# Implicitly Adaptive Importance Sampling

## TL;DR

This paper introduces an implicit adaptive importance sampling method that effectively handles complex distributions without closed-form expressions, improving Bayesian cross-validation performance with low computational cost.

## Contribution

The authors propose a novel implicit adaptive importance sampling technique that matches moments of Monte Carlo samples to importance-weighted moments for complex distributions.

## Key findings

- Outperforms existing parametric adaptive importance sampling methods
- Effective for complex distributions without closed-form expressions
- Computationally inexpensive compared to traditional methods

## Abstract

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In this work, we present an implicit adaptive importance sampling method that applies to complicated distributions which are not available in closed form. The method iteratively matches the moments of a set of Monte Carlo draws to weighted moments based on importance weights. We apply the method to Bayesian leave-one-out cross-validation and show that it performs better than many existing parametric adaptive importance sampling methods while being computationally inexpensive.