Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent
- Type
- other
- Venue
- arXiv / University of North Carolina at Chapel Hill / UC Davis / University of Chicago
Summary
Relative-entropy derivative of the N-particle joint vs π^{⊗N} splits into a dominant negative N·E[KSD²] term and a smaller positive term, giving KSD rates of order 1/√N in continuous and discrete time — a near-optimal double-exponential improvement over Shi and Mackey 2024 that matches i.i.d. rates. Bounds grow polynomially in d under mild kernel/potential assumptions. A bilinear kernel component yields W2 convergence; bilinear+Matérn shows an i.i.d.-like curse of dimensionality. Also time-averaged marginal convergence and long-time propagation of chaos. Theory only; no experiments. No official code on abs.
Keywords
svgd · ksd · wasserstein · particle-methods · sampling · unc · uc-davis · uchicago · theory
Topics
SVGD, sampling, kernelized Stein discrepancy, particle methods
Research notes
- Primary: arxiv abs (math.ST / cs.LG / math.PR / stat.ML). UNC Chapel Hill / UC Davis / UChicago; correspondence sayan@email.unc.edu, kbala@ucdavis.edu, promit@uchicago.edu. No official code on abs. HF has no paper page (API 404). Discord posted abs. Theory-only; no datasets_local row. ArXiv HTML states perpetual non-exclusive license; license field left blank per catalog convention.