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<|MaskedSetence|> <|MaskedSetence|> A real data example also illustrates that meaningful interpretation can be drawn after applying our proposed method.
The rest of the paper is structured as follows. Section 2 introduces the model setup and lays out the motivation for this work. Section 3 presents the identifiabil... | **A**: Both the population parameters and the individual membership scores can be consistently estimated on average.
In the simulation studies, we empirically verify the identifiability results and also demonstrate the superior efficiency and accuracy of our algorithm.
**B**: Section 5 conducts simulation studies to a... | CAB | CAB | CAB | BCA | Selection 3 |
This paper describes a general algorithm that solves the above problem when there exists a representation of τ𝜏\tauitalic_τ as a series with rational terms. <|MaskedSetence|> <|MaskedSetence|> Application to specific values, including Euler’s constant γ𝛾\gammaitalic_γ and π/4𝜋4\pi/4italic_π / 4, is discussed in ... | **A**: The complexity of the algorithm is analysed in §3.
**B**: Conclusions and future work are presented in §5.
**C**: The algorithm is described in §2, and its basic properties are addressed.
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<|MaskedSetence|> For example, the local principal curves (Einbeck et al., 2005, 2008) are formed by tracking the localized version of the first principal component directions, but the method requires selection of good starting points lying on or near the filaments already. <|MaskedSetence|> The medial axis of the da... | **A**:
The literature on the estimation of low-dimensional structures (or filaments) is rich, and different approaches use different geometric ideas.
**B**: The candy model (Stoica et al., 2007) uses possibly connected cylinders (in 3D) of a fixed radius and
height to represent the filaments.
**C**: (2009) proposed ... | ABC | CBA | ABC | ABC | Selection 4 |
In the two-stage scheme, the process of building the surrogate and performing the sampling is separated. <|MaskedSetence|> In the subsequent stage, our focus shifts to reducing the variance of the Monte Carlo approximation of the surrogate. Due to the inexpensive nature of evaluating the surrogate, it becomes possible... | **A**: During the initial stage, the primary objective is to minimize the bias of the surrogate.
**B**: In the exact scheme, the surrogate serves as a proposal, eliminating any bias, and allowing the algorithms to directly target the distribution of interest.
**C**: However, employing surrogates introduces a bias int... | ACB | ACB | ABC | ACB | Selection 4 |
<|MaskedSetence|> Any bounded kernel satisfies (3) [Fischer and Steinwart, 2020, Lemma 10]. A higher value of b𝑏bitalic_b corresponds to a lower effective dimension, better control of the variance of our estimator, and hence a faster rate. The limit b→∞→𝑏b\rightarrow\inftyitalic_b → ∞ gives an RKHS with finite dimen... | **A**: Figure 2 verifies polynomial decay of the empirical eigenvalues in the real world application of Section 6; the Project STAR data have a low effective dimension as required by Assumptions 5.2 and 5.3.222Specifically, we divide each empirical eigenvalue by the trace of the corresponding matrix, to convey the frac... | BAC | BCA | BCA | BCA | Selection 3 |
They consider either oblivious adversaries who fix a single corrupted distribution from which samples are generated or adaptive ones who observe samples before corrupting them. (Blanc et al., 2021) establishes that adaptive adversaries yield equivalent performance to oblivious ones in many settings.
We note that our fr... | **A**: (2020); Guo et al.
**B**: The framework we develop is anchored around a setting that allows for heterogeneous “nearby” distributions for each past observation, and is general in that it allows us to unify a variety of problems/metrics and highlight how these affect the levels of achievable performance..
**C**:... | CAB | CAB | CAB | ACB | Selection 3 |
One example of unrepresentative samples is when the distributions of some covariates (e.g. age and BMI) in the target population differ from those in the source population. <|MaskedSetence|> age and BMI may modify the effects of some medicine), the ATE in the target population can be quite different from that in the... | **A**: Chattopadhyay et al., (2022) developed a one-step weighting estimator where the weights are learned from a convex optimization problem to simultaneously model the inverse propensity score and outcome regression functions.
**B**: For instance, Dahabreh et al., (2019) and Dahabreh et al., (2020) proposed three ty... | CBA | CBA | CBA | CBA | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> On the right - many bins, but approximation gets even “worse” due to a sparsity issue. Refer to Figure 4 for additional synthetic evaluation results with loss measurements.
. | **A**:
Figure 1: For a given segment, learned segmentized step function approximations (orange) of a true function (blue) which was used to generate a synthetic data-set.
**B**: On the left - too few bins, “bad” approximation.
**C**: In the middle - a balanced number of bins, “moderate” approximation.
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<|MaskedSetence|> Additionally, the general message update results allow for a parametrised goal prior, which may me modelled by a secondary dynamical model (Sennesh et al., 2022).
Crucially, the local updates include novel backward messages that have not been expressed in traditional formulations of AIF. <|MaskedS... | **A**: These backward messages ensure the unified optimisation of the full GFE objective, without resorting to distinct schedules for state estimation and free energy evaluation.
**B**: Also, we resorted to importance sampling to compute difficult expectations..
**C**: The general update rules allow for deriving GFE-... | CAB | CAB | CAB | ABC | Selection 3 |
We use R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT score, Mean Squared Error (MSE), Mean Absolute Error (MAE), and Maximum Across All Entries (max error) to assess performance of estimated outcome matrices. We directly compare the distribution of estimated entries to the distribution of tr... | **A**: We split the data into 90/10901090/1090 / 10 train/test sets at random and repeat the experiment 10 times.
**B**: We determined the best estimate of the rank of the true outcome matrix and the rank of the observation pattern using 9-fold cross-validation with MNN.
**C**: We used 16-fold cross-validation to sep... | ABC | ABC | CBA | ABC | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> This approach was first implemented in the Mora (Bartocci et al., 2020) tool and later further improved in the Polar tool (Moosbrugger et al., 2022) to also support multi-path probabilistic loops with if-statements, symbolic constants, circular linear dependency among program state... | **A**: Automating statistical inference for these stochastic systems requires knowledge of their distribution; that is, the distribution(s) of the random variable(s) generated by executing the probabilistic program that encodes them.
Statistical moments are essential quantitative measures that characterize many proba... | ABC | ABC | ABC | CAB | Selection 1 |
<|MaskedSetence|> GAT [22] uses an attention mechanism to learn node embeddings. <|MaskedSetence|> <|MaskedSetence|> In our method, the total training and validation data used in [22]—640 for Cora, 620 for Citeseer, and 560 for Pubmed—are treated as the overall prior information. In contrast to [22], which evaluated... | **A**: These features are used to learn embedding vectors using a multi-head attention structure, and a linear map is employed to generate outputs corresponding to the number of clusters.
**B**: The node features are created using the bag-of-words representation of documents, with the dimensions of the node features f... | CBA | CBA | CBA | CAB | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> Such strategies could involve the use of ensemble learning such as the stacking of Breiman (1996), the super-learning (a weighted average the best predictions over different choices of ML algorithm) of van der
Laan et al. (2007), or selecting the best-performing learner on an appli... | **A**: This is in line with Chang (2020) to encourage researchers to adopt estimation strategies which involve the use of different ML algorithms.
