  Several factors contribute to the appearance of an object in a visual scene,
including pose, illumination, and deformation, among others. Each factor
accounts for a source of variability in the data, while the multiplicative
interactions of these factors emulate the entangled variability, giving rise to
the rich structure of visual object appearance. Disentangling such unobserved
factors from visual data is a challenging task, especially when the data have
been captured in uncontrolled recording conditions (also referred to as
"in-the-wild") and label information is not available.
  In this paper, we propose the first unsupervised deep learning method (with
pseudo-supervision) for disentangling multiple latent factors of variation in
face images captured in-the-wild. To this end, we propose a deep latent
variable model, where the multiplicative interactions of multiple latent
factors of variation are explicitly modelled by means of multilinear (tensor)
structure. We demonstrate that the proposed approach indeed learns disentangled
representations of facial expressions and pose, which can be used in various
applications, including face editing, as well as 3D face reconstruction and
classification of facial expression, identity and pose.
