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
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+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.
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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.
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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.
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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 |
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