Faculty of Engineering and Natural Sciences
Bayesian Inference for Nonnegative Matrix and Tensor Factorisations
We develop a message passing framework for a subclass of nonnegative matrix factorization (NMF) and tensor factorisation (NTF) models. The factorisation is implicit in a well-defined statistical model of superimposed components, either Gaussian or Poisson distributed, and are equivalent to maximum likelihood estimation of latent parameters (either mean, variance or intensity). By treating the components as hidden-variables, NMF and NTF algorithms can be derived in a typical data augmentation setting using an expectation-maximisation approach. One advantage of this view is that it provides a structured approach to well known methods of multiway analysis, such as Parafac or Tucker models. We also establish links with methods for fitting contingency tables to given marginals such as IPF (Iterative Proportional Fitting). This setting accommodates regularization constraints on the matrix factors through priors and extensions to full Bayesian inference for model selection. The talk will start with a gentle introduction to the subject, so we hope to make the topic accessible to a general audience. If time permits, we will discuss some applications in audio and music processing.
Taylan Cemgil received his B.Sc. (1993) and M.Sc. (1995) in Computer Engineering, Boğaziçi University, and his Ph.D. (2004),
Netherlands. He worked as a postdoctoral researcher at Intelligent Autonomous Systems Lab. at University of Amsterdam, the Netherlands and the Signal Processing and Communications Lab., Dept. of Engineering,
University of Cambridge,
UK. He is currently an assistant professor at
University, Dept. of Computer Engineering. He is interested in Bayesian statistical methods, machine learning,
Monte Carlo computation and applications in signal processing.
Wednesday, 2 December 2009 at 13:40,