arXiv Statistics ML
Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains
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arXiv Machine Learning
Jun 2
How Accurately Can a Gaussian Approximate Stochastic Approximation Iterates?
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
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 AI
Jun 8
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv Machine Learning
4d ago
Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
arXiv:2609. 12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz.
arXiv Machine Learning
Jun 9
Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
arXiv Machine Learning
Sep 1
Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD
The paper proves quantitative convergence to the target distribution and uniform‑in‑time propagation of chaos for Langevin‑regularized Stein variational gradient descent (SVGD). It shows that both the Stein interaction and the Langevin drift dissipate the same relative entropy, yielding exponential convergence under a log‑Sobolev inequality and providing finite‑particle entropy identities for empirical measures. Two finite‑time approaches—synchronous coupling and moving‑product entropy—are developed to give explicit Wasserstein, kernel Stein discrepancy, and total variation bounds, leading to polynomial uniform‑in‑time propagation of chaos rates.