Algorithms for probabilistic latent tensor factorization

We propose a general probabilistic framework for modelling multiway data. Our approach establishes a novel link between graphical representation of probability measures and tensor factorization models that allow us to design arbitrary tensor factorization models while retaining simplicity. Using an expectation-maximization (EM) approach for maximizing the likelihood of the exponential dispersion models (EDM), we obtain iterative update equations for Kullback–Leibler (KL), Euclidian (EU) or Itakura–Saito (IS) costs as special cases. Besides EM, we derive alternative algorithms with multiplicative update rules (MUR) and alternating projections. We also provide algorithms for MAP estimation with conjugate priors. All of the algorithms can be formulated as message passing algorithm on a graph where vertices correspond to indices and cliques represent factors of the tensor decomposition.