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A: (2005, Eq. 28) provide a closed form approximation of quantile q>0.95𝑞0.95q>0.95italic_q > 0.95 for the sum of Pareto-distributed variables.333The Zaliapin et alB: (2005) preprint has a typo, which in the published version has been fixed by redefining the meaning of q𝑞qitalic_q just for this equation, but ...	BCA	ACB	BAC	CBA	Selection 1
A: To enhance the visualization, we exclude street segments with wealth estimates greater than the 95th percentile ($6,272,010)B: C: Figure 2: Counts of residential burglary (slightly jittered) versus wealth estimate by neighborhood for each street segment; illustrates the nonconstant effects of wealth on ...	BCA	BAC	CBA	ACB	Selection 1
A: In this paper, we extend the recent solutions of sparse linear mixed model [8, 9] that can correct confounding factors and perform variable selection simultaneously further to account the relatedness between different responsesB: We propose the tree-guided sparse linear mixed model, namely TgSLMM, to correct...	CBA	BCA	ACB	ABC	Selection 2
A: The insulin intakes tend to be more in the evening, when basal insulin is used by most of the patientsB: 3 times the average insulin dose of others in the morning.C: The only difference happens to patient 10 and 12 whose intakes are earlier at day. Further, patient 12 takse approx	ACB	CAB	BCA	BAC	Selection 1
A: Model Implied Instrumental Variable SEM (MIIVSEM; Bollen (\APACyear1996)) uses the structural information from the model to identify variables within the system that can act as instruments for other variables, rather than recruit additional auxiliary variables from outside of the system. We illustrate this appro...	BCA	BCA	CBA	BCA	Selection 3
A: This can be improved with better dynamics models and, while generally common with model-based RL algorithms, suggests an important direction for future work. Another, less obvious limitation is that the performance of our method generally varied substantially between different runs on the same gameB: While ...	CBA	CAB	ACB	BAC	Selection 4
A: They compared their results with the results of the Bracken and Fricker and results were found to be different. They concluded that logarithmic and linear-logarithmic forms fits more appropriately as compared to the linear form found by BrackenB: They also concluded that the Bayesian approach is more appropr...	ACB	BAC	CAB	BCA	Selection 4
A: For example, we can put the momentum term on the serverB: However, these ways lead to worse performance than the way adopted in this paper. More discussions can be found in Appendix A. C: There are some other ways to combine momentum and error feedback	BCA	ABC	CBA	ACB	Selection 1
A: , where ∗∗ is the convolution333We use convolution instead of cross-correlation only as a matter of compatibility with previous literature and computational frameworksB: Using cross-correlation would produce the same results and would not require flipping the kernels during visualizationC*: operation.	CAB	ACB	ABC	BAC	Selection 3
A: In this context, we study randomization tests on regression residuals, which we will refer to as residual randomization testsB: In Section 4, we show how Condition (C1) can be simplified when testing the significance of coefficients in linear regressionC: These procedures bear strong similarities to perm...	CAB	ABC	ACB	BAC	Selection 4
A: This paper also contributes to our knowledge of the blood donations market (see Slonim et al., (2014) for an introduction to this market). This market is ideal for studying charitable givingB: For instance, Lacetera et al., (2012, 2013) and Goette and Stutzer, (2020) explore the effect of incentives on blood...	ACB	BAC	ABC	CBA	Selection 3
A: In this paper, we introduce and conduct an empirical analysis of an alternative approach to mitigate variance and overestimation phenomena using Dropout techniquesB: Our main contribution is an extension to the DQN algorithm that incorporates Dropout methods to stabilize training and enhance performanceC...	BCA	ABC	BCA	BCA	Selection 2