**B**: While we do not rule out using LASSO (and indeed do so in both our simulation study and empirical application), our approach requires only minimal assumptions (like ... | BAC | BAC | BAC | BCA | Selection 3 |
<|MaskedSetence|> While space-filling designs based on Latin Hypercube Sampling (LHS) (Stein,, 1987) or minimax distance designs (Johnson et al.,, 1990) have been widely investigated, they are not suited for the specific problem at stake where the region of interest only covers a small fraction of the input space. For... | **A**:
This is the premise of sequential designs for computer experiments (Santner et al.,, 2003; Gramacy and Lee,, 2009; Sacks et al.,, 1989).
**B**: In Bayesian inverse problems, sequential design strategies have been investigated to produce estimators for the inverse problem likelihood (Sinsbeck et al.,, 2021) or... | ACB | ACB | ACB | CBA | Selection 3 |
<|MaskedSetence|> However, there is still a separation between ancestors and non-ancestors in terms of the effect size. For long time series, there is a sweet spot with high power at a fairly low error rate. <|MaskedSetence|> Some of the curves do not start at 00 power and error rate as there are p-values that are nu... | **A**: Hence, the ordering of the p-values still gives some indication of what could be the true ancestors.
**B**: Similarly, the power of the LiNGAM algorithm remains high while the error rate is increased..
**C**:
Control of the familywise error rate at a fixed level no longer works for ancestor regression.
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Recent work by (Goel et al. 2024) benchmarks several state-of-the-art (SoTA) unlearning algorithms, such as SSD (Foster, Schoepf, and Brintrup 2024), CF-k (Goel et al. 2022) and SCRUB (Kurmanji, Triantafillou, and Triantafillou 2023), within the corrective unlearning framework.
Notably, ASSD (Schoepf, Foster, and Brint... | **A**: 2018; Zhang and Sabuncu 2018), data augmentation (Zhang et al.
**B**: 2021, 2023), robust loss functions (Wang et al.
**C**: 2020), and noise transition matrix estimation (Zhu, Wang, and Liu 2022; Cheng et al.
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which has been widely adopted in theoretical analysis of diffusion model (see e.g., Li et al., (2024); Li and Yan, (2024)). We consider the degenerated Gaussian distribution p𝖽𝖺𝗍𝖺=𝒩(0,Ik)subscript𝑝𝖽𝖺𝗍𝖺𝒩0subscript𝐼𝑘p_{\mathsf{data}}=\mathcal{N}(0,I_{k})italic_p start_POSTSUBSCRIPT sansserif_data end_POST... | **A**: We implement the experiment for four different number of steps T∈{100,200,500,1000}𝑇1002005001000T\in\{100,200,500,1000\}italic_T ∈ { 100 , 200 , 500 , 1000 }.
**B**: Instead of using the learning rate schedule (2.5), which is chosen mainly to facilitate analysis, we use the schedule in Ho et al., (2020) that ... | ABC | ABC | ABC | BCA | Selection 2 |
1.4.2 Bayesian inference
A recent body of research has melded variational inference (VI) and sequential search. These connections are realized through the development of a variational family for hidden Markov models, employing Sequential Monte Carlo (Smc) as the marginal likelihood estimator (Maddison et al., 2017; Na... | **A**: (2017) proposes ppHmc which extends Hamiltonian Monte Carlo to phylogenies.
**B**: Mcmc methods also handle model learning.
**C**: Common approaches include local search algorithms like random-walk Mcmc (Ronquist et al., 2012) and sequential search algorithms like Combinatorial Sequential Monte Carlo (Csmc) (B... | CBA | BCA | CBA | CBA | Selection 1 |
1.3 Organisation
This paper is organised as follows. In Section 2, we estimate the second-order of the large-deviation probabilities of the rare event that a sparse Erdős–Rényi random graph has a linear number of vertices in triangles, study the structure of the graph conditionally on this rare event, and provide proo... | **A**: We close in Section 5 with a discussion and a list of open problems.
.
**B**: We show that, for appropriate parameter choices, such models are sparse, i.e., lead to sparse exponential random graphs.
**C**: In Section 3, we use these results, as well as the key insights developed in their proofs, to study expo... | CAB | CBA | CBA | CBA | Selection 4 |
<|MaskedSetence|> While NFs have been successfully used for posterior approximation [16, 17, 18, 19, 20] and produce higher-quality samples, the requirement that the Jacobian of each transformation be simple to compute often requires a high number of transformations and, traditionally, these transformations do not alt... | **A**: By contrast, normalizing flow (NF) models [14, 15] work by applying a series of bijective transformations to a simple base distribution (usually uniform or Gaussian) to deterministically convert samples to a desired target distribution.
**B**: These models work by stipulating a fixed forward noising process (e.... | ABC | ABC | BCA | ABC | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> This split has been validated in (Sesia and Candès 2020). Wwe repeat all experiments 10 times, starting from the initial data splitting and the training procedure of quantile regression using both random forest (RF) and neural network (NN) models.
Both the CTI and CHR incorporate... | **A**: We assess the performance of the generated prediction intervals in terms of coverage and efficiency.
**B**:
Following the methodology outlined in (Sesia and Candès 2020), we rescale the response Y𝑌Yitalic_Y by the mean absolute value.
**C**: We randomly allocate 20%percent2020\%20 % of the samples for testin... | CAB | BCA | BCA | BCA | Selection 2 |
Our main proposed method can be described as follows. The core idea is to establish a confidence interval using the exchangeability of the groups of indices. This method involves finding the absolute value of the difference between the sum of labels in a group and its prediction, or absolute residual, and using this as... | **A**: At the group level, each index within the same group has equal chance of being assigned to either a calibration sample or a test sample.
**B**: This ensures that the residual from the sums of calibration samples and the sums of test samples have identical distributions.
**C**: Second, given prior knowledge of ... | CAB | ABC | ABC | ABC | Selection 2 |
This work aims at bridging the gap between parameter- and function-space priors in BNNs. Indeed, while a priori information is typically available in the function space, proper application of Bayes theorem – which should automatically and appropriately weight data vs. <|MaskedSetence|> In section 2 we perform a stud... | **A**: prior information – does require formulation of a parameter-space prior density.
**B**: We show that predictions appropriately fit the data while being guided by a priori functional and uncertainty information in extrapolatory conditions.
**C**: The code is available at https://github.com/AudOlivier/BNN_anchor... | ABC | ACB | ABC | ABC | Selection 3 |
Our linear-regression-based estimator integrates seamlessly into algorithms for preference-based bandits with linear human utility functions [3, 31], enabling interactive learning systems to leverage response times for faster learning. We specifically integrated our estimator into the Generalized Successive Eliminatio... | **A**: Section 3 presents our utility estimator, incorporating both choices and response times, and offers a theoretical comparison to the choice-only estimator.
**B**: Simulations using three real-world datasets [57, 16, 39] consistently show that incorporating response times significantly reduces identification erro... | BCA | BAC | BAC | BAC | Selection 3 |
<|MaskedSetence|> This paper was prepared for informative purposes and is not a product of HSBC Bank Plc. <|MaskedSetence|> Neither HSBC Bank Plc. nor any of its affiliates make any explicit or implied representation or warranty, and none of them accept any liability in connection with this paper, including, but limi... | **A**: HSBC: The authors declare no conflict of interest.
