Joni Virta (Aalto University, Helsinki, Finland)

Title: Statistical properties of second-order tensor decompositions

Authors: Joni Virta, Christoph Kösner, Niko Lietzén, Klaus Nordhausen

Abstract: Two classical tensor decompositions are considered from a statistical viewpoint: the Tucker decomposition and the higher order singular value decomposition (HOSVD). Both decompositions are shown to be consistent estimators of the parameters of a certain noisy latent variable model. The decompositions’ asymptotic properties allow comparisons between them. Also inference for the true latent dimension is discussed. The theory is illustrated with examples.