A: NRFI with and without the original data is shown for different network architecturesB: The smallest architecture has 2222 neurons in both hidden layers and the largest 128128128128C: For NRFI (gen-ori), we can see that a network with 16161616 neurons in both hidden layers (NN-16-16) is already sufficient...	ABC	CAB	CBA	BCA	Selection 1
A: We refer to the introduction of the latter article for furtherB: SBM and OBM and their local time have been recently investigated in the context of option pricing, as for instance in [20] and [16]. In [37] it is shown that a time series of threshold diffusion type captures leverage and mean-reverting effects...	BAC	CAB	BAC	CBA	Selection 4
A: However, such computational efficiency guarantees rely on the regularity condition that the state space is already well exploredB: A 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., 20...	ABC	CBA	BAC	BCA	Selection 3
A: In Wu et alB: (2018b), weights, activations, weight gradients, and activation gradients are subject to customized quantization schemes that allow for variable bit widths and facilitate integer arithmetic during training and testing. In contrast to Zhou et alC: (2016), the work of Wu et al. (2018b) accumu...	BCA	CAB	ABC	BAC	Selection 3
A: Each axis maps the entire range of each dimension, from bottom to top. A simple example is given in Figure 4(b), where we can see that the dimensions of the selected points roughly appear at the intersection between two species, versicolor (brown) and virginica (orange). B: The colors reflect the labels of t...	BAC	BCA	CBA	BCA	Selection 3
A: Roughly speaking, the network embedding approaches can be classified into 2 categories: generative models [13, 14] and discriminative models [15, 16]B: The former tries to model a connectivity distribution for each node while the latter learns to distinguish whether an edge exists between two nodes directly....	ABC	BAC	ACB	CAB	Selection 1
A: In Section 4, the main result is provided. Section 5 presents a simulation study, highlighting the small sample properties and implementation of our proposed method. Section 6 provides the proof of the main theoremB: The paper is organized as follows. Section 2 introduces and motivates the main regression p...	BAC	CAB	ABC	BCA	Selection 1
A: To assist the knowledge generation, a comparison between the currently active stack against previously stored versions is importantB: In general, this includes monitoring the historical process of the stacking ensemble, facilitating interaction and guidance (G4).C: T4: Compare the results of two stages ...	CAB	BCA	CAB	CBA	Selection 2
A: In §6.1, we introduce Q-learning and its mean-field limitB: 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. C: In this section, we extend our analysis of TD to Q-learning and pol...	ABC	CAB	BAC	BCA	Selection 4
A: Predicting a quantity for the long time scales which matter for the climate is a hard task, with a great degree of uncertainty involvedB: Many efforts have been undertaken to model and control this and other uncertainties, such as the development of standardized scenarios of future development, called Shared...	ABC	ACB	BAC	CAB	Selection 1
A: (2019); Chen et al. (2019, 2020b) consider the matrix factor model which is a special case of (1) with M=2𝑀2M=2italic_M = 2 and propose estimation procedures based on the second moments.B: (2020) and the references therein provide a thorough review of recent advances and applications of multivariate factor ...	BAC	CAB	CBA	CAB	Selection 3
A: We train the model with 90 epochsB: As recommended in [32], we use warm-up and polynomial learning rate strategy.C: To further verify the superiority of SNGM with respect to LARS, we also evaluate them on a larger dataset ImageNet [2] and a larger model ResNet50 [10]	BCA	ACB	ACB	CAB	Selection 1
A: Despite this mild difference in parameter identification, similar assumptions can be found in Zhou et alB: (2010). Recall that we recommend the choice of commonly used cubic splines (i.e., ζ=4𝜁4\zeta=4italic_ζ = 4) in Section 3 to implement our method when prior information about the Hölder smoothness condi...	ABC	CBA	ACB	BCA	Selection 3
A: In addition, Ada-LSVI-UCB-Restart has a huge gain compared to LSVI-UCB-Unknown, which agrees with our theoretical analysis. This suggests that Ada-LSVI-UCB-Restart works well when the knowledge of global variation is unavailable. Our proposed algorithms not only perform systemic exploration, but also adapt to th...	BCA	CBA	ACB	BCA	Selection 2
