M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910183501856768 |
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| author | Nichol, J. Jake Weylandt, Michael Fricke, G. Matthew Perez-Carrasquilla, Jhayron Moses, Melanie E. |
| author_facet | Nichol, J. Jake Weylandt, Michael Fricke, G. Matthew Perez-Carrasquilla, Jhayron Moses, Melanie E. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_00398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data Nichol, J. Jake Weylandt, Michael Fricke, G. Matthew Perez-Carrasquilla, Jhayron Moses, Melanie E. Machine Learning Atmospheric and Oceanic Physics 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. |
| title | M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data |
| topic | Machine Learning Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2605.00398 |