Robust Covariance Adaptation in Adaptive Importance Sampling

Abstract

Importance sampling (IS) is a Monte Carlo methodology that allows for approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to poor performance in subsequent iterations of the algorithm. In this paper, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations.

References in corpus (10)

• Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
• Pareto Smoothed Importance Sampling
• Adaptive Importance Sampling in General Mixture Classes
• Effective Sample Size for Importance Sampling based on discrepancy measures
• Generalized Multiple Importance Sampling
• Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes
• Efficient Multiple Importance Sampling Estimators
• Group Importance Sampling for Particle Filtering and MCMC
• A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models
• Heretical Multiple Importance Sampling

Cited by in corpus (7)

• Optimized Population Monte Carlo
• Hamiltonian Adaptive Importance Sampling
• Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation
• Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals
• An Analysis by Synthesis Method that Allows Accurate Spatial Modeling of Thickness of Cortical Bone from Clinical QCT
• Advances in Importance Sampling
• An Adaptive-Importance-Sampling-Enhanced Bayesian Approach for Topology Estimation in an Unbalanced Power Distribution System