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arXiv:2505.18535v2 Announce Type: replace-cross Abstract: We study the convergence properties and escape dynamics of Stochastic Gradient Descent (SGD) in one-dimensional landscapes, separately considering infinite- and finite-variance noise. Our main focus is to identify the time scales on which SGD reliably moves from an initial point to the local minimum in the same ”basin”. Under suitable conditions on the noise distribution, we prove that SGD converges to the basin’s minimum unless the initial point lies too close to a […]

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arXiv:2505.15643v2 Announce Type: replace-cross Abstract: We study best-arm identification in stochastic multi-armed bandits under the fixed-confidence setting, focusing on instances with multiple optimal arms. Unlike prior work that addresses the unknown-number-of-optimal-arms case, we consider the setting where the number of optimal arms is known in advance. We derive a new information-theoretic lower bound on the expected sample complexity that leverages this structural knowledge and is strictly tighter than previous bounds. Building on the Track-and-Stop algorithm, we propose a […]

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arXiv:2504.11279v2 Announce Type: replace-cross Abstract: The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes mixed-effects models widely applied in fields such as biology, pharmacokinetics, and sociology. In this work, we propose a novel methodology for scalable Bayesian inference in hierarchical mixed-effects models. Our framework first constructs amortized approximations of the likelihood and the posterior distribution, which are […]

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arXiv:2503.18012v2 Announce Type: replace-cross Abstract: Physics-informed deep learning approaches have been developed to solve forward and inverse stochastic differential equation (SDE) problems with high-dimensional stochastic space. However, the existing deep learning models have difficulties solving SDEs with high-dimensional spatial space. In the present study, we propose a scalable physics-informed deep generative model (sPI-GeM), which is capable of solving SDE problems with both high-dimensional stochastic and spatial space. The sPI-GeM consists of two deep learning models, i.e., (1) physics-informed […]

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arXiv:2502.05459v2 Announce Type: replace-cross Abstract: White blood cells (WBC) are important parts of our immune system, and they protect our body against infections by eliminating viruses, bacteria, parasites and fungi. The number of WBC types and the total number of WBCs provide important information about our health status. A traditional method, convolutional neural networks (CNN), a deep learning architecture, can classify the blood cell from a part of an object and perform object recognition. Various CNN models exhibit […]

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arXiv:2406.14059v3 Announce Type: replace-cross Abstract: Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems. For strongly convex optimization problems or strongly monotone games, these results provide tracking guarantees under the assumption that the variation of the time-varying problem is restrained, that is, problems with a sublinear solution path. In this work we extend existing results in two ways: […]

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arXiv:2405.20856v2 Announce Type: replace-cross Abstract: Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent variables. Our focus is on the commonly studied acyclic setting, where each model corresponds to a directed acyclic graph (DAG). For this case, prior literature has demonstrated that connections to overcomplete independent component analysis yield effective criteria to decide parameter […]

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arXiv:2403.10889v2 Announce Type: replace-cross Abstract: List learning is a variant of supervised classification where the learner outputs multiple plausible labels for each instance rather than just one. We investigate classical principles related to generalization within the context of list learning. Our primary goal is to determine whether classical principles in the PAC setting retain their applicability in the domain of list PAC learning. We focus on uniform convergence (which is the basis of Empirical Risk Minimization) and on […]

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arXiv:2302.00941v3 Announce Type: replace-cross Abstract: We propose a novel statistical learning method for multi-item auctions that incorporates credible intervals. Our approach employs nonparametric density estimation to estimate credible intervals for bidder types based on historical data. We introduce two new strategies that leverage these credible intervals to reduce the time cost of implementing auctions. The first strategy screens potential winners’ value regions within the credible intervals, while the second strategy simplifies the type distribution when the length of […]

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arXiv:2601.16120v2 Announce Type: replace Abstract: Imbalanced classification often causes standard training procedures to prioritize the majority class and perform poorly on rare but important cases. A classic and widely used remedy is to augment the minority class with synthetic samples, but two basic questions remain under-resolved: when does synthetic augmentation actually help, and how many synthetic samples should be generated? We develop a unified statistical framework for synthetic augmentation in imbalanced learning, studying models trained on imbalanced data […]

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