A: The framework is general and can utilize any DGMB: The key observation that we make is that the DR learning problem can be cast as a style transfer task [DBLP:conf/cvpr/GatysEB16], thus allowing us to borrow techniques from this extensively explored area. C: Furthermore, even though it involves two stage...	BAC	CAB	BAC	ACB	Selection 4
A: The results for the breast cancer data can be observed in Table 3B: However, the interpolating predictor selects over 80 times as many views as the lasso, and is less stable. Again, the interpolating predictor and NNFS do not align with the pattern that less sparsity is associated with higher stability. *C...	ABC	CBA	ACB	CAB	Selection 3
A: Though they establish a regret bound that does not depend on the aforementioned parameter κ𝜅\kappaitalic_κ, they work with an inaccurate version of the MNL model. More specifically, in the MNL model, the probability of a consumer preferring an item is proportional to the exponential of the utility parameter and...	CBA	CAB	BAC	ACB	Selection 2
A: Evolutionary optimization, however, has not experienced similar consideration by the InfoVis and VA communities, with the exception of more general visualization approaches such as EAVis [KE05, Ker06] and interactive evolutionary computation (IEC) [Tak01]B: Visualization tools have been implemented for seque...	BCA	ACB	BAC	ACB	Selection 3
A: Dolphins: this network consists of frequent associations between 62 dolphins in a community living off Doubtful SoundB: The network splits naturally into two large groups females and males dolphins1 ; dolphinnewman , which are seen as the ground truth in our analysis.C: In the Dolphins network, node den...	ACB	CBA	CBA	CBA	Selection 1
A: Our ContributionB: Our contribution is two foldC: First, utilizing the optimal transport framework and the variational form of the objective functional, we propose a novel variational transport algorithmic framework for solving the distributional optimization problem via particle approximation. In each i...	ACB	CAB	ABC	BAC	Selection 3
A: A use case present in a visual diagnosis tool revealed that feature generation involving the combination of two features is capable of a slight increase in performance [30]. The authors tested the same mathematical operations as in our system (i.e., addition, subtraction, multiplication, and division), but the g...	BCA	CAB	ABC	ACB	Selection 3
A: Systems can exploit correlated variables even if they are not directly a part of the input e.g., through inferred zip codes [21], failing to work effectively on minority groups. B: Systems designed to aid human resources, help with medical diagnosis, determine probation, or loan qualification could be biased...	CBA	BCA	ABC	CAB	Selection 1
A: The idea is that GP emulators model the underlying function (in this case, the flow map) as a probabilistic distribution, and their sample paths provide a characterisation of the function throughout its entire domain. These sample paths extend the notion of merely being a distribution over individual function va...	BAC	BAC	ACB	BCA	Selection 4
A: [Pfister et alB: The traditional approach for testing independence is based on Pearson’s correlation coefficient; for instance, refer to Binet and Vaschide (1897), Pearson (1920), Spearman (1904), Kendall (1938). However, its lack of robustness to outliers and departures from normality eventually led researc...	BCA	ABC	ABC	ACB	Selection 4
A: The ZOO oracle is often implicitly assumed to be included with the FOO oracle; we make this explicit here for clarityB: The FOO and LMO oracles are standard in the FW literatureC: Finally, the DO oracle is motivated by the properties of generalized self-concordant functions. It is reasonable to assume t...	ACB	BAC	ACB	BCA	Selection 2
A: We prove these theorems via a new notion, pairwise concentration (PC) (Definition 4.2), which captures the extent to which replacing one dataset by another would be “noticeable,” given a particular query-response sequenceB: This is thus a function of particular differing datasets (instead of worst-case over...	BAC	BAC	CBA	ABC	Selection 4
