Doubly Adaptive Importance Sampling

TL;DR

This paper introduces a hybrid adaptive importance sampling method that combines variational inference and importance sampling, optimizing posterior approximations efficiently and accurately.

Contribution

It presents a novel hybrid scheme that adaptively interpolates between variational inference and importance sampling for Gaussian posteriors.

Findings

Effective sample size is maintained at fixed computational cost.

Method is embarrassingly parallel and adaptable to different posteriors.

Numerical results demonstrate competitiveness with existing methods.

Abstract

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow. Therefore, we propose a hybrid where, at each iteration, the Monte Carlo effective sample size can be guaranteed at a fixed computational cost by interpolating between natural-gradient variational inference and importance sampling. The amount of damping in the updates adapts to the posterior and guarantees the effective sample size. Gaussianity enables the use of Stein's lemma to obtain gradient-based optimization in the highly damped variational inference regime and a reduction of Monte Carlo error for undamped adaptive importance sampling. The result is a generic, embarrassingly parallel and adaptive posterior approximation method. Numerical studies on simulated and real data show its competitiveness with other, less general methods.