A Sparsity Principle for Partially Observable Causal Representation Learning

Abstract

Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal vari- ables are captured in the high-dimensional obser- vations. 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 observ- ability pattern. Our main contribution is to estab- lish 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 propose two methods for estimating the underlying causal variables by enforcing spar- sity in the inferred representation. Experiments on different simulated datasets and established benchmarks highlight the effectiveness of our approach in recovering the ground-truth latents.