**B**: This document is not intended as investment research or investment advice; or a recommendation, offer, or solicitation for the purchase or sale of any security, financial instrument, financial product, or service; or to be used in any way for evaluating ... | CAB | ACB | ACB | ACB | Selection 2 |
This paper concentrates on the second step of the RLHF pipeline, focusing on learning a high-quality reward function, and induces the optimal policy as a by-product. This raises at least three challenges. <|MaskedSetence|> <|MaskedSetence|> Consequently, their feedback varies significantly due to their differences... | **A**: However, acquiring adequate training data often requires to hire multiple teachers, each possessing different levels of expertise and rationality (Park et al., 2024; Zeng et al., 2024).
**B**: Ignoring such heterogeneity can produce suboptimal policies for alignment (Zhong et al., 2024; Chakraborty et al., 2024... | CAB | CAB | ABC | CAB | Selection 2 |
We advance the variational autoencoder paradigm for time-dependent, non-stochastic data dynamics by introducing latent dynamics with a geometric flow. Our methods are computationally efficient in the offline stage by choice of a simple geometric flow. <|MaskedSetence|> Our method advances strategies towards robustnes... | **A**: We find our methods rarely underperform a baseline.
While our method can accommodate considerable diversity in initial conditions, alternative methods including Transformer architectures [48], state-space models [19], and neural operators tend to generalize more effectively for input data.
**B**: We find our ... | BCA | CBA | CBA | CBA | Selection 4 |
We are interested in multi-agent BO, where multiple agents can sample the objective function at a single timestep. Much of existing multi-agent BO literature studies batch BO, in which a central coordinator has access to each agent’s acquired information [21], [22]. It then computes the sampling decisions for all agen... | **A**: Distributed networks are prevalent in real-world applications, such as in multi-robot source seeking and sensor networks [21], [26].
**B**: Prior literature providing theoretical guarantees for distributed Bayesian optimization require fully connected communication graphs, even in asynchronous cases [22], [28],... | CAB | CAB | CAB | CAB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> However, model misspecification or shifts in the utility function during deployment could impact the performance of the amortized model (Rainforth et al.,, 2024). Future work could address the challenge of robust experimental design under model misspecification (Huang et al., 2023a... | **A**: If modeling correlations between points is crucial for the downstream task, we can replace the output with a joint multivariate normal distribution (Markou et al.,, 2022) or predict the output autoregressively (Bruinsma et al.,, 2023).
Following most BED approaches, our work assumes that the model is well-specif... | CAB | CAB | CAB | ABC | Selection 2 |
Baselines
We use three types of baseline: GNNs (GCN (Kipf and Welling 2017), GAT (Velickovic et al. 2018), APPNP (Klicpera, Bojchevski, and Gunnemann 2019)), fairness-aware GNNs (FairGNN (Dai and Wang 2023), FairSIN (Yang et al. 2024), FMP (Jiang et al. <|MaskedSetence|> 2024b)), and GTs (DIFFormer (Wu et al. 2023a)... | **A**: 2024), FUGNN (Luo et al.
**B**: 2024c)).
.
**C**: 2023b), Polynormer (Deng, Yue, and Zhang 2024), CoBFormer (Xing et al.
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One of our initial assumptions was that the data had been observed at a dense grid. In the case where the data is only available at a sparse grid, further extensions would require smoothing by an appropriate basis, e.g., CB-splines (Machalová et al., 2021) specifically developed for Bayes spaces. Naturally, the next s... | **A**: During multivariate functional data analysis, each observation contains the recording of several “functional" variables.
**B**: Another class of meaningful operators that utilize the functional nature of the data are differential operators often used in Tikhonov regularization.
**C**: (2018); Dai and Genton (2... | ACB | ACB | ACB | ACB | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> This unique property of homomorphic encryption makes it highly valuable in the fields of data privacy and federated analytics, where sensitive data are processed.
The first practical Fully Homomorphic Encryption (FHE) scheme was proposed by Craig Gentry in 2009... | **A**:
Homomorphic encryption, as introduced by Rivest et al.
**B**: (1978) [17], is a form of encryption that enables computations to be performed directly on ciphertexts.
**C**: The resulting encrypted output, when decrypted, corresponds to the outcome of operations applied to the plaintext.
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<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> [2021]). The population considered was extended from married women to all women, using a local implementation of the global model for estimation among unmarried women (Kantorová et al. [2020], Guranich et al. [2021]). In 2024, several updates were introduced to f... | **A**: [2018]), and to improve the use of service statistics data (Cahill et al.
**B**:
Subsequently, FPET evolved to better capture local contexts.
**C**: Model updates were introduced to improve predictive performance and to better account for survey data quality issues (Cahill et al.
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Hence, the research community focused on the development of efficient random number generators (L’Ecuyer, 1994) and their infrastructure (Tan et al., 2021; Nagasaka et al., 2018) shares similarities to this work. Physical (true) random number generators (TRNG) using physical devices is an active research field since t... | **A**: Furthermore, they address integer generation only, making their work unsuitable for machine learning applications..
**B**: (2024) propose using a conditional probability table for this purpose.
**C**: Zhang et al.
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<|MaskedSetence|> By transforming the SIR model using dynamical survival analysis within the edge-based configuration network framework, the resulting system of equations captures the intricate dynamics of network-based interactions. Despite the complexity of these interactions, the equations remain mathematically tra... | **A**: This stochastic SIR framework thus provides a versatile tool for modeling infectious diseases and other dynamic processes beyond the scope of traditional SIR models..
**B**:
The proposed model is broadly applicable to various domains, including social interactions, biological systems (e.g., neural or protein i... | BCA | ACB | BCA | BCA | Selection 1 |
It then combines this prior with demonstration data from a human expert acting approximately optimally with respect to the unknown reward, to produce a posterior distribution over rewards. In apprenticeship learning, this posterior over rewards is then used to produce a policy that should perform well with respect to t... | **A**: We instead suggest using the principled tools of Bayesian active learning for the task.
.
**B**: There is one previous paper on active IRL with full trajectories [5] suggesting a heuristic acquisition function whose shortcomings can, however, completely prevent learning.
**C**: Bayesian active learning can hel... | CBA | CBA | CBA | ABC | Selection 3 |
<|MaskedSetence|> This can oversimplify complex datasets where documents also have temporal or spatial dimensions, or demographic characteristics leading to latent clusters. In other words, simply flattening all dimensions and neglecting the correlations between documents fails to accommodate their unique properties a... | **A**:
A major drawback of both types of approaches is that they are inherently designed to analyze data based on two-dimensional interactions between documents and topics.
**B**: In microbiome studies, temporal and demographic characteristics of samples may impact microbioa abundances.
**C**: This approach can resu... | ACB | ACB | ACB | CBA | Selection 3 |
<|MaskedSetence|> Tibshirani (1996) made the first such connection for
lasso regression, the Bayesian side of which was more fully developed by Park and Casella (2008) and
Hans (2009, 2010). <|MaskedSetence|> (2012), Leng et al. (2014), Alhamzawi and Ali (2018), Kang et al. <|MaskedSetence|> (2019),. | **A**: (2019), and Wang et al.
**B**: Bayesian connections to the adaptive lasso (Zou, 2006) have been considered
by Griffin and Brown (2007, 2011), Alhamzawi et al.
**C**: The literature on the connection between Bayesian posterior modes and estimators described as solutions
to penalized optimization problems is qui... | CBA | CBA | CBA | BAC | Selection 3 |
2.