A: The dropout probability was optimized over the interval [0.05,0.5]0.050.5[0.05,0.5][ 0.05 , 0.5 ] with steps of 0.050.050.050.05. B: An early stopping criterion, based on the minimum of the loss function, was employed to avoid overfittingC: Dropout ensemble: An ensemble average of 50 MC samples was used	CBA	CAB	ACB	CAB	Selection 1
A: Consider, for example, the time allocation problem faced by a researcher involved in multiple projects with different sets of coauthors. The researcher has a limited amount of time and concentration power to dedicate towards coauthored projects and her own research activity. Allocating attention to coauthored p...	ACB	ABC	ACB	BAC	Selection 2
A: Thus, we will formulate and consider requirements on the future crowdedness values up to hℎhitalic_h-steps ahead of a given time t𝑡titalic_tB: Each requirement that we formulate can be checked for every areal unit i=1,…,I𝑖1…𝐼i=1,...,Iitalic_i = 1 , … , italic_I.C: While the framework is rather general...	BCA	BAC	CAB	CAB	Selection 1
A: This process is somewhat elaborate and the reader is referred to [31] and [32] for all of the detailsB: However, for the exposition in this section it sufficient to know what the properties of the operators 𝐋𝐋\mathbf{L}bold_L and 𝐖𝐖\mathbf{W}bold_W are. C: The operator 𝐋𝐋\mathbf{L}bold_L and 𝐖𝐖\m...	BAC	CAB	BCA	ABC	Selection 3
A: This notion is more general than the one initially introduced in Vapnik andB: While different definitions of VC classes exist, here we rely on the definition used in the previous references which is based on the covering numbersC: Guillou, 2002, 2001) or for multiple ordinary least-squares procedures (Pl...	BCA	CAB	ABC	CBA	Selection 4
A: On the other hand, the volume of Factor 2 is typically small in the winter timeB: The volumes of night-life pattern in Factor 1 remain to be volatileC: It has many small-value outliers, mostly on the day before a business day (Sundays or the end of holiday.) These can be seen more clearly in the more det...	BAC	CAB	ABC	CAB	Selection 3
A: A threat in this case is the overconfidence effect and overinterpretation of the models’ capabilities by both domain-specific and ML experts, especially in noisy data scenarios. Despite that, we believe our first user study was an appropriate choice of method to understand preliminarily if VisRuler is usable and...	CBA	BCA	BCA	BAC	Selection 1
A: The first approach leverages global parametrizations to represent surfaces, employing either an L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT metric \parencitechung2008encoding, epifanio2014hippocampal,ferrando2020detecting or a non-Euclidean metric \parencitejermyn2012elastic, jermyn...	CBA	ABC	BCA	BAC	Selection 4
A: In Table 1, for networks with known memberships or K𝐾Kitalic_K, their ground truth and K𝐾Kitalic_K are suggested by the original authors or data curators. For the Gahuku-Gama subtribes network, it can be downloaded from http://konect.cc/networks/ucidata-gama/ and its node labels are shown in Figure 9 (b) [29]...	CAB	BCA	ACB	CAB	Selection 3
A: In Section 4 we illustrate the use of our model for semiparametric CCA on simulated datasets and apply the model to two real datasets: one containing measurements of climate variables in Brazil, and one containing monthly stock returns from the materials and communications market sectors. We conclude with a disc...	CBA	ABC	ACB	ACB	Selection 1
A: The authors also extend their sincere appreciation to the anonymous reviewers for their insightful comments, which have contributed to the enhancement of the quality of this paper.B: The first author was partially supported by JSPS KAKENHI Grant Numbers JP21K03358 and JST CREST JPMJCR14D7, JapanC: The s...	CAB	ABC	ACB	CBA	Selection 1
A: However, their methods can not cover the regime when the expected degree is Ω⁢(1)Ω1\Omega(1)roman_Ω ( 1 ) due to the lack of concentrationB: Additionally, [72] proposed Projected Tensor Power Method as the refinement stage to achieve strong consistency, as long as the first stage partition is partially corre...	CAB	BCA	BAC	ABC	Selection 2
