STOAT: Spatial-Temporal Probabilistic Causal Inference Network

TL;DR

STOAT is a novel framework that combines causal inference with spatial-temporal probabilistic modeling to improve forecasting accuracy and uncertainty estimation in region-specific time series data, such as epidemic spread.

Contribution

The paper introduces STOAT, a new method that integrates spatial relations and causal inference into probabilistic forecasting for spatial-temporal data, enhancing predictive performance.

Findings

Outperforms existing probabilistic models on COVID-19 data

Effectively captures spatial dependencies and regional variability

Provides calibrated uncertainty estimates

Abstract

Spatial-temporal causal time series (STC-TS) involve region-specific temporal observations driven by causally relevant covariates and interconnected across geographic or network-based spaces. Existing methods often model spatial and temporal dynamics independently and overlook causality-driven probabilistic forecasting, limiting their predictive power. To address this, we propose STOAT (Spatial-Temporal Probabilistic Causal Inference Network), a novel framework for probabilistic forecasting in STC-TS. The proposed method extends a causal inference approach by incorporating a spatial relation matrix that encodes interregional dependencies (e.g. proximity or connectivity), enabling spatially informed causal effect estimation. The resulting latent series are processed by deep probabilistic models to estimate the parameters of the distributions, enabling calibrated uncertainty modeling. We further explore multiple output distributions (e.g., Gaussian, Student's-$t$, Laplace) to capture region-specific variability. Experiments on COVID-19 data across six countries demonstrate that STOAT outperforms state-of-the-art probabilistic forecasting models (DeepAR, DeepVAR, Deep State Space Model, etc.) in key metrics, particularly in regions with strong spatial dependencies. By bridging causal inference and geospatial probabilistic forecasting, STOAT offers a generalizable framework for complex spatial-temporal tasks, such as epidemic management.