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This paper introduces a scalable variational inference framework for non-Gaussian spatial fields by mirroring the sparse autoregressive structure of the GP prior within the variational family, employing normalizing-flow conditionals for expressiveness. The approach amortizes variational parameters using a shared neural conditioner and achieves polylogarithmic complexity per iteration through doubly stochastic optimization with reduced ancestor sets. This enables efficient inference on large non-Gaussian spatial datasets where traditional methods are intractable or too slow.
Normalizing-flow conditionals and amortized variational inference unlock scalable, non-Gaussian spatial field modeling previously hindered by intractability.
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.