The embeddings from GLoVe and BERT were trained with much larger sized corpora than our SA-Tweedie model. The corpus size of our SA-Tweedie is 4 Billon tokens from Wikipedia. <|MaskedSetence|> The BERT embeddings were from pretraining on English Wikepedia plus additional BooksCorpus (800M words) data. <|MaskedSet... | **A**: We do not have access to BooksCorpus data.
**B**: Therefore SA-Tweedie’s embedding has seen less training data.
.
**C**: The pretrained GLoVe embeddings were based on training corpus size of 42 billion tokens.
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In all the aforementioned examples, there are explicitly observed covariates or factors. Furthermore, the two parts of the model parameters are
pendicular to each other, allowing model estimation by fitting two separate regressions: binomial regression and Gamma regression. Unfortunately, such models cannot be appli... | **A**: Therefore, in this paper, we consider shared parameter modeling of zero-inflated Gamma data using alternating regression.
**B**: Examples include user-item or item-item co-occurrence data from online shopping platforms and co-occurring word-word pairs in sequences of texts.
One reason is the absence of observe... | BCA | BCA | BCA | CAB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Illustration of this potential problem using Leukemia2 dataset is presented in Table 1. Moreover PAM selects too many features which makes it difficult to perform follow up experiments in cancer studies. We believe one of the reasons for this drawback is the soft... | **A**: Then, x∗superscript𝑥x^{*}italic_x start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT will be classified to the class having the smallest discriminant score.
When examining the details of how PAM chose the thresholding parameter for Leukemia2 dataset (Armstrong et al., 2002), we observed that the number of genes surv... | ABC | ABC | ABC | ACB | Selection 3 |
The study of behavioral responses to tax changes has long been a central area of economic research. Historically, much of the focus was on labor supply, with the primary question being how labor supply responds to tax reforms. In a series of influential papers, Feldstein (1995, 1999) argued that individuals respond t... | **A**: By estimating how taxable income responds to changes in the marginal net-of-tax rate, one can capture a broader set of these relevant margins.
**B**: Following Feldstein’s work, a large body of literature emerged, producing a wide range of elasticity estimates, from -1.3 (Goolsbee, 1999) to 3 (Feldstein, 1995).... | CBA | ABC | ABC | ABC | Selection 4 |
<|MaskedSetence|> We present the speed advantage of LRMC at the inference stage, provided appropriate training.
Fig. 3 compares the convergence behavior of LRMC and the baseline ScaledGD. Both algorithms achieve linear convergence which matches Theorem 5. LRMC consistently demonstrates faster convergence than ScaledGD... | **A**: In contrast, the per-iteration runtime of LRPCA is insensitive to α𝛼\alphaitalic_α and is significantly faster than ScaledGD.
**B**:
Computational efficiency.
**C**: On the right, we find title runtime of LRMC is substantially faster than SclaedGD.
Note that when the observation rate p𝑝pitalic_p is smaller,... | BAC | BAC | BAC | BCA | Selection 2 |
The idea to use kernel smoothing for sequence to sequence was called “attention”, or cross-attention, by Bahdanau et al. <|MaskedSetence|> When used for self-supervised learning, it is called self-attention. <|MaskedSetence|> <|MaskedSetence|> [2023] who developed a smoothing method that they called the transforme... | **A**: [2014].
**B**: When a sequence is mapped to a matrix M𝑀Mitalic_M, it is called multi-head attention.
**C**: The concept of self-attention and attention for natural language processing was further developed by Vaswani et al.
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<|MaskedSetence|> Unlike previous studies, we identified the precise conditions under which only an authorized learner can achieve superior learning results. <|MaskedSetence|> <|MaskedSetence|> However, these conditions do not entirely prevent an eavesdropping learner from obtaining some level of learning quality, w... | **A**: 4 Conclusion
In this study, we have explored the conditions to ensure a specific quality of learning outcomes for an authorized learner, building on quantum label encoding and secure data transformation.
**B**: Our findings demonstrated that under certain conditions, an authorized learner can attain a guarante... | ACB | ACB | ACB | CAB | Selection 3 |
The remainder of the article is organized as follows. In Section 2, we briefly review instrumental variable models with a binary treatment, instrument, and outcome. <|MaskedSetence|> In Section 4, we establish a novel Bernstein-von Mises theorem for our framework. Simulation studies are presented in Section 5. <|Mask... | **A**: Section 6 describes a real data application on evaluating the effect of consuming Vitamin A supplementation on reducing mortality rates.
Section 7 and Section 8 discuss a variety of causal estimands and assumptions under our framework.
The article concludes with a discussion of future work in Section 9.
**B**: ... | BAC | ABC | BAC | BAC | Selection 4 |
<|MaskedSetence|> It is so-called because Okrent’s first group of managers often met at “La Rotisserie Francaise” in New York City. <|MaskedSetence|> During the fantasy season, which is generally the majority of a professional season, these teams accrue scores across categories based on how their players perform. At ... | **A**: The format is still popular today and played for other sports in addition to baseball, including basketball (Barutha, 2024).
Like other kinds of fantasy leagues, Rotisserie leagues begin with an auction or draft through which managers select players for their teams.
**B**: The team which earns the most total ... | CAB | CAB | BCA | CAB | Selection 4 |
<|MaskedSetence|> We selected data point increments in sizes of 1, 5, 10, 20, 40, 80, 160, 320, 640 and 1280 to incrementally challenge the algorithm, assessing its scalability and performance as more data were introduced. <|MaskedSetence|> Smaller increments (e.g., 1, 5, 10, 20, 40) simulate environments with freque... | **A**: These values were chosen to represent a range of typical scenarios in real-world applications, where data streams in at different rates.
**B**: Larger increments (e.g., 640, 1280) simulate batch processing scenarios, where data is collected over time and processed periodically, such as in big data analytics and... | CAB | BAC | CAB | CAB | Selection 1 |
<|MaskedSetence|> Figure 15 highlights a key limitation of the Bonferroni correction: the individual interval widths from WLS necessarily increase with the number of comparisons. This issue does not arise with our method, as individual comparisons are derived from projections of d𝑑ditalic_d-dimensional confidence reg... | **A**:
From Figure 14, we observe that the widths of simultaneous confidence intervals from HCCT are roughly comparable to those from WLS, though the former exhibit higher variability.
**B**: In this sense, WLS intervals with the largest Bonferroni corrections provide a more equitable comparison to the corresponding ... | ABC | ABC | ABC | ABC | Selection 1 |
This paper extends prior research by evaluating the α𝛼\alphaitalic_α-transformation within a non-functional CoDA framework. <|MaskedSetence|> The analysis focuses on male and female populations across 31 European countries/regions from year 1983 to 2018 using the data retrieved from the Human Mortality Database (HMD)... | **A**: Lastly, Section 4 concludes the paper by summarizing key findings and suggesting possible extensions for future research.
.
**B**: Subsequently, Section 3 presents the results, along with a comprehensive discussion revolving around the forecast accuracy of each transformation.
**C**: Using CLR transformation a... | BAC | CBA | CBA | CBA | Selection 2 |
<|MaskedSetence|> Both issues are related to the problem of the exhaustive exploration of the state space. <|MaskedSetence|> <|MaskedSetence|> This issue makes also difficult the use of gradient approaches since many solutions can be outside the allowed support domain.
