Korba, A;
Salim, A;
Arbel, M;
Luise, G;
Gretton, A;
(2020)
A Non-Asymptotic Analysis for
Stein Variational Gradient Descent.
In: Larochelle, H. and Ranzato, M. and Hadsell, R. and Balcan, M.F. and Lin, H., (eds.)
NIPS'20: Proceedings of the 34th International Conference on Neural Information Processing Systems.
Neural Information Processing Systems Conference: Vancouver, Canada.
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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 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.
| Type: | Proceedings paper |
|---|---|
| Title: | A Non-Asymptotic Analysis for Stein Variational Gradient Descent |
| Event: | NIPS'20: 34th International Conference on Neural Information Processing Systems |
| ISBN-13: | 978-1-7138-2954-6 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.neurips.cc/paper/2020/hash/320... |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10166658 |
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