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

arXiv: https://arxiv.org/abs/2409.19208 · HTML: https://mlsanity.com/paper/2409.19208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 28 Sep 2024.

## Builds on (most cited first, 16 of 16)

- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Sparse Cholesky factorization by Kullback-Leibler minimization](https://mlsanity.com/paper/2004.14455/) (2020)
- [Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity](https://mlsanity.com/paper/1706.02205/) (2017)
- [Vecchia approximations of Gaussian-process predictions](https://mlsanity.com/paper/1805.03309/) (2018)
- [Correlation-based sparse inverse Cholesky factorization for fast Gaussian-process inference](https://mlsanity.com/paper/2112.14591/) (2021)
- [Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields](https://mlsanity.com/paper/2108.04211/) (2021)
- [Vecchia-Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data](https://mlsanity.com/paper/1906.07828/) (2019)
- [Hierarchical sparse Cholesky decomposition with applications to high-dimensional spatio-temporal filtering](https://mlsanity.com/paper/2006.16901/) (2020)
- [Modeling spatial data using local likelihood estimation and a Mat'ern to SAR translation](https://mlsanity.com/paper/2002.01124/) (2020)
- [Modeling and emulation of nonstationary Gaussian fields](https://mlsanity.com/paper/1711.08077/) (2017)
- [Bayesian nonparametric generative modeling of large multivariate non-Gaussian spatial fields](https://mlsanity.com/paper/2311.06220/) (2023)
- [Bayesian nonstationary and nonparametric covariance estimation for large spatial data](https://mlsanity.com/paper/2012.05967/) (2020)

## Built on by (most cited first, 1 of 1)

- [LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data](https://mlsanity.com/paper/2505.09803/) (2025)

## Abstract (arXiv)

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.