. | **A**:
However, the Monte Carlo techniques find several difficulties that jeopardize their performance in many scenarios, for instance, when working in high-dimensional spaces, and with narrow, tight posteriors.
**B**: For these reasons, many Monte Carlo algorithms try to work in sub-dimensional spaces (step by step... | ABC | ABC | CAB | ABC | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> The covariance structures considered account for spatio-temporal correlations among measurements within the same block and repetition. The expansion in cubic B-splines accommodates intra-block spatial and temporal correlations. The block structure of the model is designed to captur... | **A**: In Section 3, we develop Bayesian inference for the proposed model.
**B**: Each observation is modeled by fixed and random spatio-temporal effects, which are approximated by linear combinations of tensor product of B-spline bases evaluated in time and space 9.
**C**: This work aims to develop a spatio-temporal... | ACB | CBA | CBA | CBA | Selection 4 |
Specifically, \textciteli2024robust introduced a robust hypothesis testing approach using a truncated goodness-of-fit test, which remains effective even when the text has been edited by humans. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> On the other hand, our study examines the differences in the latent ... | **A**: \textciteli2024statistical proposed a statistical framework for designing rigorous watermark detection rules by precisely evaluating Type I and Type II errors.
**B**: All these methods focus on determining whether a given text was generated by an LLM when only the text itself is provided.
**C**: \textcitexie20... | ACB | CBA | ACB | ACB | Selection 1 |
In terms of the methodology and applications, an immediate future direction is working to effectively estimate and deploy deeper DDEs with D≥3𝐷3D\geq 3italic_D ≥ 3 latent layers. <|MaskedSetence|> <|MaskedSetence|> For example, the MNIST dataset comes with the actual digit labels as well as the spatial structure o... | **A**: The current theory and computational pipeline conceptually readily generalizes to deeper architectures than considered in this initial paper.
**B**: For example, one may consider a dataset consisting of images uploaded in social media alongside text data such as tags.
**C**: It remains to test and refine these... | ACB | ACB | ACB | ACB | Selection 1 |
<|MaskedSetence|> Since we use a CNN, we can take each network layer as the feature space. Specifically, we consider the four convolutional layers and input space as candidate choices for the encoder. Once choosing a layer, we take all layers before it (including itself) as the encoder. In this ablation study, we use ... | **A**: 6(a) shows that deeper layers are not always better, showing a clear increase-then-decrease accuracy curve.
**B**: 5.4 Ablation Studies
Choice of Encoder (ℰℰ\mathcal{E}caligraphic_E)
Here, we study how the choice of the encoder (i.e., feature space) affects the performance of GOAT.
**C**: Hence, we keep usin... | BAC | BAC | BAC | CAB | Selection 3 |
<|MaskedSetence|> Reliably estimating the frequency of extreme storm tides is challenging, particularly in regions with insufficient observations, such as Bangladesh. <|MaskedSetence|> Khan et al. [20] applied the same downscaling-hydrodynamic method to assess storm tide hazards in coastal Bangladesh but confined the... | **A**:
3.1 Comparison With Previous Studies
Several noteworthy findings from our results deserve further discussion.
**B**: Even studies evaluating Bangladesh’s storm tide hazard under current climate conditions are limited, let alone those addressing future scenarios.
**C**: For example, Jakobsen et al. [32] esti... | ABC | BCA | ABC | ABC | Selection 1 |
The positivity assumption guarantees that each unit has a non-zero probability to be exposed to each treatment level for all possible values of pre-treatment variables, at least in large samples. While in principle this assumption is empirically verifiable, there is not a well-established approach to doing so for mul... | **A**: Though not the focus of our work here, in Appendix D.4 we outline two distinct approaches to assess the plausibility of the multivariate positivity assumption and to examine how robust our results are to this critical assumption.
**B**: Unconfoundedness requires that the treatment 𝑾𝑾\bm{W}bold_italic_W is ind... | CBA | ACB | ACB | ACB | Selection 3 |
<|MaskedSetence|> This approach fits naturally with the iterative nature of neural network training, where parameters are updated using mini-batches of data. <|MaskedSetence|> This balanced representation helps prevent the model from overfitting spurious patterns created during the augmentation process, thereby impro... | **A**: To address these limitations, we propose an online data augmentation framework that generates synthetic samples during training.
**B**: By creating synthetic samples for each batch alongside their original counterparts, we maintain a balanced representation between real and synthetic data throughout the trainin... | ABC | ABC | ABC | ABC | Selection 1 |
In our re-analysis, we focus on the impact of first-grade classroom assignment on first-grade Stanford Achievement Test (SAT) scores. <|MaskedSetence|> Specifically, we compare small classes to regular classes without an aide. For simplicity, we excluded students with missing data on test scores, classroom type, or sc... | **A**: Among these, 71 schools included all three treatment types, while 4 schools had only small and regular classes without an aide.
To create a BIBD, we (i) retained the 4 schools with only two treatments (small and regular classes without an aide), (ii) randomly assigned a pair of treatments to each of the 71 rem... | ACB | BAC | BAC | BAC | Selection 2 |
To the best of our knowledge, matching was rarely utilized for policy learning except matched learning (Wu
et al., 2020, M-learning), where a general matched pair-based objective function is formulated and shown to be consistent of the value function for some special case and the optimal policy is learned by weighted s... | **A**: Second, we acknowledge and tackle the conditional bias due to matching, correlation due to sampling with replacement, and we fix the number of matches in the establishment of the asymptotic property and the non-asymptotic regret bound for MB-learning.
**B**: In contrast, MB-learning is more intuitive because it... | CAB | BAC | BAC | BAC | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> Sometimes we reject the unit root hypothesis, sometimes we fail to reject it. <|MaskedSetence|> One question of interest is again: Is b=1𝑏1b=1italic_b = 1 or b<1𝑏1b<1italic_b < 1? Is there unit root or mean reversion? The answer here, again, is more ambiguous; see the Table 2. B... | **A**: However, the unit root testing is more ambiguous.
**B**: Here we also see that dividing residuals by VIX significantly decreases skewness and excess kurtosis from (6).
**C**: Now we consider the linear regression after normalization.
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Our model permits flexible marginal interventions. This modeling choice is suited to online marketplaces, because the operators in charge of them can finely target policies that function as taxes and subsidies, including commission rates, discount coupons, free advertising, etc.—and regularly experiment with such pertu... | **A**: As a result, the policies our interventions recommend—which project all variation onto these eigenvectors—will often be close to a policy that depends mostly on category—e.g., a subsidy on smartphones along with a tax on certain types of accessories.
**B**: This is related to, but distinct from, the problem we ... | ACB | CAB | CAB | CAB | Selection 4 |
<|MaskedSetence|> (2017) laid the theoretical groundwork for integrating multiple views in the PAC-Bayes framework, introducing the first PAC-Bayes bounds for multi-view learning by combining weight vectors from different views. This approach leveraged complementary information across views for consistent predictions.... | **A**: (2017) made significant strides by introducing PAC-Bayes bounds for multi-view learning, their approach is constrained to two views, limiting its applicability in scenarios where data comes from numerous sources.
