛼\alphaitalic_α variable... | A |
The similarity function serves as a measure of the local sensitivity of the issued queries with respect to the replacement of the two datasets, by quantifying the extent to which they differ from each other with respect to the query q𝑞qitalic_q. The case of noise addition mechanisms provides a natural intuitive interp... |
The dependence of our PC notion on the actual adaptively chosen queries places it in the so-called fully-adaptive setting (Rogers et al., 2016; Whitehouse et al., 2023), which requires a fairly subtle analysis involving a set of tools and concepts that may be of independent interest. In particular, we establish a seri... |
We note that the first part of this definition can be viewed as a refined version of zCDP (Definition B.18), where the bound on the Rényi divergence (Definition B.5) is a function of the sample sets and the query. As for the second part, since the bound depends on the queries, which themselves are random variables, it... | We measure the harm that past adaptivity causes to a future query by considering the query as evaluated on a posterior data distribution and comparing this with its value on a prior. The prior is the true data distribution, and the posterior is induced by observing the responses to past queries and updating the prior. ... | Using the first part of the lemma, we guarantee Bayes stability by bounding the correlation between specific q𝑞qitalic_q and K(⋅,v)𝐾⋅𝑣{K}\left(\cdot,v\right)italic_K ( ⋅ , italic_v ) as discussed in Section 6. The second part of this Lemma implies that bounding the appropriate divergence is necessary and sufficient... | B |
To conclude, we reflect on the running time of Corollary 6.11 compared to running times of the form 2𝒪(fvs(G))⋅n𝒪(1)⋅superscript2𝒪fvs𝐺superscript𝑛𝒪12^{\mathcal{O}(\operatorname{\textsc{fvs}}(G))}\cdot n^{\mathcal{O}(1)}2 start_POSTSUPERSCRIPT caligraphic_O ( fvs ( italic_G ) ) end_POSTSUPERSCRIPT ⋅ italic_n st... | The goal of this paper is to open up a new research direction aimed at understanding the power of preprocessing in speeding up algorithms that solve NP-hard problems exactly [26, 31]. In a nutshell, this new direction can be summarized as: how can an algorithm identify part of an optimal solution in an efficient prepro... | We therefore propose the following novel research direction: to investigate how preprocessing algorithms can decrease the parameter value (and hence search space) of FPT algorithms, in a theoretically sound way. It is nontrivial to phrase meaningful formal questions in this direction. To illustrate this difficulty, not... |
We start by motivating the need for a new direction in the theoretical analysis of preprocessing. The use of preprocessing, often via the repeated application of reduction rules, has long been known [3, 4, 44] to speed up the solution of algorithmic tasks in practice. The introduction of the framework of parameterized... | We have taken the first steps into a new direction for preprocessing which aims to investigate how and when a preprocessing phase can guarantee to identify parts of an optimal solution to an 𝖭𝖯𝖭𝖯\mathsf{NP}sansserif_NP-hard problem, thereby reducing the running time of the follow-up algorithm. Aside from the techni... | D |
Category-specific object placement methods can be categorized into generative approach and discriminative approach. The generative approach targets at predicting one or multiple reasonable bounding boxes for the foreground category, whereas the discriminative approach aims to predict the rationality score of a boundin... | Specifically, one element in the appearance consistency heatmap measures the similarity between the visual context at this point and original visual context. Georgakis et al. [39] proposed to combine support surface detection and semantic segmentation to find proper location for placing the object. With the determined ... | Lee et al. [73] investigated on taking a background semantic map instead of a background image as input. Given a background semantic map, they designed a network consisting of two generative modules, in which the first module accounts for the bounding box of inserted object and the second module accounts for the mask s... | Generative approaches:
Tan et al. [145] proposed to predict the location and scale of inserted object by taking the background image and object layout as input. Besides, the bounding box prediction task is converted to a classification task by discretizing the locations and scales. | Object placement aims to paste the foreground on the background with suitable location, size, and shape. As shown in Fig. 4, the cases of unreasonable object placement are including but not limited to: a) the foreground object has inappropriate size (e.g., the dog is too large); b) the foreground object has unreasonabl... | C |
We utilized the k-means algorithm to cluster regions within city c𝑐citalic_c based on their POI vectors (𝐱cpoisuperscriptsubscript𝐱𝑐𝑝𝑜𝑖\mathbf{x}_{c}^{poi}bold_x start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_p italic_o italic_i end_POSTSUPERSCRIPT). Additionally, we clustered reg... | Interrelationship:
We have classified the sub-datasets into two categories: service data and context data, as depicted in Fig. 1(c). Service data pertains to the status of urban service providers (e.g. taxi companies), while context data refers to the urban environment (e.g. weather). Based on this categorization, we h... | The average regional daily patterns of taxi mobility data from each POI-based cluster in Beijing, Chengdu, and Xi’an are plotted in Fig. 2. As shown in Fig. 2LABEL:sub@fig:cluster-bj, taxi mobility patterns in Beijing exhibit a high level of cohesion within each POI-based cluster, while remaining distinguishable across... |
