  We propose a novel VAE-based deep auto-encoder model that can learn
disentangled latent representations in a fully unsupervised manner, endowed
with the ability to identify all meaningful sources of variation and their
cardinality. Our model, dubbed Relevance-Factor-VAE, leverages the total
correlation (TC) in the latent space to achieve the disentanglement goal, but
also addresses the key issue of existing approaches which cannot distinguish
between meaningful and nuisance factors of latent variation, often the source
of considerable degradation in disentanglement performance. We tackle this
issue by introducing the so-called relevance indicator variables that can be
automatically learned from data, together with the VAE parameters. Our model
effectively focuses the TC loss onto the relevant factors only by tolerating
large prior KL divergences, a desideratum justified by our semi-parametric
theoretical analysis. Using a suite of disentanglement metrics, including a
newly proposed one, as well as qualitative evidence, we demonstrate that our
model outperforms existing methods across several challenging benchmark
datasets.
