BR-SNIS: Bias Reduced Self-Normalized Importance Sampling

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Gabriel Cardoso, Sergey Samsonov, Achille Thin, Eric Moulines, Jimmy Olsson


Importance Sampling (IS) is a method for approximating expectations with respect to a target distribution using independent samples from a proposal distribution and the associated to importance weights. In many cases, the target distribution is known up to a normalization constant and self-normalized IS (SNIS) is then 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 SNIS and which significantly reduces bias. This method is a wrapper, in the sense that it uses the same proposal samples and importance weights but makes a clever use of iterated sampling-importance-resampling (i-SIR) to form a bias-reduced version of the estimator. We derive the proposed algorithm with rigorous theoretical results, including novel bias, variance, and high-probability bounds. We illustrate our findings with numerical examples.