Deep Importance Sampling based on Regression for Model Inversion and Emulation

TL;DR

This paper introduces RADIS, an adaptive importance sampling framework that uses regression-based deep architectures to construct non-parametric proposal densities, improving efficiency and accuracy in Bayesian inference and model emulation.

Contribution

RADIS is a novel adaptive importance sampling method that employs regression and deep architectures to create flexible proposal densities, enhancing convergence and surrogate modeling capabilities.

Findings

RADIS converges asymptotically to an exact sampler.

The emulator can serve as a cheap surrogate model.

Numerical experiments demonstrate improved performance over existing methods.

Abstract

Understanding systems by forward and inverse modeling is a recurrent topic of research in many domains of science and engineering. In this context, Monte Carlo methods have been widely used as powerful tools for numerical inference and optimization. They require the choice of a suitable proposal density that is crucial for their performance. For this reason, several adaptive importance sampling (AIS) schemes have been proposed in the literature. We here present an AIS framework called Regression-based Adaptive Deep Importance Sampling (RADIS). In RADIS, the key idea is the adaptive construction via regression of a non-parametric proposal density (i.e., an emulator), which mimics the posterior distribution and hence minimizes the mismatch between proposal and target densities. RADIS is based on a deep architecture of two (or more) nested IS schemes, in order to draw samples from the constructed emulator. The algorithm is highly efficient since employs the posterior approximation as proposal density, which can be improved adding more support points. As a consequence, RADIS asymptotically converges to an exact sampler under mild conditions. Additionally, the emulator produced by RADIS can be in turn used as a cheap surrogate model for further studies. We introduce two specific RADIS implementations that use Gaussian Processes (GPs) and Nearest Neighbors (NN) for constructing the emulator. Several numerical experiments and comparisons show the benefits of the proposed schemes. A real-world application in remote sensing model inversion and emulation confirms the validity of the approach.