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Anna KORBA (CREST) – ” A Non Asymptotic Analysis of Stein Variational Gradient Descent “
September 14, 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 14th of september 2020
Anna KORBA (CREST) – “A Non Asymptotic Analysis of Stein Variational Gradient Descent “
Abstract: 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 ℝd. 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 provide a descent lemma establishing that the algorithm decreases the objective at each iteration, and rates of convergence.
We also provide a convergence result of the finite particle system corresponding to the practical implementation of SVGD to its population version.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Zoltan SZABO (CMAP)