发表机构
Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Jigsaw-CRL框架，针对多客户端仅干预部分潜在变量的碎片化场景，利用软干预下精度矩阵差异的低秩结构恢复全局潜在因果顺序，建立可识别性保证并经合成数据验证。
AI 中文摘要
因果表示学习（CRL）旨在从高维观测中恢复潜在因果变量及其结构关系。现有CRL方法通常假设所有环境都定义在相同的潜在变量上，或至少共享一个共同的潜在表示空间。本文研究一种碎片化多客户端场景：多个客户端与同一全局潜在因果系统交互，但每个客户端仅访问并干预潜在变量的一个子集。在该场景下，对未使用的潜在变量求边际会诱导出双向边，因此单个客户端不再对应逐节点的潜在因果图，必须通过组装客户端特定的结构片段来恢复全局潜在因果顺序。我们提出Jigsaw-CRL框架，用于从这类碎片化干预中恢复全局潜在因果顺序。在软干预下，不同环境间精度矩阵的差异呈现由潜在祖先关系决定的低秩结构，这使我们能为每个客户端恢复块划分、对应块级祖先顺序和潜在子空间，再将这些片段组装成全局逐节点潜在因果顺序。我们建立了可识别性保证，开发了实用算法，并在合成数据上验证了该框架，代码可在指定https URL获取。
英文摘要
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
