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Title: A Robust Solution to Variational Importance Sampling of Minimum Variance
Author: Hernández González, Jerónimo
Cerquides Bueno, Jesús
Keywords: Mètode de Montecarlo
Estadística bayesiana
Distribució (Teoria de la probabilitat)
Factorització (Matemàtica)
Algorismes computacionals
Monte Carlo method
Bayesian statistical decision
Distribution (Probability theory)
Factorization (Mathematics)
Computer algorithms
Issue Date: 12-Dec-2020
Publisher: MDPI
Abstract: Importance sampling is a Monte Carlo method where samples are obtained from an alternative proposal distribution. This can be used to focus the sampling process in the relevant parts of space, thus reducing the variance. Selecting the proposal that leads to the minimum variance can be formulated as an optimization problem and solved, for instance, by the use of a variational approach. Variational inference selects, from a given family, the distribution which minimizes the divergence to the distribution of interest. The Rényi projection of order 2 leads to the importance sampling estimator of minimum variance, but its computation is very costly. In this study with discrete distributions that factorize over probabilistic graphical models, we propose and evaluate an approximate projection method onto fully factored distributions. As a result of our evaluation it becomes apparent that a proposal distribution mixing the information projection with the approximate Rényi projection of order 2 could be interesting from a practical perspective.
Note: Reproducció del document publicat a:
It is part of: Entropy, 2020, vol. 22, num. 12, p. 1405
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ISSN: 1099-4300
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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