ISA-VAE: Independent Subspace Analysis with Variational Autoencoders

Recent work has shown increased interest in using the Variational Autoencoder (VAE) framework to discover interpretable representations of data in an unsupervised way. These methods have focussed largely on modifying the variational cost function to achieve this goal. However, we show that methods like beta-VAE simplify the tendency of variational inference to underfit causing pathological over-pruning and over-orthogonalization of learned components. In this paper we take a complementary approach: to modify the probabilistic model to encourage structured latent variable representations to be discovered. Specifically, the standard VAE probabilistic model is unidentifiable: the likelihood of the parameters is invariant under rotations of the latent space. This means there is no pressure to identify each true factor of variation with a latent variable. We therefore employ a rich prior distribution, akin to the ICA model, that breaks the rotational symmetry. Extensive quantitative and qualitative experiments demonstrate that the proposed prior mitigates the trade-off introduced by modified cost functions like beta-VAE and TCVAE between reconstruction loss and disentanglement. The proposed prior allows to improve these approaches with respect to both disentanglement and reconstruction quality significantly over the state of the art.