STACI: Spatio-Temporal Aleatoric Conformal Inference

David Park (Brookhaven National Laboratory) · Xihaier Luo (Brookhaven National Laboratory) · Shinjae Yoo (Brookhaven National Lab) · Brandon Feng (Massachusetts Institute of Technology) · Arantxa Urdangarin (North Carolina State University) · Brian Reich (North Carolina State University)

aleatoric uncertaintyapproximation biasconformal inferencecorrelation structurecovariance kernel functioncovariance matrix deep learning models gaussian processesgpu trainingnon-stationaryprediction intervals scalable methodsspatio-temporal fieldsuncertainty quantificationvariational bayesian neural network

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.