Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies

Understand

This work introduces a novel principle for disentanglement we call mechanism sparsity regularization, which applies when the latent factors of interest depend sparsely on observed auxiliary variables and/or past latent factors.

• We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that explains them.
• We develop a nonparametric identifiability theory that formalizes this principle and shows that the latent factors can be recovered by regularizing the learned causal graph to be sparse, under some assumptions such as the absence of instantaneous causal effects between latent factors.
• More precisely, we show identifiability up to a novel equivalence relation we call consistency, which allows some latent factors to remain entangled (hence the term partial disentanglement).