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

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This work introduces a novel principle we call disentanglement via mechanism\nsparsity regularization, which can be applied when the latent factors of\ninterest depend sparsely on past latent factors and/or observed auxiliary\nvariables. We propose a representation learning method that induces\ndisentanglement by simultaneously learning the latent factors and the sparse\ncausal graphical model that relates them. We develop a rigorous identifiability\ntheory, building on recent nonlinear independent component analysis (ICA)\nresults, that formalizes this principle and shows how the latent variables can\nbe recovered up to permutation if one regularizes the latent mechanisms to be\nsparse and if some graph connectivity criterion is satisfied by the data\ngenerating process. As a special case of our framework, we show how one can\nleverage unknown-target interventions on the latent factors to disentangle\nthem, thereby drawing further connections between ICA and causality. We propose\na VAE-based method in which the latent mechanisms are learned and regularized\nvia binary masks, and validate our theory by showing it learns disentangled\nrepresentations in simulations.\n

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