A: Let n≥2𝑛2n\geq 2italic_n ≥ 2 and assume that the result holds for all inputs of length n−1𝑛1n-1italic_n - 1. We shall consider two cases. B: We shall use induction on n𝑛nitalic_nC: The result is trivial if n=1𝑛1n=1italic_n = 1, since both sides of (3.3) are 0	BCA	BCA	CAB	CBA	Selection 3
A: From the other sets of controls emerges that specific features of studies included in the MRA differently explain the diversity in the results within clusters. The positive coefficients of controls for corridors such as Internal and Urbanization state that people respond to adverse climatic change with increased...	ACB	ABC	CAB	ACB	Selection 2
A: (2017)B: More precisely, these authors established the third term on the right-hand side inC: The result in Theorem 4 for s≥1/2𝑠12s\geq 1/2italic_s ≥ 1 / 2 (that is, 2⁢k+2≥d2𝑘2𝑑2k+2\geq d2 italic_k + 2 ≥ italic_d) was already derived in Sadhanala et al	ABC	BCA	BAC	ABC	Selection 2
A: In many cases, the degree sequence is the only information available and many other important properties are constrained by itB: However, the degree may carry confidential and sensitive information, such as the sexually transmitted disease [Helleringer and Kohler (2007)]C: To solve it, we can add noises...	ACB	CBA	CBA	ABC	Selection 4
A: We have applied our methodologies using practical cross-covariance choices such as models of coregionalization built on independent stationary covariancesB: Recent work (Jin et al., 2021) highlights that DAG choice must be made carefully when considering explicit models of nonstationary, as spatial process ...	BAC	BAC	ACB	BCA	Selection 3
A: While most practical inference needs additional modelling assumptions, the data example of section 7 allowed for non-parametric estimationB: In addressing identifiability, we have chosen the re-weighting route which appears natural in view of the simplicity of Proposition 1 and corresponds to a change of mea...	CBA	ACB	BCA	ACB	Selection 3
A: A Bayesian algorithm is initialized with a prior belief, and the forecaster learns from each sample to build a posterior belief. Given that, we know the dynamics of the posterior belief as a distribution, exact minimization of the Bayes risk can be formulated as dynamic programming. Nonetheless, exact dynamic pr...	ACB	ABC	CAB	BAC	Selection 3
A: Training binary latent VAEs with K=2,3𝐾23K=2,3italic_K = 2 , 3 (except for RELAX which uses 3333 evaluations) on MNIST, Fashion-MNIST, and OmniglotB: We report the average ELBO (±1plus-or-minus1\pm 1± 1 standard error) on the training set after 1M steps over 5 independent runsC: Test data bounds are rep...	CBA	CAB	BCA	ABC	Selection 4
A: See also Dolera and Favaro [2020a, b] and references therein.B: See Charalambides [2005, Chapter 7] for an account on compound Poisson sampling models and their distributional properties, and to Dolera and Favaro [2020c] for a comprehensive treatment of the large n𝑛nitalic_n asymptotic behaviour of 𝐌⁢(n,z)...	BAC	ACB	CBA	CAB	Selection 3
A: As shown in example 3, the Lorenz map reduces to a simple function of the marginal Lorenz curves in case marginal attribute allocations are independentB: This feature is shared with the multivariate Lorenz proposal in Arnold (1983,2012) but not the alternative proposals. C: Decomposition under independen...	CBA	CAB	BCA	BAC	Selection 3
A: Regarding decision boundaries and borderline examples, Melnik [Mel02] analyzes their structure using connectivity graphs [MS94]. And finally, Ramamurthy et al. [RVM19] utilize persistent homology inference to describe the ambiguity (or even lack) of decision boundaries. All described methods, while being valuabl...	CBA	CAB	ACB	BAC	Selection 2
A: In Section 3, we give conditions on our model that guarantee existence and uniqueness of equilibria in the mean-field regime, the limiting regime where at each time step, an infinite number of agents are considered for the treatmentB: In Section 4, we translate these results to the finite regime, where a fin...	BCA	BAC	ACB	BAC	Selection 3
A: We conclude this section with a brief review of the theory of density estimation in Section 2.3.B: In Section 2.2, we discuss the distance filtration, which is the backbone of the traditional TDA approach, as well as various alternatives to the distance filtration, and we will explain their relevance to the ...	CBA	BCA	BAC	ABC	Selection 1
