Gradient-based adaptive importance samplers

Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability distribution. 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.& COPY; 2023 The Author(s). Published by Elsevier Inc. on behalf of The Franklin Institute.This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

In this paper, we propose an adaptive importance sampler called GRAMIS that iteratively improves the set of proposal distributions by utilizing geometric information of the target. We also introduce a repulsion term to allow for coordinated exploration and provide a theoretical justification for it. The results show that GRAMIS performs well in problems with challenging shapes that cannot be easily approximated by a standard uni-modal proposal.