2024 | Kun Zhang, Shaoan Xie, Ignavier Ng, Yujia Zheng
This paper presents a general nonparametric approach to causal representation learning from multiple distributions, without assuming hard interventions or parametric models. The goal is to recover latent causal variables and their relationships from observational data, even when the causal mechanisms change across domains or over time. The key insight is that under sparsity constraints on the recovered graph and sufficient changes in causal influences, one can recover the moralized graph of the underlying directed acyclic graph (DAG), and the recovered latent variables are related to the true causal model in a specific, nontrivial way. The paper shows that in some cases, most latent variables can be recovered up to component-wise transformations. Theoretical results are supported by experiments on simulated data, demonstrating the effectiveness of the approach. The paper also discusses the implications of different assumptions in causal representation learning and highlights the importance of sparsity constraints in achieving identifiability. The proposed method is implemented using a variational autoencoder framework, with two different implementations of the prior distribution: nonparametric and parametric. The results show that the method can recover the true causal structure and latent variables from multiple domains. The paper concludes that causal representation learning from multiple distributions is a promising area of research with potential applications in various fields.This paper presents a general nonparametric approach to causal representation learning from multiple distributions, without assuming hard interventions or parametric models. The goal is to recover latent causal variables and their relationships from observational data, even when the causal mechanisms change across domains or over time. The key insight is that under sparsity constraints on the recovered graph and sufficient changes in causal influences, one can recover the moralized graph of the underlying directed acyclic graph (DAG), and the recovered latent variables are related to the true causal model in a specific, nontrivial way. The paper shows that in some cases, most latent variables can be recovered up to component-wise transformations. Theoretical results are supported by experiments on simulated data, demonstrating the effectiveness of the approach. The paper also discusses the implications of different assumptions in causal representation learning and highlights the importance of sparsity constraints in achieving identifiability. The proposed method is implemented using a variational autoencoder framework, with two different implementations of the prior distribution: nonparametric and parametric. The results show that the method can recover the true causal structure and latent variables from multiple domains. The paper concludes that causal representation learning from multiple distributions is a promising area of research with potential applications in various fields.