BR-SNIS: Bias Reduced Self-Normalized Importance Sampling

• URL: http://arxiv.org/abs/2207.06364v1
• Date: Wed, 13 Jul 2022 17:14:10 GMT
• Title: BR-SNIS: Bias Reduced Self-Normalized Importance Sampling
• Authors: Gabriel Cardoso, Sergey Samsonov, Achille Thin, Eric Moulines, Jimmy Olsson
• Abstract summary: Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. We propose a new method, BR-SNIS, whose complexity is essentially the same as that of SNIS and which significantly reduces bias without increasing the variance. We furnish the proposed algorithm with rigorous theoretical results, including new bias, variance and high-probability bounds.
• Score: 11.150337082767862
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. In many applications, the target distribution is known only up to a normalization constant, in which case self-normalized IS (SNIS) can be used. While the use of self-normalization can have a positive effect on the dispersion of the estimator, it introduces bias. In this work, we propose a new method, BR-SNIS, whose complexity is essentially the same as that of SNIS and which significantly reduces bias without increasing the variance. This method is a wrapper in the sense that it uses the same proposal samples and importance weights as SNIS, but makes clever use of iterated sampling--importance resampling (ISIR) to form a bias-reduced version of the estimator. We furnish the proposed algorithm with rigorous theoretical results, including new bias, variance and high-probability bounds, and these are illustrated by numerical examples.

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