Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA
This work addresses the challenge of disentanglement in representation learning for machine learning, offering a novel theoretical framework that bridges ICA and causality, though it is incremental in building on recent nonlinear ICA results.
The paper tackles the problem of learning disentangled latent factors in nonlinear ICA by introducing a principle based on mechanism sparsity regularization, showing that latent variables can be recovered up to permutation under certain conditions and validating this with simulations.
This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, which can be applied when the latent factors of interest depend sparsely on past latent factors and/or observed auxiliary variables. 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 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.