April 2021 Safe adaptive importance sampling: A mixture approach
Bernard Delyon, François Portier
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Ann. Statist. 49(2): 885-917 (April 2021). DOI: 10.1214/20-AOS1983


This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a “safe” heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward the target density; (ii) a central limit theorem is obtained for the resulting integral estimates. The fact that the asymptotic variance is the same as the variance of an “oracle” procedure with variance-optimal policy, illustrates the benefits of the approach. In addition, a subsampling step (among the particles) can be conducted before constructing the kernel estimate in order to decrease the computational effort without altering the performance of the method. The practical behavior of the algorithms is illustrated in a simulation study.


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Bernard Delyon. François Portier. "Safe adaptive importance sampling: A mixture approach." Ann. Statist. 49 (2) 885 - 917, April 2021. https://doi.org/10.1214/20-AOS1983


Received: 1 September 2019; Revised: 1 March 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1983

Primary: 62G07 , 65C05
Secondary: 60F05

Keywords: Adaptive importance sampling , kernel density estimation , martingale methods , Monte Carlo methods

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 2 • April 2021
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