M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data

2026-05-01

AI Summary

This study addresses the challenge of causal structure discovery in high-dimensional multivariate spatiotemporal grid data, where the number of temporal samples is vastly smaller than the spatial dimensionality. The work proposes an extended CaStLe framework that, for the first time, adapts local causal discovery methods to such settings by modeling intra- and inter-variable local causal relationships within fixed-size spatiotemporal neighborhoods. To enhance sample efficiency, it introduces spatial replication pooling. Leveraging assumptions of spatiotemporal locality and stationarity, the framework incorporates multivariate causal graph learning, local embedding, parent identification, and a decomposition mechanism separating response graphs from spatial graphs, substantially improving interpretability. Evaluated on both synthetic and real-world datasets—including atmospheric chemistry and El Niño systems—the method accurately recovers multivariate causal structures and uncovers key physical coupling mechanisms.

Abstract

Causal graph discovery for space-time systems is challenging in high-dimensional gridded data, which often has many more grid cells than temporal observations per cell. The Causal Space-Time Stencil Learning (CaStLe) meta-algorithm was developed to address that niche under space-time locality and stationarity assumptions, but it is currently limited to univariate analyses. In this work, we present M-CaStLe. M-CaStLe generalizes the local embedding and parent-identification phases of CaStLe to jointly model local within-variable and cross-variable space-time causal structures in gridded data. Like CaStLe, by constraining candidate parents to a constant-size space-time neighborhood and pooling spatial replicates, M-CaStLe increases effective sample size to make discovery tractable in high-dimensional settings. We further decompose the resulting multivariate stencil graph into reaction and spatial graphs to aid interpretation in complex settings. We study M-CaStLe in four settings: a multivariate space-time vector autoregression benchmark with known ground truth, an advective-diffusive-reaction partial differential equation verification problem with derived physical reference structure, an atmospheric chemistry case study in a low-temporal-sample regime, and an El Niño Southern Oscillation study on reanalysis data, identifying phase-dependent ocean--atmosphere coupling. Across these settings, M-CaStLe more accurately recovers multivariate causal structure in controlled settings and identifies important physical dynamics in real-world case studies. Overall, M-CaStLe advances causal discovery for multivariate space-time systems while retaining interpretability at the grid level.

Problem

• causal discovery
• multivariate spatio-temporal data
• high-dimensional gridded data
• local causal structure
• space-time systems

Innovation

• multivariate causal discovery
• space-time gridded data
• local causal structure
• stencil graph decomposition
• high-dimensional time series