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PreprintCC BY 4.0arXiv

Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

  • Paul F. V. Wiemann
  • Matthias Katzfuss
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{wiemann2026scalable,
  title = {{Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields}},
  author = {Paul F. V. Wiemann and Matthias Katzfuss},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13656},
  eprint = {2610.13656},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13656},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields
AU  - Paul F. V. Wiemann
AU  - Matthias Katzfuss
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13656
UR  - https://arxiv.org/abs/2610.13656
AB  - 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.
ER  -