**B**: Sun et al.
**C**: They later incorporated stability (Bousquet & Elisseeff, 2002) into their... | BCA | BAC | BCA | BCA | Selection 3 |
3 Proof of Archimedean axiom
Our goal is to show for Archimedean copulas that the Archimedean axiom also holds for non-continuous F𝐹Fitalic_F. <|MaskedSetence|> <|MaskedSetence|> First, we present lemmas that will help us establish the proof. <|MaskedSetence|> From which we derive how the limiting distribution of ... | **A**: As F𝐹Fitalic_F is non-continuous, there may be regions in which C𝐶Citalic_C and VCsubscript𝑉𝐶V_{C}italic_V start_POSTSUBSCRIPT italic_C end_POSTSUBSCRIPT is also non-continuous.
**B**: Hence, we develop a topological proof using VCsubscript𝑉𝐶V_{C}italic_V start_POSTSUBSCRIPT italic_C end_POSTSUBSCRIPT tha... | ACB | ABC | ABC | ABC | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> the spatial design (how to locate the observation points), the dimension of the Euclidean space where the spatial domain is embedded, the covariance kernel attached to a Gaussian spatial random field (or, equivalently, its spectral density) and the mean-square di... | **A**: Such a problem has been of interest to geostatisticians for decades (Chilès and Delfiner, 2012) because it translates into the optimality property of reducing considerably the computational burden associated with the kriging predictor when handling large data sets.
Quantifying screening effects under a specified... | BCA | BCA | ACB | BCA | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> In summary, instead of finding the exact maximum likelihood estimates (MLEs), VB optimizes the Kullback-Leibler (KL) divergence between the proposed family of approximation distributions and the posterior distribution. By using simple approximation distributions and making certain ... | **A**: However, VB is not unbiased and lacks accuracy.
**B**: VB is an natural extension of the EM algorithm with a wide range of applications, for instance, in reinforcement learning, and is well-studied in the literature; for example, see [11], [34] and [32].
**C**:
3.3 Comparison with variational Bayes – simulat... | CBA | CBA | CBA | CBA | Selection 2 |
In online convex optimization exponential concavity usually leads to better regret bounds, see [18].
The article is structured as follows. <|MaskedSetence|> In Section 3, we state the theorem on mixability (exp-concavity) of integral loss functions and prove it. In Section 4, we apply our result to prove mixability ... | **A**: The results are summarised in Table 1 of Subsection 4.1.
**B**: In B, we review the strategy of AA and recall derivation of algorithm’s constant regret bound.
.
**C**: In Section 2, we recall the definitions of mixability and exponential concavity of loss functions.
| CAB | BCA | CAB | CAB | Selection 1 |
The limited historical data cannot be used to reliably assess the threat of tanking. However, they provide a solid basis to simulate the outcomes of the games. Thus, an arbitrary number of fictional but reasonable tournaments can be generated as usual in the tournament design literature (Lasek and Gagolewski,, 2018; L... | **A**: Poisson models, first suggested by Maher, (1982), are perhaps the most popular to generate football match results.
**B**: In particular, team i𝑖iitalic_i scores k𝑘kitalic_k goals against team j𝑗jitalic_j with a probability.
**C**: According to the underlying assumption, the number of goals scored by both te... | BAC | ACB | ACB | ACB | Selection 4 |
In the context of self-supervised learning with data augmentation, von Kügelgen et al. (2021) considered the identifiability of shared part, which stays invariant between views. <|MaskedSetence|> <|MaskedSetence|> (2020) extend the identifiability result of iVAE (Khemakhem et al., 2020a) to a general exponential fa... | **A**: However, this line of work assumes the availability of paired instances in two domains.
**B**: In the context of out-of-distribution generalization, Lu et al.
**C**: Most importantly, this study resorts to finding a conditionally invariant sub-part of 𝐳𝐳{\mathbf{z}}bold_z, even though there may be parts of �... | ABC | ABC | ABC | ABC | Selection 4 |
We now turn to the evaluation and comparison of TestCat with other clusterability evaluation methods, employing the validation strategy described above. Our investigation reveals that, using TestCat for evaluation, most of these UCI data sets are identified as being clusterable and all their CRDSs are identified as bei... | **A**: The resulting median p𝑝pitalic_p-value from 101 runs is used for determining whether each target data set is clusterable.
**B**: Following this transformation, we utilized PCA or SPCA to further condense this numerical data.
**C**: More details are as follows.
Figure 4: Count of correctly identified data se... | CAB | CAB | ACB | CAB | Selection 2 |
Early works by Gart and Zweifel (1967) and Wells and Donner (1987) focus on analysing the bias and mean-square error of several estimators of the odds under binomial (i.e. fixed-size) sampling. Siegmund (1982) studies the asymptotic properties of estimators of the odds and the odds ratio. <|MaskedSetence|> (2021) pro... | **A**: Sungboonchoo et al.
**B**: (2021, 2023) consider correlation between observations of the two populations, assuming sample sets of fixed size; and propose estimators of the probability ratio or its logarithm, for which they derive asymptotic confidence intervals.
**C**: Ngamkham et al.
| ACB | ACB | ACB | ABC | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> These strategies together can cohesively assist GraphComBO in adapting to various tasks. For example, a small failtol will encourage exploration in the combinatorial space when restart_method is set to a random combo-node, which is useful when optimizing an underlying function with... | **A**: restart_method that either restarts at a random combo-node, the best-visited combo-node, or the initial starting location if specified.
In addition, the combo-subgraph size Q𝑄Qitalic_Q, which can be viewed as the “volume” of the trust region under graph setting, also controls the step size of exploration.
**... | BAC | ACB | BAC | BAC | Selection 1 |
The power behavior results are shown in Table 3. The new test detects the alternative hypothesis for all scenarios. Furthermore, the results are coherent with the shape of the sampling distributions. For example, the power of the test increases as the distance between the two modes increases (Model 6 vs. Model 7). ... | **A**: The power also rises with the excess mass of the secondary mode (Model 9 vs. Model 10).
**B**: For Model 8 the proportions of rejections are much smaller, but always above the significance level.
**C**: Additionally, the proportions of rejections grows as the sample size gets larger in all the scenarios..
| CBA | ABC | ABC | ABC | Selection 4 |
The literature on the estimation of bid-ask spreads from a time series of displayed prices started with Roll’s estimator, which is based on the empirical covariance of successive price increments [63]. <|MaskedSetence|> <|MaskedSetence|> In this last case, when two consecutive observations of the time series of price... | **A**: On the other hand, the serial dependence of the sign of the trades seems to be a well-established fact, observable at high frequencies [2, 48, 19].
.
**B**: The observable price is considered to be the sum of the mid price, that is the average between the bid and the ask, and a microstructure noise correspondin... | BCA | BCA | BCA | BCA | Selection 1 |
Figure 6 follows Figure 9 and reports the detailed reconstructed spatial context (bottom row) with the real spatial context (top row). The three colored spots are random anchor points chosen within the test dataset. <|MaskedSetence|> In the meantime, the relative locations and distances of the three points are also a... | **A**: It can be seen that the three imputed anchor points are placed in the correct relative position within the reconstructed spatial context.
**B**: As the regularization coefficient increases, the test (out-of-sample) spatial reconstruction error decreases logarithmically.
