  Factor analysis (FA) is a statistical tool for studying how observed
variables with some mutual dependences can be expressed as functions of
mutually independent unobserved factors, and it is widely applied throughout
the psychological, biological, and physical sciences. We revisit this classic
method from the comparatively new perspective given by advancements in causal
discovery and deep learning, introducing a framework for Neuro-Causal Factor
Analysis (NCFA). Our approach is fully nonparametric: it identifies factors via
latent causal discovery methods and then uses a variational autoencoder (VAE)
that is constrained to abide by the Markov factorization of the distribution
with respect to the learned graph. We evaluate NCFA on real and synthetic data
sets, finding that it performs comparably to standard VAEs on data
reconstruction tasks but with the advantages of sparser architecture, lower
model complexity, and causal interpretability. Unlike traditional FA methods,
our proposed NCFA method allows learning and reasoning about the latent factors
underlying observed data from a justifiably causal perspective, even when the
relations between factors and measurements are highly nonlinear.
