Causal Component Analysis

TL;DR

This paper introduces Causal Component Analysis (CauCA), a new framework that generalizes ICA by modeling causal dependencies among latent variables, providing identifiability results and a likelihood-based estimation method.

Contribution

It defines CauCA as an intermediate problem between ICA and CRL, characterizes its identifiability from interventional data, and proposes a normalizing flow-based approach for estimation.

Findings

CauCA can be identified from multiple datasets with interventions.

Fewer datasets are needed for nonlinear ICA under CauCA assumptions.

The proposed method effectively estimates causal mechanisms in synthetic experiments.

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 results. We introduce a likelihood-based approach using normalizing flows to estimate both the unmixing function and the causal mechanisms, and demonstrate its effectiveness through extensive synthetic experiments in the CauCA and ICA setting.