Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions
Machine Learning
Summary
The authors study how to learn cause-and-effect relationships hidden in complex data when different groups (clients) only see and change parts of the system. Because each client sees only a piece, the usual way to find cause-and-effect connections doesn’t work directly. They propose a new method called Jigsaw-CRL that puts together these partial views to find the overall cause-effect order. Their approach uses math properties of how the data changes across different settings and guarantees that the full causal order can be identified. They tested their method on simulated data and made their code available.
Authors
Haijie Xu, Chen Zhang
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