Scalable method speeds complex spatial data modeling with neural networks
Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields
Machine Learning
Summary
Modeling spatial data that doesn’t follow simple patterns is very hard because the usual math tricks don’t work well. The authors developed a new method that uses a special kind of neural network to approximate these tricky spatial patterns much faster and more flexibly than older methods. Their approach keeps important local connections between data points and optimizes efficiently, making it practical for very large datasets. This opens the door to analyzing complex spatial information that was too slow or hard before.
What this means in practice
- •For geospatial data engineers: Process large non-Gaussian spatial datasets faster by using scalable inference with neural conditioners preserving local spatial dependencies.
- •For environmental monitoring teams: Improve modeling of complex environmental data that deviate from common assumptions using a flexible and efficient inference method for large locations.
Authors
Paul F. V. Wiemann, Matthias Katzfuss
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.