Complexity Analysis of Stein Variational Gradient Descent Under Talagrand's Inequality T1

• URL: http://arxiv.org/abs/2106.03076v1
• Date: Sun, 6 Jun 2021 09:51:32 GMT
• Title: Complexity Analysis of Stein Variational Gradient Descent Under Talagrand's Inequality T1
• Authors: Adil Salim and Lukang Sun and Peter Richt\'arik
• Abstract summary: We study the complexity of Stein Variational Gradient Descent (SVGD), which is an algorithm to sample from $pi(x) propto exp(-Fx)) Our key assumption is that the target distribution satisfies the inequality's inequality T1.
• Score: 12.848239550098697
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the complexity of Stein Variational Gradient Descent (SVGD), which is an algorithm to sample from $\pi(x) \propto \exp(-F(x))$ where $F$ smooth and nonconvex. We provide a clean complexity bound for SVGD in the population limit in terms of the Stein Fisher Information (or squared Kernelized Stein Discrepancy), as a function of the dimension of the problem $d$ and the desired accuracy $\varepsilon$. Unlike existing work, we do not make any assumption on the trajectory of the algorithm. Instead, our key assumption is that the target distribution satisfies Talagrand's inequality T1.

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