  We would like to learn a representation of the data which decomposes an
observation into factors of variation which we can independently control.
Specifically, we want to use minimal supervision to learn a latent
representation that reflects the semantics behind a specific grouping of the
data, where within a group the samples share a common factor of variation. For
example, consider a collection of face images grouped by identity. We wish to
anchor the semantics of the grouping into a relevant and disentangled
representation that we can easily exploit. However, existing deep probabilistic
models often assume that the observations are independent and identically
distributed. We present the Multi-Level Variational Autoencoder (ML-VAE), a new
deep probabilistic model for learning a disentangled representation of a set of
grouped observations. The ML-VAE separates the latent representation into
semantically meaningful parts by working both at the group level and the
observation level, while retaining efficient test-time inference. Quantitative
and qualitative evaluations show that the ML-VAE model (i) learns a
semantically meaningful disentanglement of grouped data, (ii) enables
manipulation of the latent representation, and (iii) generalises to unseen
groups.
