Identifiable Latent Polynomial Causal Models Through the Lens of Change

TL;DR

This paper extends causal representation learning to nonlinear polynomial models with exponential family noise, providing theoretical identifiability results and a new empirical method validated on synthetic and real data.

Contribution

It generalizes previous linear Gaussian models to nonlinear polynomial causal models with exponential family noise and introduces a novel empirical estimation method.

Findings

Theoretical identifiability results for nonlinear polynomial causal models.

Proposed empirical method achieves consistent learning of latent causal representations.

Experimental validation on synthetic and real-world data supports theoretical claims.

Abstract

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments \citep{liu2022identifying}. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.