A Sparsity Principle for Partially Observable Causal Representation Learning

Danru Xu, Dingling Yao, Sebastien Lachapelle, Perouz Taslakian, Julius von Kügelgen, Francesco Locatello, Sara Magliacane

Keywords: causal representation learning, identifiability, sparse representation learning

TL;DR: Two identifiability results for partial observable settings: one for linear mixing functions without parametric assumptions on the underlying causal model, and one for piecewise linear mixing functions with Gaussian latent causal variables.

Abstract: Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially observed setting, in which each measurement only provides information about a subset of the underlying causal state. Prior work has studied this setting with multiple domains or views, each depending on a fixed subset of latents. Here we focus on learning from unpaired observations from a dataset with an instance-dependent partial observability pattern. Our main contribution is to establish two identifiability results for this setting: one for linear mixing functions without parametric assumptions on the underlying causal model, and one for piecewise linear mixing functions with Gaussian latent causal variables. Based on these insights, we estimate the underlying causal variables by enforcing sparsity in the inferred representation. Based on these insights, we propose two methods for estimating the underlying causal variables by enforcing sparsity in the inferred representation.

Submission Number: 9