Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions

arXiv:2608.28991v1 Announce Type: cross Abstract: Causal representation learning (CRL) aims to recover latent causal variables and their structural relations from high-dimensional observations. Existing CRL methods typically assume that all environments are defined over the same latent variables, or at least share a common latent representation space. We study a fragmented multi-client setting, where multiple clients interact with the same global latent causal system but each client only accesses and intervenes on a subset of the latent variables. In this regime, marginalizing unused latent variables induces bidirected edges, so a single client no longer admits a node-wise latent causal graph, and the global latent causal order must be recovered by assembling client-specific structural fragments. We propose \textbf{Jigsaw-CRL}, a framework for recovering global latent causal order from such fragmented interventions. Under soft interventions, differences between precision matrices across environments exhibit a low-rank structure governed by latent ancestor relations. This enables recovery, for each client, of a block partition, the corresponding block-level ancestral order, and latent subspaces, and then assembly of these fragments into the global node-level latent causal order. We establish identifiability guarantees, develop practical algorithms, and validate the framework on synthetic data. Our codes are available on https://anonymous.4open.science/r/code-for-Jigsaw-CRL-7B26

Abstract:Causal representation learning (CRL) aims to recover latent causal variables and their structural relations from high-dimensional observations. Existing CRL methods typically assume that all environments are defined over the same latent variables, or at least share a common latent representation space. We study a fragmented multi-client setting, where multiple clients interact with the same global latent causal system but each client only accesses and intervenes on a subset of the latent variables. In this regime, marginalizing unused latent variables induces bidirected edges, so a single client no longer admits a node-wise latent causal graph, and the global latent causal order must be recovered by assembling client-specific structural fragments. We propose \textbf{Jigsaw-CRL}, a framework for recovering global latent causal order from such fragmented interventions. Under soft interventions, differences between precision matrices across environments exhibit a low-rank structure governed by latent ancestor relations. This enables recovery, for each client, of a block partition, the corresponding block-level ancestral order, and latent subspaces, and then assembly of these fragments into the global node-level latent causal order. We establish identifiability guarantees, develop practical algorithms, and validate the framework on synthetic data. Our codes are available on this https URL

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2608.28991 [stat.ML]

(or arXiv:2608.28991v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2608.28991 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions

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