Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:00 pm
Date: 31th March
Place: 3001

Krishna BALASUBRAMANIAN (UC DAVIS)- Finite-Particle Convergence of (Regularized) Stein Variational Gradient Descent

 Abstract: 

Stein Variational Gradient Descent (SVGD) is a widely used particle-based algorithm for approximate Bayesian inference. To address the intrinsic bias of SVGD, a regularized variant (R-SVGD) has been proposed that applies a resolvent-type preconditioner to the kernelized Wasserstein gradient. In this talk, I present recent results establishing explicit non-asymptotic finite-particle convergence guarantees for both SVGD and R-SVGD. The analysis is based on an entropy method for interacting particle systems, showing that the time derivative of the relative entropy between the joint law of the particles and the product target measure decomposes into a dominant negative term proportional to the number of particles times the expected squared Kernelized Stein Discrepancy (KSD²), together with a smaller positive correction. This structure yields finite-particle convergence rates of order (N^{-1/2}) in KSD and Fisher information for SVGD and R-SVGD respectively. Under mild assumptions on the kernel and the target potential, the resulting bounds grow only polynomially with the dimension. The analysis further yields Wasserstein convergence rates for both algorithms, as well as marginal convergence and long-time propagation of chaos for the interacting particle system.

Organizers:

Anna KORBA (CREST), Vincent DIVOL (CREST) , Jaouad MOURTADA (CREST)

Sponsors:
CREST-CMAP