A: We could in principle modify our framework so that the distribution of cluster sizes is allowed to depend on the number of clusters G𝐺Gitalic_GB: Such a modification, however, would complicate the exposition and the resulting procedures would ultimately be the same. We therefore see no apparent benefit and ...	BAC	ABC	ACB	CBA	Selection 3
A: In the contexture of reinforcement learning with function approximations, our work is related to a vast body of recent progress (Yang and Wang, 2020; Jin et al., 2020b; Cai et al., 2020; Du et al., 2021; Kakade et al., 2020; Agarwal et al., 2020; Zhou et al., 2021; Ayoub et al., 2020) on the sample efficiency of...	ACB	ABC	CBA	BCA	Selection 2
A: These initial successes notwithstanding, the development of e-values is, of course, still in its infancy, competing with almost a century of p-value developmentB: As such, many challenges remainC: To appreciate these, we first note that the aforementioned GRO-type approaches can in principle be made comp...	CBA	CAB	CBA	ABC	Selection 4
A: Importantly, inference must be done in a way that takes into account the incentives of the strategic agents. Our work most closely relates to that of Tetenov (2016), who consider setting the type-I error level of a hypothesis test to account for an agent’s payoffs. That work establishes a minimax protocol simila...	CAB	CBA	BCA	ABC	Selection 2
A: We now state the conditions we will work withB: Throughout this work, we will assume the stable unit treatment value assumption, commonly abbreviated as SUTVA, in Assumption 1.3C: We will also assume consistency of the observed outcome throughout as given in Assumption 1.4. Moreover, our inference is val...	CAB	BCA	CBA	ABC	Selection 4
A: The purpose of defining different types of knowledge is to efficiently extract the underlying representation learned by the teacher model from the large-scale data. If we consider a network as a mapping function of input distribution to output, then different knowledge types help to approximate such a function. ...	ABC	BAC	CBA	CAB	Selection 3
A: To learn a sufficient embedding for control, we utilize the low-rank transition of POMDPsB: In particular, the state transition of a low-rank MDP aligns with that in our low-rank POMDP model. Nevertheless, we remark that such states are observable in a low-rank MDP but are unobservable in POMDPs with the low...	ABC	CAB	BAC	ACB	Selection 4
A: Table 1: We compare with most related representative works in closely related lines of researchB: The second line of research studies online RL in POMDPs where the actions are specified by history-dependent policies. Thus, the actions does not directly depends on the latent states and thus these works do not...	CAB	CBA	ACB	BAC	Selection 3
A: Without constraints, one can apply stochastic gradient descent (SGD) and its many variates, whose statistical properties (e.g., asymptotic normality) have been comprehensively studied from different aspects (Robbins1951stochastic; Kiefer1952Stochastic; Polyak1992Acceleration; Ruppert1988Efficient). However, unli...	ACB	CBA	CBA	CAB	Selection 4
A: The two networks share block 1111 (for instance basal species) but the remaining nodes of each network cannot be considered as equivalent in terms of connectivityB: One may think of species belonging to trophic chains with different connectivity patterns. C: Finally, let us consider two networks with pa...	ACB	BCA	CAB	ABC	Selection 2
A: This could be improved if structural information on the covariates were a priori known. Indeed, in this article, the i.i.d. Bernoulli prior on the indicators 𝜹𝜹\boldsymbol{\delta}bold_italic_δ (4e), entails the assumption that each covariate has the same probability a priori of being included in the model.*B...	BCA	CBA	BCA	BAC	Selection 2
A: Figure (a) illustrates a setting with 3 subpopulations and 2 learnersB: The dsolid lines correspond to the risk trajectory for the unstable balanced equilibrium at initializationC: Dotted and dashed lines illustrate risk trajectories under three different slight perturbations from the initialization. In ...	BAC	ABC	ACB	ACB	Selection 2
