mlsanityData to 14 Oct 2026

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

arXiv 2608.28991 ↗First posted 29 Aug 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

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 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

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References · 16

  1. 2022Interventional Causal Representation Learningcited by 142
  2. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  3. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  4. 2022Linear Causal Disentanglement via Interventionscited by 84
  5. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  6. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 74
  7. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 68
  8. 2014Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Setscited by 48
  9. 2022Identifying Weight-Variant Latent Causal Modelscited by 34
  10. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  11. 2023Unpaired Multi-Domain Causal Representation Learningcited by 32
  12. 2024Score-based Causal Representation Learning: Linear and General Transformationscited by 27
4 more
  1. 2023Identifiable Latent Polynomial Causal Models Through the Lens of Changecited by 23
  2. 2023Identifying Linearly-Mixed Causal Representations from Multi-Node Interventionscited by 18
  3. 2019Integrating overlapping datasets using bivariate causal discoverycited by 12
  4. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5

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