Implicitly Adaptive Importance Sampling

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.

arXiv commentMajor revision: More comparisons to adaptive importance sampling with parametric distributions

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• Projective Inference in High-dimensional Problems: Prediction and Feature Selection
• Detecting and diagnosing prior and likelihood sensitivity with power-scaling
• Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors
• Robust leave-one-out cross-validation for high-dimensional Bayesian models
• Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
• Uncertainty in Bayesian Leave-One-Out Cross-Validation Based Model Comparison
• $R^{\ast }$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers
• Adaptive Path Sampling in Metastable Posterior Distributions
• Doubly Adaptive Importance Sampling