International Seminar on Monte Carlo Methods

A weekly online seminar on all aspects of Monte Carlo methods.

Join us weekly to explore recent developments and connect with a diverse community of passionate researchers in this exciting field!

Videos of past talks available on YouTube.

• Speaker: Nicolas Chopin (ENSAE, Institut Polytechnique de Paris) [Zoom Link]

• Title: A connection between Tempering SMC and Entropic Mirror Descent

• Abstract: In this talk, I will discuss the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density pi is known. My co-authors and myself have established that tempering SMC corresponds to entropic mirror descent applied to the reverse Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be seen as a descent scheme of the KL divergence with respect to the Fisher-Rao geometry, in contrast to Langevin dynamics that perform descent of the KL with respect to the Wasserstein-2 geometry. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and derive adaptive tempering rules that improve over other alternative benchmarks in the literature.

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