Learning a Spatial Partitioning and its Causal Relations from Temporal Data

Philippe Brouillard, Sebastien Lachapelle, Julia Kaltenborn, Yaniv Gurwicz, Dhanya Sridhar, Alexandre Drouin, Peer Nowack, Jakob Runge, David Rolnick
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:547-592, 2026.

Abstract

Scientific research often seeks to understand the causal structure underlying high-level variables in a system. For example, climate scientists study how phenomena, such as El Niño, affect other climate processes at remote locations across the globe. However, scientists typically collect low-level measurements, such as geographically distributed temperature readings. From these, one needs to learn both a mapping to causally-relevant latent variables, such as a high-level representation of the El Niño phenomenon and other processes, as well as the causal model over them. The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies. In this work, we consider the task of partitioning observed variables into disentangled factors, such as extracting regions from geographically gridded measurement data in climate research or capturing brain regions from neural activity data. We demonstrate the identifiability of the resulting model and propose a differentiable method, Causal Discovery with Single-parent Decoding (CDSD), that simultaneously learns, from temporal data, the underlying latents and a causal graph over them. We assess the validity of our theoretical results using simulated data and showcase the practical validity of our method in an application to real-world data from the climate science field.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-brouillard26a, title = {Learning a Spatial Partitioning and its Causal Relations from Temporal Data}, author = {Brouillard, Philippe and Lachapelle, Sebastien and Kaltenborn, Julia and Gurwicz, Yaniv and Sridhar, Dhanya and Drouin, Alexandre and Nowack, Peer and Runge, Jakob and Rolnick, David}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {547--592}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/brouillard26a/brouillard26a.pdf}, url = {https://proceedings.mlr.press/v323/brouillard26a.html}, abstract = {Scientific research often seeks to understand the causal structure underlying high-level variables in a system. For example, climate scientists study how phenomena, such as El Niño, affect other climate processes at remote locations across the globe. However, scientists typically collect low-level measurements, such as geographically distributed temperature readings. From these, one needs to learn both a mapping to causally-relevant latent variables, such as a high-level representation of the El Niño phenomenon and other processes, as well as the causal model over them. The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies. In this work, we consider the task of partitioning observed variables into disentangled factors, such as extracting regions from geographically gridded measurement data in climate research or capturing brain regions from neural activity data. We demonstrate the identifiability of the resulting model and propose a differentiable method, Causal Discovery with Single-parent Decoding (CDSD), that simultaneously learns, from temporal data, the underlying latents and a causal graph over them. We assess the validity of our theoretical results using simulated data and showcase the practical validity of our method in an application to real-world data from the climate science field.} }
Endnote
%0 Conference Paper %T Learning a Spatial Partitioning and its Causal Relations from Temporal Data %A Philippe Brouillard %A Sebastien Lachapelle %A Julia Kaltenborn %A Yaniv Gurwicz %A Dhanya Sridhar %A Alexandre Drouin %A Peer Nowack %A Jakob Runge %A David Rolnick %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-brouillard26a %I PMLR %P 547--592 %U https://proceedings.mlr.press/v323/brouillard26a.html %V 323 %X Scientific research often seeks to understand the causal structure underlying high-level variables in a system. For example, climate scientists study how phenomena, such as El Niño, affect other climate processes at remote locations across the globe. However, scientists typically collect low-level measurements, such as geographically distributed temperature readings. From these, one needs to learn both a mapping to causally-relevant latent variables, such as a high-level representation of the El Niño phenomenon and other processes, as well as the causal model over them. The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies. In this work, we consider the task of partitioning observed variables into disentangled factors, such as extracting regions from geographically gridded measurement data in climate research or capturing brain regions from neural activity data. We demonstrate the identifiability of the resulting model and propose a differentiable method, Causal Discovery with Single-parent Decoding (CDSD), that simultaneously learns, from temporal data, the underlying latents and a causal graph over them. We assess the validity of our theoretical results using simulated data and showcase the practical validity of our method in an application to real-world data from the climate science field.
APA
Brouillard, P., Lachapelle, S., Kaltenborn, J., Gurwicz, Y., Sridhar, D., Drouin, A., Nowack, P., Runge, J. & Rolnick, D.. (2026). Learning a Spatial Partitioning and its Causal Relations from Temporal Data. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:547-592 Available from https://proceedings.mlr.press/v323/brouillard26a.html.

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