Factor analysis (FA) is a statistical method for explaining how mutually dependent observed variables can be represented in terms of mutually independent latent factors, and it is widely used in the psychological, biological, and physical sciences. We revisit this classic method from the perspective of recent advances in causal structure learning and deep generative models, introducing a framework for Neuro-Causal Factor Analysis (NCFA). Our approach is fully nonparametric: it learns a directed graph between latent and observed variables, and then fits a deep generative model constrained to respect the Markov factorization of the graph. Empirically, on synthetic and real data, NCFA attains better reconstruction error compared to standard FA and better latent distribution recovery compared to a standard variational autoencoder, all with the advantages of sparser architecture, lower model complexity, and causal interpretability.

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