January 2026

arXiv:2503.09887v3 Announce Type: replace-cross Abstract: We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This operator-theoretic framework yields explicit exponential decay rates of Sinkhorn iterates toward Schr”odinger bridges with respect to a broad class of $phi$-divergences and Kantorovich-type distances, including relative entropy, squared Hellinger integrals, $alpha$-divergences, weighted total variation norms, and Wasserstein distances. To the best of our knowledge, […]

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arXiv:2503.06917v4 Announce Type: replace-cross Abstract: In zeroth-order optimization, we seek to minimize a function $d(cdot)$, which may encode combinatorial feasibility, using only function evaluations. We focus on the setting where solutions must also satisfy qualitative constraints or conform to a complex prior distribution. To address this, we introduce a new framework in which such constraints are represented by an initial generative prior $L(cdot)$, for example, a Large Language Model (LLM). The objective is to find solutions $s$ that […]

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arXiv:2502.07580v3 Announce Type: replace-cross Abstract: We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to iteratively narrow down the unknown sample starting from a broad initial belief. In addition to a rigorous theoretical analysis, we establish a connection between our model and diffusion models […]

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arXiv:2502.02580v3 Announce Type: replace-cross Abstract: In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional anisotropic mixtures. We propose a new clustering method, Covariance Projected Spectral Clustering (COPO), which adapts to a wide range of dependent noise structures. We first project the data onto a low-dimensional space via eigen-decomposition of a diagonal-deleted Gram matrix. Our central methodological idea is […]

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arXiv:2501.00677v2 Announce Type: replace-cross Abstract: Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to […]

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arXiv:2410.14485v5 Announce Type: replace-cross Abstract: Artificial Neural Networks (ANNs), including fully-connected networks and transformers, are highly flexible and powerful function approximators, widely applied in fields like computer vision and natural language processing. However, their inability to inherently respect causal structures can limit their robustness, making them vulnerable to covariate shift and difficult to interpret/explain. This poses significant challenges for their reliability in real-world applications. In this paper, we introduce Causal Transformers (CaTs), a general model class designed to […]

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arXiv:2407.10070v3 Announce Type: replace-cross Abstract: Kernel ridge regression (KRR) is a fundamental computational tool, appearing in problems that range from computational chemistry to health analytics, with a particular interest due to its starring role in Gaussian process regression. However, full KRR solvers are challenging to scale to large datasets: both direct (i.e., Cholesky decomposition) and iterative methods (i.e., PCG) incur prohibitive computational and storage costs. The standard approach to scale KRR to large datasets chooses a set of […]

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arXiv:2407.05895v2 Announce Type: replace-cross Abstract: Travel time estimation is a key task in navigation apps and web mapping services. Existing deterministic and probabilistic methods, based on the assumption of trip independence, predominantly focus on modeling individual trips while overlooking trip correlations. However, real-world conditions frequently introduce strong correlations between trips, influenced by external and internal factors such as weather and the tendencies of drivers. To address this, we propose a deep hierarchical joint probabilistic model ProbETA for travel […]

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arXiv:2407.02700v4 Announce Type: replace-cross Abstract: This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a Simulated Annealing (SA) algorithm tailored to operate within constrained domains and ensure convergence towards global optima. The method effectively addresses the challenges posed by the lack of local geometric information and the high non-linearity inherent to DNNs, making it applicable to a wide variety of architectures, with a special focus on Residual Networks […]

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arXiv:2309.13183v3 Announce Type: replace-cross Abstract: Information Value (IV) is a widely used technique for feature selection prior to the modeling phase, particularly in credit scoring and related domains. However, conventional IV-based practices rely on fixed empirical thresholds, which lack statistical justification and may be sensitive to characteristics such as class imbalance. In this work, we develop a formal statistical framework for IV by establishing its connection with Jeffreys divergence and propose a novel nonparametric hypothesis test, referred to […]

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