A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

Adil Salim; Lukang Sun; Peter Richtárik

A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

Adil Salim^*, Lukang Sun, Peter Richtárik

^*Corresponding author for this work

Research output: Contribution to conference › Paper › peer-review

9 Scopus citations

Abstract

Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.

Original language	English (US)
Pages	19139-19152
Number of pages	14
State	Published - 2022
Event	39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States Duration: Jul 17 2022 → Jul 23 2022

Conference

Conference	39th International Conference on Machine Learning, ICML 2022
Country/Territory	United States
City	Baltimore
Period	07/17/22 → 07/23/22

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Cite this

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title = "A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1",

abstract = "Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.",

author = "Adil Salim and Lukang Sun and Peter Richt{\'a}rik",

note = "Publisher Copyright: Copyright {\textcopyright} 2022 by the author(s); 39th International Conference on Machine Learning, ICML 2022 ; Conference date: 17-07-2022 Through 23-07-2022",

year = "2022",

language = "English (US)",

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T1 - A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

AU - Salim, Adil

AU - Sun, Lukang

AU - Richtárik, Peter

PY - 2022

Y1 - 2022

N2 - Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.

AB - Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a target density which is known up to a multiplicative constant. Although SVGD is a popular algorithm in practice, its theoretical study is limited to a few recent works. We study the convergence of SVGD in the population limit, (i.e., with an infinite number of particles) to sample from a non-logconcave target distribution satisfying Talagrand's inequality T1. We first establish the convergence of the algorithm. Then, we establish a dimension-dependent complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike existing works, we do not assume that the KSD is bounded along the trajectory of the algorithm. Our approach relies on interpreting SVGD as a gradient descent over a space of probability measures.

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M3 - Paper

AN - SCOPUS:85163085137

SP - 19139

EP - 19152

T2 - 39th International Conference on Machine Learning, ICML 2022

Y2 - 17 July 2022 through 23 July 2022

ER -

A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1

Abstract

Conference

ASJC Scopus subject areas

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