**C**: This confirms the nuanced rationa... | ACB | CAB | ACB | ACB | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> Under certain assumptions, we establish connections between our online testing approach and optimal transport [62] as a mechanism for distribution matching. (iii) This observation sets the foundation of the entropy-matching loss function used in POEM. (iv) Numerical experiments in ... | **A**:
Contributions
(i) We present a sequential test for classification entropy drift detection, building on betting martingales [55, 56, 57] and online learning optimization [58, 59, 60] to provably attain fast reactions to shifting data.
**B**: (ii) Inspired by [61], we show how to utilize the test martingale to ... | ABC | ABC | ACB | ABC | Selection 4 |
<|MaskedSetence|> (1997) demonstrated that analyzing functional data is often more suitable than handling large finite-dimensional vectors derived from discrete approximations of functions. This is particularly relevant for computational reasons, as efficiently computing multivariate depth in high-dimensional spaces i... | **A**: In higher dimensions, the concept of order statistics becomes more complex.
**B**: From another perspective, when the volume of data is large, Ramsay and Silverman (1997) Ramsay et al.
**C**: Although these definitions are differ greatly for multivariate data, they are very similar when applied to univariate d... | BAC | BAC | BAC | CBA | Selection 3 |
The coefficients of Income and RacialHet, which are estimated to be nearly constant over time, are plotted for August 2019 in Fig. <|MaskedSetence|> <|MaskedSetence|> Although the coefficients of RacialHet tend to be high in several northwestern districts, their influence is marginal owing to their weak explanatory ... | **A**: 12.
**B**: The coefficients on Income show large positive values in the southeastern area where income levels are low, suggesting that a higher income might increase the risk of larceny in this area.
**C**: Based on the empirical result, the determinants of larceny risk vary spatially but exhibit less temporal... | ABC | ABC | ABC | ABC | Selection 3 |
Several challenges need to be handled for exploring the robust offline non-Markovian RL with unknown transitions. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> It is thus critical to relax such a condition to design desirable offline algorithms. These challenges pose the following fundamental open question... | **A**: (ii) Existing coverage condition for offline non-Markovian RL (Huang et al., , 2023) is strong and can incur more stringent coverage conditions for robust offline RL.
**B**: (i) Considering non-Markovian processes in the entire uncertainty set can cause dramatic increase of sample complexity.
**C**: The challe... | BCA | BCA | BCA | BCA | Selection 4 |
<|MaskedSetence|> <|MaskedSetence|> The decoder is updated by minimizing the loss between the input image and its reconstruction from the optimal latent space representation. Although slower, this method converges faster and demonstrates superior data efficiency and ultimately achieves better reconstructions with a m... | **A**: However, these solvers can slow down training when the ODE becomes stiff, as step sizes shrink and make integration time-consuming [3, 7].
**B**: This decoder-only method explicitly determines the optimal latent space representation at each training step via a gradient flow, namely, an ordinary differential equ... | CBA | BAC | CBA | CBA | Selection 1 |
Traditional approaches to predicting non-contractual user level customer values rely on recency, frequency and monetary value (RFM)(doi:10.1509/jmkr.2005.42.4.415, ) from the user’s past history to extrapolate future purchasing behaviors. A prominent model family in this class is a set of parametric generative models ... | **A**: Thirdly, for new users with less transactions, the model does not have enough data to discriminate between potentially high value users and low value ones.
**B**: Along with a flexible model form with no distribution assumptions, they need a large amount of features to increase forecast accuracy.
**C**: Specif... | ABC | ABC | ABC | ABC | Selection 3 |
5. Conclusion
This work establishes the asymptotic oversmoothing rates for deep GNNs with and without residual connections using the multiplicative ergodic theorem. <|MaskedSetence|> <|MaskedSetence|> These findings highlight that incorporating residual connections effectively mitigates or prevents the oversmoothin... | **A**: Under suitable assumptions, we show that the normalized vertex similarity of deep non-residual GNNs converges to zero at an exponential rate determined by the second-largest eigenvalue magnitude of the aggregation coefficient matrix.
**B**: Furthermore, we precisely characterize the asymptotic behavior of the n... | ABC | ABC | CBA | ABC | Selection 2 |
<|MaskedSetence|> A low-dimensional subspace can be discovered using principal component analysis (PCA) [27, 28] or random embedding [29]. <|MaskedSetence|> Where gradient information is unavailable, the PCA covariance can be weighted using output data [34], or the PCA components can be interrogated when combined wit... | **A**: Alternatively, gradient information about the QOI can be used to discover a low-dimensional ”active” subspace [30, 31, 32, 33].
**B**: In Section 3, we present the proposed PPLS-BO algorithm for adaptive sampling in reduced dimension.
**C**:
BO approaches for high-dimensional problems have received substantia... | CAB | CAB | CAB | CAB | Selection 3 |
The decrease in volatility could be explained by the fact that averaging is a common technique used to reduce variance. <|MaskedSetence|> <|MaskedSetence|> To further enhance the forecast accuracy, various strategies were explored, including experimenting with different lag lengths and conducting thorough hyperparame... | **A**: By incorporating the HMM means, the inflation rate forecast adjusts accordingly and does not predict a severe recession as indicated by the original data.
**B**: Despite these efforts, the model’s performance for the 2.5-year forecast fell short compared to the 1-year forecast.
**C**: Though none of the curves... | ABC | ACB | ACB | ACB | Selection 3 |
In this paper, we focus on the classification of mechanisms generating blood spatter patterns, to be specific, gun-shot backspatters and impact beating spatters. <|MaskedSetence|> The dataset studied in this article is publicly accessible, consisting of 169 blood spatter patterns, which are a subset of bloodstain patt... | **A**: The former leverages directional statistics to extract interpretable angular features but results in low classification accuracy.
**B**: Unlike previous studies that relied on complex and less interpretable features or suffered from unsatisfactory classification performance, our method considers basic local fea... | BAC | CAB | CAB | CAB | Selection 2 |
In our analysis, we assume that the activation is quadratic and the first-layer weights are random. <|MaskedSetence|> the intrinsic dimension of the subspaces. Moreover, our results empirically hold under more generic settings. <|MaskedSetence|> <|MaskedSetence|> Our findings also offer insights into the role of ove... | **A**: The resulting width of the network scales polynomially w.r.t.
**B**: Additionally, the widths of ReLU and quadratic activation layers have similar dependence on the intrinsic dimension and number of subspaces to achieve linear separability (see Section 2 and LABEL:fig:rank-K-sweep).
Our results complement pre... | ACB | ACB | CBA | ACB | Selection 1 |
<|MaskedSetence|> (2024a) study the construction of simultaneous prediction sets for multiple outcomes under covariate shift,
and Lee et al. <|MaskedSetence|> <|MaskedSetence|> (2023),
which study the outlier detection problem; see also Marandon et al. (2024); Bashari et al. (2024); Liang et al. (2024); Gui et al. (... | **A**: (2024b) propose a method for inference on a function of test points.
Our work is closely related to Jin and Candès (2023b, a), which introduce a methodology for selecting test points
under the i.i.d. assumption or distribution shift.
**B**: These works extend the results of Bates et al.
**C**: Lee et al.
| CAB | CAB | CAB | CAB | Selection 1 |
4 Conclusions
In this work, we presented a new method of estimating Granger causality to solve one of its significant criticisms of not being causal but rather a predictive tool. Our approach leveraged the causal Bayesian network and interpreted GC as conditional independence tests. <|MaskedSetence|> <|MaskedSetence... | **A**: Our simulation experiments indicated that this method is efficient with its ability to unravel cycles in structures.
