The Multiple Multiplicative Factor Model For Collaborative Filtering
Benjamin Marlin - University of Toronto
Richard Zemel - University of Toronto
We describe a class of causal, discrete latent variable models called Multiple Multiplicative Factor models (MMFs). A data vector is represented inthe latent space as a vector of factors that have discrete, non-negativeexpression levels. Each factor proposes a distribution over the data vector.The distinguishing feature of MMFs is that they combine the factors' proposeddistributions multiplicatively, taking into account factor expression levels.The product formulation of MMFs allow factors to specialize to a subset of theitems, while the causal generative semantics mean MMFs can readily accommodatemissing data. This makes MMFs distinct from both directed models with mixturesemantics and undirected product models. In this paper we present empiricalresults from the collaborative filtering domain showing that abinary/multinomial MMF model matches the performance of the best existingmodels while learning an interesting latent space description of the users.