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.
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