Causal Component Analysis
Liang Wendong 1,212{}^{1,2}start_FLOATSUPERSCRIPT 1 , 2 end_FLOATSUPERSCRIPT、Armin Kekić 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT、Julius von Kügelgen 1,313{}^{1,3}start_FLOATSUPERSCRIPT 1 , 3 end_FLOATSUPERSCRIPT、Simon Buchholz 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Michel Besserve 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Luigi Gresele 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Bernhard Schölkopf 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT 11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Max Planck Institute for Intelligent Systems, Tübingen, Germany 22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT ENS Paris-Saclay, Gif-sur-Yvette, France 33{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT University of Cambridge, United Kingdom Shared last author. Code available at https://github.com/akekic/causal-component-analysis.
Abstract
Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent variables, together with the unknown graph encoding their causal relationships. We introduce an intermediate problem termed Causal Component Analysis (CauCA). CauCA can be viewed as a generalization of ICA, modelling the causal dependence among the latent components, and as a special case of CRL. In contrast to CRL, it presupposes knowledge of the causal graph, focusing solely on learning the unmixing function and the causal mechanisms. Any impossibility results regarding the recovery of the ground truth in CauCA also apply for CRL, while possibility results may serve as a stepping stone for extensions to CRL. We characterize CauCA identifiability from multiple datasets generated through different types of interventions on the latent causal variables. As a corollary, this interventional perspective also leads to new identifiability results for nonlinear ICA—a special case of CauCA with an empty graph—requiring strictly fewer datasets than previous resu
中文速览
潜在变量混合在一起的真实世界数据中，独立成分分析（ICA）要求各潜变量相互独立，而因果表示学习（CRL）虽能处理因果依赖，却面临因果图和解混函数同时未知的双重难题。这篇论文在两者之间引入了一个名为"因果成分分析"（Causal Component Analysis, CauCA）的中间问题：假设因果图已知，只需同时学习解混函数和各变量的因果机制。作者从理论上严格推导了在不同类型干预（intervention）所产生的多组数据下，CauCA 可识别性的充分必要条件，并作为推论还为经典非线性 ICA 给出了所需数据集数量更少的新可识别性结果。在方法层面，他们提出了基于归一化流（normalizing flows）的似然估计框架，并通过大量合成实验验证了该方法能有效还原潜在的因果成分。这项工作的价值在于：CauCA 的不可能性结论直接适用于更困难的 CRL，而其可能性结论则为最终攻克 CRL 提供了清晰的理论跳板。
原文 arXiv:2305.17225;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2305.17225v3