# Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

arXiv: https://arxiv.org/abs/2610.13656 · HTML: https://mlsanity.com/paper/2610.13656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [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)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields](https://mlsanity.com/paper/2108.04211/) (2021)
- [Bayesian nonparametric generative modeling of large multivariate non-Gaussian spatial fields](https://mlsanity.com/paper/2311.06220/) (2023)

## Abstract (arXiv)

Latent field models are essential for spatial statistics, but the posterior distribution of the latent field, even with a Gaussian process (GP) prior, is analytically intractable whenever the likelihood is non-Gaussian. Existing approximations are either too slow or too restrictive for large non-Gaussian datasets. We present a scalable variational inference framework that mirrors the sparse nearest-neighbor autoregressive structure of the prior in the variational family, uses normalizing-flow conditionals for expressiveness, and amortizes all variational parameters via a single shared neural conditioner. Doubly stochastic optimization with reduced ancestor sets achieves polylogarithmic complexity per iteration.