A: Finally, given the LP approximation detailed above, the algorithm for solving Eq. (29) follows the same lines as Alg. 1.B: This condition is trivially incorporated in the box constraints of Eq. (32)C: where ∥⋅∥∞\\|\cdot\\|_{\infty}∥ ⋅ ∥ start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT is the maximum norm	CBA	ABC	BAC	BAC	Selection 1
A: Based on the advantages of the decentralized information structure, the online algorithm and the regularization method, we propose a decentralized online regularized algorithm for the linear regression problem over random time-varying graphsB: In each iteration, the innovation term is used to update the nod...	BAC	ABC	ACB	BAC	Selection 3
A: The above results clarify the fundamental relation among the limiting behavior of abc posteriors and the learning properties of the chosen discrepancy, when measured via Rademacher complexity. Moreover, the bounds derived clarify that a sufficient condition to recover a limiting pseudo–posterior with the same t...	ACB	BCA	ABC	CBA	Selection 1
A: We thank Arkadev Chattopadhyay for helpful feedback and Todd Millstein for discussing [42] with us which led us to think about monotone neural networksB: Finally, we thank Bruno Pasqualotto Cavalar for bringing to our attention the work done in [9, 17].C: We are grateful to David Kim for implementing ou...	BCA	CAB	BCA	ACB	Selection 4
A: A further extension might consider weighting the classification probabilities by a utility function accounting for the degree of the error (i.e., mistakenly refusing an applicant who is right above the classification threshold is less costly than refusing an applicant much higher on the latent ability; see, e.g....	ABC	CBA	CAB	ACB	Selection 2
A: A typical paradigm for such contrastive RL is to construct an auxiliary contrastive loss for representation learning, add it to the loss function in RL, and deploy an RL algorithm with the learned representation being the state and action input. However, the theoretical underpinnings of such an enterprise remain...	BCA	BAC	CBA	BAC	Selection 3
A: The decoupling approach was developed for importance sampling in MV-SDEs (dos Reis et al., 2023; Ben Rached et al., 2023), where the idea is to approximate the MV-SDE law empirically as in (4), use the approximation as input to define a decoupled MV-SDE and apply a change of measure to itB: First, we introdu...	ACB	CBA	BCA	CAB	Selection 1
A: Second, we iteratively predict West Germany’s GDP from 1963 to 1989.B: First, we iteratively predict the 1990 GDP of each country in the control groupC: Again, we perform two exercises to assess the accuracy of alternative causal inference methods in this setting	CBA	BAC	BAC	BCA	Selection 1
A: Informative sampling occurs when there is a discrepancy between design variables and auxiliary variables used for regression analysis, notably even in widely utilized methods such as Poisson sampling and probability proportional to size sampling [29].B: In probability sampling, first-order inclusion probabil...	CAB	BCA	ACB	CBA	Selection 4
A: (2007). B: The above definition could be extended to less regular paths, namely to paths of finite p𝑝pitalic_p-variation with p<2𝑝2p<2italic_p < 2. In this case, the integrals can be defined in the sense of Young (1936)C: However, if p≥2𝑝2p\geq 2italic_p ≥ 2, it is no longer possible to define the it...	BCA	CAB	ABC	BCA	Selection 2
A: In this respect we note that the clipping operator, being a projection onto a ball, is not a compressor and moreover it is invoked dynamically with time-varying radii.B: Finally we note that stochastic gradient methods have been also studied in conjunction with biased compressor (nonlinear) operatorsC: S...	ACB	BAC	CAB	ABC	Selection 3
A: Based on Petrov-Galerkin method, the hp-variational PINNs (hp-VPINNs) [17] allows for localized parameters estimation with given test functions via domain decomposition. The hp-VPINNs generates a global approximation to the weak solution of the PDE with local learning algorithm that uses a domain decomposition w...	ABC	CAB	CAB	CBA	Selection 4
A: Finally, the analysis in the case of the projected quantum kernel is slightly more complicated as estimating the kernel requires us to first obtain the statistical estimates of the 2-norms between the reduced data encoding states on all individual qubits from quantum computersB: In Appendix C.2, we again use...	BAC	ACB	BAC	ABC	Selection 2
