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This paper introduces a scalable variational inference framework designed to handle non-Gaussian spatial fields by leveraging sparse autoregressive structures and normalizing flows. By amortizing parameters through a shared neural conditioner, the method achieves polylogarithmic complexity, addressing key bottlenecks in training large-scale latent field models. The work represents a significant advancement in probabilistic machine learning for complex statistical datasets.
Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields
arXiv:2610.13656v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO); Methodology (stat.ME)
arXiv:2610.13656 [stat.ML]
(or arXiv:2610.13656v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.13656 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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