Doubly Adaptive Importance Sampling

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.

37 pages, 13 figures

References in corpus (4)

• A weakly informative default prior distribution for logistic and other regression models
• Expectation Propagation for approximate Bayesian inference
• A Contrastive Divergence for Combining Variational Inference and MCMC
• Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence