A Non-Asymptotic Analysis for Stein Variational Gradient Descent

by   Anna Korba, et al.

We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution π∝ e^-V on R^d. In the population limit, SVGD performs gradient descent in the space of probability distributions on the KL divergence with respect to π, where the gradient is smoothed through a kernel integral operator. In this paper, we provide a novel finite time analysis for the SVGD algorithm. We obtain a descent lemma establishing that the algorithm decreases the objective at each iteration, and provably converges, with less restrictive assumptions on the step size than required in earlier analyses. We further provide a guarantee on the convergence rate in Kullback-Leibler divergence, assuming π satisfies a Stein log-Sobolev inequality as in Duncan et al. (2019), which takes into account the geometry induced by the smoothed KL gradient.



There are no comments yet.


page 1

page 2

page 3

page 4


Stein Variational Gradient Descent as Gradient Flow

Stein variational gradient descent (SVGD) is a deterministic sampling al...

Complexity Analysis of Stein Variational Gradient Descent Under Talagrand's Inequality T1

We study the complexity of Stein Variational Gradient Descent (SVGD), wh...

Homeomorphic-Invariance of EM: Non-Asymptotic Convergence in KL Divergence for Exponential Families via Mirror Descent

Expectation maximization (EM) is the default algorithm for fitting proba...

Kernel Stein Discrepancy Descent

Among dissimilarities between probability distributions, the Kernel Stei...

Sampling with Mirrored Stein Operators

We introduce a new family of particle evolution samplers suitable for co...

Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry

We study the Proximal Langevin Algorithm (PLA) for sampling from a proba...

Accelerated Flow for Probability distributions

This paper presents a methodology and numerical algorithms for construct...

Code Repositories

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.