TABLE III: Adjusted Rand index (ARI) and adjusted mutual information (AMI) to evaluate the clustering assignments based on POIs and taxi mobility data. Both metrics range from -1 to 1, with larger values indicating a higher degree of coincidence between the two clusters. | Comprehensiveness: Fig. 1(a), illustrates that CityNet comprises three types of raw data (mobility data, geographical data, and meteorological data) collected from seven different cities. Furthermore, we have processed the raw data into several sub-datasets (as shown in Fig. 1(b)) to to capture a wider range of urban p... | B |
By differentiating the argument on the right-hand side with respect to q𝑞qitalic_q and equating it to 0, one obtains definition (19) of the α𝛼\alphaitalic_α-quantile. The pinball loss (26) is then simply the loss function for the sample α𝛼\alphaitalic_α-quantile, i.e. the α𝛼\alphaitalic_α-quantile of the empirical ... | Instead of estimating the conditional mean of a distribution, quantile regression models estimate the conditional quantiles. This has the benefit that one immediately obtains measures of the spread of the underlying distribution and, therefore, of the confidence of future predictions. A neural network quantile regresso... |
In the section on quantile regression it was noted that this approach tends to have a problem with modelling the tails of the distribution, with the added consequence that this can influence the validity at extreme significance levels. However, when combining such models with conformal prediction, validity is not an i... | For each of the selected models, Fig. 4 shows the best five models in terms of average width, excluding those that do not (approximately) satisfy the coverage constraint (2). This figure shows that there is quite some variation in the models. There is not a clear best choice. Because on most data sets the models produc... |
To estimate multiple quantiles at the same time, one simply has to add multiple output nodes to the network and add terms of the form (26) for every quantile. Although quantile regression models do not produce a point estimate in the form of a conditional mean, they can give a prediction of the conditional median. The... | D |
To our best knowledge, the work of \textcitetsai20ismir represents the first attempt to use PTMs for symbolic-domain music classification. They showed that either a RoBERTa-based Transformer encoder PTM \parenciteroberta or a GPT2-based Transformer encoder PTM \parencitegpt2 outperform non-pre-trained baselines for a ... | To facilitate a comprehensive evaluation, we additionally incorporate a officially released version of MusicBERT \parencitemusicbert in the sequence-classification tasks.
Specifically, we use the model checkpoint MusicBERT-small,171717https://github.com/microsoft/muzic/tree/main/musicbert which is pre-trained on the La... | Second, we aim at establishing a benchmark for symbolic music classification and include not only sequence-level but also note-level tasks. Furthermore, the labelled data we employ for our downstream tasks is comparatively modest, with each dataset containing fewer than 1,000 annotated pieces. This differs from MusicBE... | \textcite
musicbert presented MusicBERT, a PTM tailored for symbolic MIDI data. MusicBERT was trained on a non-public dataset of over one million multi-track MIDI pieces. The authors showcased the efficacy of MusicBERT by applying it to two generative music tasks, melody completion and accompaniment suggestion and two ... | The results show that MusicBERT achieves a testing accuracy of 37.25% for style classification and 77.78% for emotion classification. Specifically, in the style classification task, MusicBERT exhibits clear signs of overfitting and falls short in performance when compared to our model (81.75%). This outcome can be attr... | C |
Observe that for a tree on n𝑛nitalic_n vertices we can compute for every vertex v𝑣vitalic_v and its neighbor u𝑢uitalic_u functions f(v,u)𝑓𝑣𝑢f(v,u)italic_f ( italic_v , italic_u ) and g(v,u)𝑔𝑣𝑢g(v,u)italic_g ( italic_v , italic_u ) denoting the sizes of subsets of C1(T)subscript𝐶1𝑇C_{1}(T)italic_C start_PO... | In every tree T𝑇Titalic_T there exists a central vertex v∈V(T)𝑣𝑉𝑇v\in V(T)italic_v ∈ italic_V ( italic_T ) such that every connected component of T−v𝑇𝑣T-vitalic_T - italic_v has at most |V(T)|2𝑉𝑇2\frac{|V(T)|}{2}divide start_ARG | italic_V ( italic_T ) | end_ARG start_ARG 2 end_ARG vertices.
| Next, let us count the total number of jumps necessary for finding central vertices over all loops in Algorithm 1. As it was stated in the proof of Lemma 2.2, while searching for a central vertex we always jump from a vertex to its neighbor in a way that decreases the largest remaining component by one. Thus, if in the... | The idea is to start from any vertex w𝑤witalic_w, and then jump to its neighbor with the largest component size in T−w𝑇𝑤T-witalic_T - italic_w, until we hit a vertex with desired property.
Note that for any vertex v𝑣vitalic_v there can be at most one neighbor u𝑢uitalic_u such that its connected component Tusubscri... | The linear running time follows directly from the fact that we compute c𝑐citalic_c only once and we can pass additionally through recursion the lists of leaves and isolated vertices in an uncolored induced subtree. The total number of updates of these lists is proportional to the total number of edges in the tree, hen... | B |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.