Uncertainty-Aware Neural Multivariate Geostatistics

TL;DR

This paper introduces Deep Neural Coregionalization, a scalable framework for multivariate geostatistics that models spatial effects with deep Gaussian processes, enabling efficient uncertainty quantification and capturing complex spatial dependencies.

Contribution

It presents a novel variational formulation linking deep Gaussian processes to neural networks, allowing fast training and principled uncertainty estimates in multivariate spatial modeling.

Findings

Competitive with existing models under nonstationarity

Provides calibrated uncertainty quantification through MC-dropout

Scales efficiently to large environmental datasets

Abstract

We propose Deep Neural Coregionalization, a scalable framework for uncertainty-aware multivariate geostatistics. DNC models multivariate spatial effects through spatially varying latent factors and loadings, assigning deep Gaussian process (DGP) priors to both the factors and the entries of the loading matrix. This joint construction learns shared latent spatial structure together with response-specific, location-dependent mixing weights, enabling flexible nonlinear and space-dependent associations within and across variables. A key contribution is a variational formulation that makes the DGP to deep neural network (DNN) correspondence explicit: maximizing the DGP evidence lower bound (ELBO) is equivalent to training DNNs with weight decay and Monte Carlo (MC) dropout. This yields fast mini-batch stochastic optimization without Markov Chain Monte Carlo (MCMC), while providing principled uncertainty quantification through MC-dropout forward passes as approximate posterior draws, producing calibrated credible surfaces for prediction and spatial effect estimation. Across simulations, DNC is competitive with existing spatial factor models, particularly under strong nonstationarity and complex cross-dependence, while delivering substantial computational gains. In a multivariate environmental case study, DNC captures spatially varying cross-variable interactions, produces interpretable maps of multivariate outcomes, and scales uncertainty quantification to large datasets with orders-of-magnitude reductions in runtime.