Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage

TL;DR

This paper introduces ShrinkTM, an improved Bayesian transport map method that combines parametric Gaussian shrinkage and scalable approximations to better learn complex non-Gaussian spatial distributions from limited data.

Contribution

The paper proposes ShrinkTM, a novel Bayesian transport map method that enhances existing approaches by incorporating parametric Gaussian shrinkage and scalability techniques.

Findings

ShrinkTM outperforms existing BTM in small-sample scenarios.

ShrinkTM can outperform the base Gaussian family with minimal training data.

Numerical experiments validate ShrinkTM's superior accuracy on simulated and climate data.

Abstract

Many applications, including climate-model analysis and stochastic weather generators, require learning or emulating the distribution of a high-dimensional and non-Gaussian spatial field based on relatively few training samples. To address this challenge, a recently proposed Bayesian transport map (BTM) approach consists of a triangular transport map with nonparametric Gaussian-process (GP) components, which is trained to transform the distribution of interest distribution to a Gaussian reference distribution. To improve the performance of this existing BTM, we propose to shrink the map components toward a ``base'' parametric Gaussian family combined with a Vecchia approximation for scalability. The resulting ShrinkTM approach is more accurate than the existing BTM, especially for small numbers of training samples. It can even outperform the ``base'' family when trained on a single sample of the spatial field. We demonstrate the advantage of ShrinkTM though numerical experiments on simulated data and on climate-model output.