A: The results by different methods on the resampled PACS are presented in Figure 5B: We can observe that as the increase of KL divergence of label distribution, the performances of MCDA, M3DA, LtC-MSDA and T-SVDNet, which are based on learning invariant representations, gradually degenerate. In the case where ...	CBA	BCA	ACB	CAB	Selection 3
A: We also evaluated our estimators using a large-scale ride-sharing simulator adapted from Farias et al. (2022)B: The simulator generates drivers and riders based on data from the NYC taxi trip records dataset (Commission, N.D.). In this simulator, drivers enter the system continuously, each with a fixed capa...	CAB	ACB	CAB	ABC	Selection 4
A: Previous work went beyond this paper in other aspects, howeverB: Given a concrete model such as Gaussian VAEs, convergence to entropies was also numerically investigatedC: It was for instance asked, how close the original ELBO is to the sum of entropies result in practice, i.e., when only the vicinity o...	CAB	CAB	CAB	ABC	Selection 4
A: Specifically, we first extend the work of Bernanke et alB: (2005) on macroeconomic responses to a shock in monetary policy to a HDLP setting.C: We consider two canonical macroeconomic applications and demonstrate the performance of the proposed desparsified-lasso based estimator for HDLPs in recovering ...	BAC	ACB	CBA	BCA	Selection 4
A: Note that a remedial intervention is defined to allow multiple root causes to be corrected simultaneouslyB: Such an intervention is of course always non-singular within the CEG representation.C: Assume that the root causes of a specific defect or failure could be multiple and are well-defined	BAC	BCA	ABC	BAC	Selection 2
A: While the outcome and the inference models are ideally the same, in practice our model will at best approximate the “true” predictor-response relationships. In the code below, we show how to use BKMR as the inference modelB: Additional arguments specific to the inference model (e.g. iter, varsel) can be pas...	ACB	ABC	ABC	ABC	Selection 1
A: The distribution of eigenvalues plays a crucial role in statistical learning and is of significant interest in the high-dimensional settingB: Random matrix theory provides a systematic tool for deriving the distribution of eigenvalues of a squared matrix (Anderson, Guionnet and Zeitouni, 2010; Pastur and Sh...	CAB	BCA	ABC	CAB	Selection 3
A: Fig. 9 shows three annual temperature anomaly series from distinct regions: the Northern Hemisphere, the Southern Hemisphere and the Tropics from 1850 to 2021, which are described in detail in [19]B: Global warming has attracted significant attention in recent research, as demonstrated by studies such as [8]...	BCA	CBA	BCA	BAC	Selection 4
A: This scenario – which also links to out-of-distribution generalization – has attracted various contributions in recent years, such as [22, 23, 24]B: Generalization error bounds have also been developed to address scenarios where the training data distribution differs from the test data distribution, known as...	ACB	ACB	BCA	BAC	Selection 4
A: Hence, the current methodologies amount to testing the null hypothesis of equal means in all the populations; see, e.g., [16] for an early contribution and [52] for a broader perspective. Our proposal is therefore quite related to more general approaches, not requiring any homoscedasticity assumption and still v...	CBA	ACB	ACB	ACB	Selection 1
A: We verify that all calibrated parameters fall into the recommendation ranges according to [38]B: The calibration results in Table I demonstrate the reliability of our methods to calibrate plausible IDM parametersC: In the following, we make some comparisons among several pairs of calibration results.	CAB	ACB	ACB	ABC	Selection 4
A: In [19], Hachem et al. derived the CLT for the MI of correlated Gaussian MIMO channels and gave the closed-form mean and variance. Hachem et al. extended the CLT to the non-Gaussian MIMO channel with a given variance profile and the non-centered MIMO channel in [20] and [21], respectively, which shows that the p...	ACB	ACB	BCA	BAC	Selection 4

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