  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.
