arXiv Machine Learning
Jul 9
Finding a stationary point of a stochastic convex problem
arXiv:2607. 06883v1 Announce Type: cross Abstract: We consider the problem of finding stationary points for stochastic convex optimization problems.
Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels
The paper investigates the large‑sample variational problem for t‑Distributed Stochastic Neighbor Embedding (t‑SNE) using a broad class of input and output kernels. It shows that an entropy equation uniquely determines the scale parameter of the input kernel at interior points of positive density, and provides sufficient conditions for the existence and uniform boundedness of solutions across the entire support. Under these conditions, together with a decay assumption on the output kernel, the discrete optimal values converge to a continuum minimum, and empirical measures of approximate minimizers are tight after translation, yielding compactly supported minimizers that satisfy the equilibrium equation. The study includes Gaussian and, in two dimensions, Cauchy output kernels, and presents numerical comparisons of two‑dimensional representations obtained with different kernels.
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arXiv Machine Learning
Jul 28
Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
arXiv Machine Learning
Jun 30
Concentration bounds on response-based vector embeddings of black-box generative models
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arXiv Machine Learning
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Uniform Discrete Diffusion Models are Minimax Optimal for Estimating Distributions with Small Effective Support Size
arXiv:2610.07655v1 Announce Type: cross Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...
arXiv AI
Oct 9
A PDE Perspective on Generative Diffusion Models
arXiv:2511. 05940v3 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains.
arXiv Statistics ML
Sep 30
A functional central limit theorem for kernel gradient flow and infinitesimal gradient boosting
arXiv:2606.25494v2 Announce Type: replace-cross Abstract: Building on the large-sample analysis of infinitesimal gradient boosting (Dombry and Duchamps, 2024), we study the fluctuations of the proces...
arXiv Machine Learning
Aug 10
A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-{\L}ojasiewicz condition
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
arXiv Computer Vision
Aug 25
Stochastic Separability of Embedding Manifolds
arXiv:2608.22874v1 Announce Type: cross Abstract: Neurobiological studies and representation learning have observed that representations of objects belonging to the same category in high-dimensional...
arXiv Machine Learning
Aug 7
On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities
arXiv:2608. 06182v1 Announce Type: cross Abstract: We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set.
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Aug 24
Stochastic Separability of Embedding Manifolds
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arXiv Machine Learning
Jul 7
Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
arXiv Machine Learning
Jul 21
Concentration and Mean-Square Bounds for Contractive Stochastic Approximation: A Unified Elementary Approach
arXiv:2607. 17595v1 Announce Type: new Abstract: We establish mean-square and concentration bounds for stochastic approximation (SA) with arbitrary norm contractive mappings, under a multiplicative noise model where the noise may scale affinely with the norm of the iterates, and the iterates are potentially unbounded.