Gradient-based Adaptive Importance Samplers

TL;DR

The paper introduces GRAMIS, an adaptive importance sampling algorithm that iteratively refines proposals using geometric information and a repulsion mechanism, improving exploration and approximation of complex target distributions.

Contribution

It proposes a novel adaptive importance sampler with a repulsion term for cooperative proposal adaptation, enhancing exploration of complex target distributions.

Findings

GRAMIS effectively handles challenging target shapes.

The repulsion term improves proposal diversity.

Experimental results show superior performance over standard methods.

Abstract

Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of the proposal distributions where the samples are simulated from. In this paper, we propose an adaptive importance sampler, called GRAMIS, that iteratively improves the set of proposals. The algorithm exploits geometric information of the target to adapt the location and scale parameters of those proposals. Moreover, in order to allow for a cooperative adaptation, a repulsion term is introduced that favors a coordinated exploration of the state space. This translates into a more diverse exploration and a better approximation of the target via the mixture of proposals. Moreover, we provide a theoretical justification of the repulsion term. We show the good performance of GRAMIS in two problems where the target has a challenging shape and cannot be easily approximated by a standard uni-modal proposal.