%0 Generic
%A Korba, A
%A Salim, A
%A Arbel, M
%A Luise, G
%A Gretton, A
%C Vancouver, Canada
%D 2020
%E Larochelle, H.
%E Ranzato, M.
%E Hadsell, R.
%E Balcan, M.F.
%E Lin, H.
%F discovery:10166658
%I Neural Information Processing Systems Conference
%T A Non-Asymptotic Analysis for  Stein Variational Gradient Descent
%U https://discovery.ucl.ac.uk/id/eprint/10166658/
%V 2020
%X 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 provide a descent lemma  establishing that the algorithm decreases the objective at each iteration, and rates  of convergence for the averaged Stein Fisher divergence (also referred to as Kernel  Stein Discrepancy). We also provide a convergence result of the finite particle  system corresponding to the practical implementation of SVGD to its population  version.
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