Latent Variable Identifiability in Nonlinear Causal Models with Single-domain Data under Minimality Condition

Jianing Li, Hongtao Zhang, Wei Chen, Xueqi Cheng

Keywords: Identifiability theory, Disentangled representation learning, Structural causal model

TL;DR: We proposed a new identifiability theory with a novel minimality condition for latent variables in nonlinear causal models with single-domain data.

Abstract: The identifiability of latent variables given observational data is one of the core issues in the field of disentangled representation learning. Recent progresses have been made on establishing identifiablity theories for latent causal models. However with much restrictions or unrealistic assumptions, their practicality on real applications are limited. In this paper, we propose a novel identifiablity theory for learning latent variables in nonlinear causal models, requiring only single-domain data. We prove that all latent variables in a powerset bipartite graph can be identified up to an invertible transformation, if the generation process of observable data is globally invertible, latent variables are independent, and shared latent variables entail minimal information. Experiments on synthetic data support the conclusions of our theory.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 11291