Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions
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
Related
- Recovering Collective Structure in Congressional Voting: A Fused Latent Factor and Network Approach
- Statistical Inference for Causal Discovery under Selection and Latent Variables via Single-Target Interventions
- Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations
- Routing Frictions and Executable Liquidity in Fragmented Markets
- Recovering curves from isogeny classes of Prym varieties
BibTeX
@misc{xu2026jigsawcrl,
title = {{Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions}},
author = {Haijie Xu and Chen Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28991},
eprint = {2608.28991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28991},
}
RIS
TY - UNPB
TI - Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions
AU - Haijie Xu
AU - Chen Zhang
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.28991
UR - https://arxiv.org/abs/2608.28991
AB - 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
ER -