.
**B**: Taking the logical-and operation on both BVGC and MVGC results will solve the criticism of GC being only predictive.
**C**: A notable point, however, is that this framework has not sol... | BCA | BCA | ACB | BCA | Selection 2 |
4.1 Datasets and Hyperparameter settings
We first conduct experiments with various teacher-student pair settings on the CIFAR-100 dataset [42]. CIFAR-100 contains 50,000 training images with 500 images per class and 10,000 test images. <|MaskedSetence|> <|MaskedSetence|> For other models in CIFAR-100 classificatio... | **A**: In knowledge distillation process, the teacher model is well-trained previously and fine-tuned during training..
**B**: During each iteration of the training process, for models such as MobileNetV2, ShuffleNetV1, and ShuffleNetV2, we use a learning rate of 0.01 and train for 30 epochs.
**C**: Except for the lo... | CBA | CBA | CBA | CBA | Selection 3 |
[1, 16, 22, 19, 22]. More specifically, these algorithms require solving a sequence of LPs to make online decisions. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
. | **A**: For example, in the aforementioned online advertising example, a decision has to be made in milliseconds, while LP-based methods can take minutes to hours on large-scale problems.
**B**: However, the high computational cost of these LP-based methods prevents their application in time-sensitive or large-scale pr... | BAC | CBA | BAC | BAC | Selection 3 |
Several studies, including Gordaliza et al. (2019); Jiang et al. (2020b); Chzhen et al. (2020); Silvia et al. (2020); Buyl & Bie (2022), have employed the OT map for algorithmic fairness.
Gordaliza et al. <|MaskedSetence|> <|MaskedSetence|> (2020); Silvia et al. <|MaskedSetence|> | **A**: (2020) proposed aligning prediction scores from different protected groups using the OT map or OT-based barycenter.
Buyl & Bie (2022) developed a method that projects prediction scores onto a fair space by optimizing the projection through minimizing the transport cost calculated on all pairs of inputs.
.
**B**... | CBA | ACB | CBA | CBA | Selection 4 |
<|MaskedSetence|> To address these tasks simultaneously, we employ Sparse Bayesian Linear Regression, leveraging the inherent sparsity of dynamical systems. Dynamical systems are typically governed by a small subset of functions, making them sparse within the high-dimensional function space. Sparsity is induced by ass... | **A**: The regression problem underlying the discovery of time-delayed differential equations involves two key tasks: (1) Model Selection and (2) Parameter Estimation.
**B**: The library is parameterized alongside the time delay, but this parameterization lacks an explicit functional form, rendering the joint posterio... | BAC | ACB | ACB | ACB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> Primary headings are designated with Roman numerals, secondary with capital letters, tertiary with Arabic numbers; and quaternary with lowercase letters. Reference and Acknowledgment headings are unlike all other section headings in text. <|MaskedSetence|> They are simply primary ... | **A**: When numbered, please be consistent throughout the article, that is, all headings and all levels of section headings in the article should be enumerated.
**B**: They are never enumerated.
**C**:
Enumeration of section headings is desirable, but not required.
| ABC | CAB | CAB | CAB | Selection 2 |
Our estimation framework employs a penalized maximum likelihood objective optimized via a custom stochastic gradient ascent based algorithm. Explicit computation of high-dimensional integrals in the objective function is avoided by forming unbiased estimates of their gradients via Monte-Carlo approximations, thereby av... | **A**: Proofs for all propositions and theorems can be found in Supplemental Section S1.
.
**B**: Section 5 presents simulation studies and a real data application in brain structural network modeling.
**C**: Section 3 details the proposed network architecture and provides some theoretical analysis of its approximati... | BCA | CBA | CBA | CBA | Selection 4 |
Our framework is applied to bond recovery rate prediction using a global dataset spanning 1996-2023. <|MaskedSetence|> By identifying the market-related variables group as the most influential predictor, our results highlight the practical relevance of Group Shapley values for advancing Explainable AI in finance. Furt... | **A**: This approach allows for robust testing under diverse scenarios, including cases with skewed or sparse data and small sample sizes, and provides competitive performance compared to alternative methods such as the Wald and CQ tests.
**B**: This extension achieves computational gains compared to prior methods suc... | CBA | CBA | CBA | BAC | Selection 2 |
The Test case objects describe the selected IID-sampleable target distributions.
These objects are designed to be compatible with the Distributions.jl package [19, 20], which makes them easy to use as parts of test cases. Typically, the user will choose a test case from the list described in Section 3. <|MaskedSetenc... | **A**: In such a case, the user needs to implement the Base.rand and Distributions.logpdf functions for these types, which are needed for generating IID samples.
Most of the target functions presented in Section 3 are implemented using the Distributions.jl package.
**B**: But also custom test cases can be implemented ... | ACB | BCA | BCA | BCA | Selection 2 |
(statistical) arbitrage strategy (Marshall et al., 2013). The trading behavior of this strategy resembles a ”contrarian” approach, as it takes positions that counteract market overreactions. <|MaskedSetence|> This finding offers a microscopic perspective on the cross-effects of market dynamics, as discussed in Lo and ... | **A**: Section 2 introduces the high-frequency data structure in CFFEX and how we process the raw data, as well as the basic liquidity measures of different futures contracts.
**B**: Finally, we conclude the paper in Section 5.
.
**C**: In this paper, we rigorously examine that the predictive power of the ”lead-lag s... | CAB | CAB | BAC | CAB | Selection 4 |
5 Discussions and Future Work
Our approach presents a departure from the existing SGD family of algorithms and adopts a different philosophical outlook toward the optimization problem. Specifically, SGD adopts a “function landscape” based optimization approach, where it moves down the the function landscape until it r... | **A**: A similar conclusion in the context of adapting to function regularity was noted in Vakili et al.
**B**: (2019).
.
**C**: The “function landscape” based approach is inherently tied to the steepness of the function valley.
| BAC | CAB | CAB | CAB | Selection 4 |
In this work, we address these questions directly. We show how to adapt standard doubly robust estimators in order to yield doubly robust tests and confidence intervals in semiparametric regression problems, and spell out the implications for the ‘variance-weighted’ treatment effect (Crump et al., 2006; Robins et al.,... | **A**: In comparison, the framework in the current paper is generic in that it can allow for arbitrary nonparametric estimators of the propensity score and conditional outcome mean.
**B**: (2017), we do not rely on Donsker conditions on the nuisance parameters estimators but rather use cross-fitting as in cross-valida... | ACB | BCA | BCA | BCA | Selection 4 |
Recently, bilevel optimization methods have also been studied in composition optimization (Wang et al., 2017), distributed learning (Tarzanagh et al., 2022; Lu et al., 2022; Yang et al., 2022; Chen et al., 2023b), corset selection (Zhou et al., 2022), overparametrized setting (Vicol et al., 2022), multi-block min-max... | **A**: Several acceleration methods have been proposed to improve the complexity (Khanduri et al., 2021; Yang et al., 2021; Huang et al., 2022; Dagréou et al., 2022).
**B**: The works (Liu et al., 2021b) and (Mehra and Hamm, 2021) propose penalty-based methods respectively with log-barrier and gradient norm penalty, a... | ABC | ABC | ABC | ABC | Selection 4 |
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