Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA

This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, based on the idea that the dynamics of high-level concepts are often sparse. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that relates them. We develop a rigorous identifiability theory, building on recent nonlinear independent component analysis (ICA) results, that formalizes this principle and shows how the latent variables can be recovered up to permutation if one regularizes the latent mechanisms to be sparse and if some graph connectivity criterion is satisfied by the data generating process. As a special case of our framework, we show how one can leverage unknown-target interventions on the latent factors to disentangle them, thereby drawing further connections between ICA and causality. We also propose a VAE-based method in which the latent mechanisms are learned and regularized via binary masks, and validate our theory by showing it learns disentangled representations in simulations.