Long-time asymptotics of noisy SVGD outside the population limit - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Long-time asymptotics of noisy SVGD outside the population limit

Abstract

Stein Variational Gradient Descent (SVGD) is a widely used sampling algorithm that has been successfully applied in several areas of Machine Learning. SVGD operates by iteratively moving a set of interacting particles (which represent the samples) to approximate the target distribution. Despite recent studies on the complexity of SVGD and its variants, their long-time asymptotic behavior (i.e., after numerous iterations ) is still not understood in the finite number of particles regime. We study the long-time asymptotic behavior of a noisy variant of SVGD. First, we establish that the limit set of noisy SVGD for large is well-defined. We then characterize this limit set, showing that it approaches the target distribution as increases. In particular, noisy SVGD provably avoids the variance collapse observed for SVGD. Our approach involves demonstrating that the trajectories of noisy SVGD closely resemble those described by a McKean-Vlasov process.
Fichier principal
Vignette du fichier
SVGDv2.pdf (384.67 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04612246 , version 1 (14-06-2024)
hal-04612246 , version 2 (20-06-2024)

Licence

Identifiers

  • HAL Id : hal-04612246 , version 2

Cite

Victor Priser, Pascal Bianchi, Adil Salim. Long-time asymptotics of noisy SVGD outside the population limit. 2024. ⟨hal-04612246v2⟩
141 View
1 Download

Share

Gmail Mastodon Facebook X LinkedIn More