# Causal Representation Learning from Multiple Distributions: A General Setting

CoRR（2024）

摘要

In many problems, the measured variables (e.g., image pixels) are just
mathematical functions of the hidden causal variables (e.g., the underlying
concepts or objects). For the purpose of making predictions in changing
environments or making proper changes to the system, it is helpful to recover
the hidden causal variables Z_i and their causal relations represented by
graph 𝒢_Z. This problem has recently been known as causal
representation learning. This paper is concerned with a general, completely
nonparametric setting of causal representation learning from multiple
distributions (arising from heterogeneous data or nonstationary time series),
without assuming hard interventions behind distribution changes. We aim to
develop general solutions in this fundamental case; as a by product, this helps
see the unique benefit offered by other assumptions such as parametric causal
models or hard interventions. We show that under the sparsity constraint on the
recovered graph over the latent variables and suitable sufficient change
conditions on the causal influences, interestingly, one can recover the
moralized graph of the underlying directed acyclic graph, and the recovered
latent variables and their relations are related to the underlying causal model
in a specific, nontrivial way. In some cases, each latent variable can even be
recovered up to component-wise transformations. Experimental results verify our
theoretical claims.

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