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

arXiv: https://arxiv.org/abs/2605.00398 · HTML: https://mlsanity.com/paper/2605.00398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 67 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 7 of 7)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [Linear Systems can be Hard to Learn](https://mlsanity.com/paper/2104.01120/) (2021)
- [pg-Causality: Identifying Spatiotemporal Causal Pathways for Air Pollutants with Urban Big Data](https://mlsanity.com/paper/1610.07045/) (2016)

## Abstract (arXiv)

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 Ni~no 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.