Nüsken, N. and Renger, M.
(2021)
*Stein Variational Gradient Descent:
many-particle and long-time asymptotics.*
arXive
.
pp. 1-25.
(Unpublished)

PDF
733kB |

Official URL: https://arxiv.org/pdf/2102.12956.pdf

## Abstract

Stein variational gradient descent (SVGD) refers to a class of methods for Bayesian inference based on interacting particle systems. In this paper, we consider the originally proposed deterministic dynamics as well as a stochastic variant, each of which represent one of the two main paradigms in Bayesian computational statistics: variational inference and Markov chain Monte Carlo. As it turns out, these are tightly linked through a correspondence between gradient flow structures and large-deviation principles rooted in statistical physics. To expose this relationship, we develop the cotangent space construction for the Stein geometry, prove its basic properties, and determine the large-deviation functional governing the many-particle limit for the empirical measure. Moreover, we identify the Stein-Fisher information (or kernelised Stein discrepancy) as its leading order contribution in the long-time and many-particle regime in the sense of T-convergence, shedding some light on the finite-particle properties of SVGD. Finally, we establish a comparison principle between the Stein-Fisher information and RKHS-norms that might be of independent interest.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2505 |

Deposited By: | Monika Drueck |

Deposited On: | 02 Mar 2021 14:46 |

Last Modified: | 02 Mar 2021 14:46 |

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