Bayesian Approaches to Decomposing Tensors

• Activity Number: 52
• Type: Invited
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Morten Mørup*+
• Companies: DTU Informatics
• Keywords: Tensor Decomposition ; Bayesian Modeling ; Bayesian non-parametrics ; Automatic Relevance Determination

Abstract

Bayesian modeling form a principled framework for handling parameter uncertainty and inferring model complexity. Estimating the adequate number of components is an important yet difficult problem in multi-way modeling. We demonstrate how a Bayesian framework for model selection based on automatic relevance determination (ARD) can be adapted to the regular Tucker and CandeComp/PARAFAC (CP) models. By assigning priors for the model parameters and learning the hyperparameters of these priors the method is able to turn off excess components and simplify the core structure at a computational cost of fitting the conventional Tucker/CP model. We further illustrate how Bayesian nonparametrics can be used to estimate the model order in networks with multiple relations.