# Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields

arXiv: https://arxiv.org/abs/2108.04211 · HTML: https://mlsanity.com/paper/2108.04211/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2021.

## Built on by (most cited first, 10 of 10)

- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences](https://mlsanity.com/paper/2309.15366/) (2023)
- [Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transport](https://mlsanity.com/paper/2201.09485/) (2022)
- [Learning non-Gaussian spatial distributions via Bayesian transport maps with parametric shrinkage](https://mlsanity.com/paper/2409.19208/) (2024)
- [Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport](https://mlsanity.com/paper/2603.19058/) (2026)
- [Density correction for multivariate spatial fields of global climate model output using deep learning](https://mlsanity.com/paper/2411.18799/) (2024)
- [Multifidelity Formulations for Triangular Transport](https://mlsanity.com/paper/2610.00698/) (2026)
- [Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields](https://mlsanity.com/paper/2610.13656/) (2026)

## Abstract (arXiv)

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while still resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output.