A Sparsity Principle for Partially Observable Causal Representation Learning
This work addresses a partially observed setting in causal representation learning, which is incremental as it builds on prior work by focusing on instance-dependent patterns without requiring multiple domains or views.
The paper tackles the problem of causal representation learning under partial observability, where each measurement only provides information about a subset of latent causal variables, and establishes identifiability results for linear and piecewise linear mixing functions, with experiments showing effectiveness in recovering ground-truth latents.
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 propose two methods for estimating the underlying causal variables by enforcing sparsity in the inferred representation. Experiments on different simulated datasets and established benchmarks highlight the effectiveness of our approach in recovering the ground-truth latents.