Reviews: Deep Homogeneous Mixture Models: Representation, Separation, and Approximation

The paper discusses connections between multiple density models within the unifying framework of homogeneous mixture models: tensorial mixtures models [1], hidden Markov models, latent tree models and sum-product networks [2] are discussed. The authors argue that there is a hierarchy among these models by showing that a model lower in the hierarchy can be cast into a model higher in the hierarchy using linear size transformations. Furthermore, the paper gives new theoretical insights in depth efficiency in these models, by establishing a connection between properties of the represented mixture coefficient tensor (e.g. Finally, the paper gives positive and somewhat surprising approximation results using [3]. Strengths: connections between various models, which so far were somewhat folk wisdom, are illustrated a unifying tensor mixture framework.