Bayesian nonparametric latent feature models

Abstract

Latent feature modelling is a multivariate technique used to explain the hidden structure underlying an observed dataset. One common problem which arises when fitting a latent feature model is that of deciding the number of features required to adequately capture the variability within the data. In this dissertation we delve into latent feature modelling using a Bayesian nonparametric approach. Nonparametric means that the number of parameters (features) is not specified as part of the model, rather it is inferred from the data. This makes Bayesian nonparametric estimation ideal for dealing with the problem of specifying the number of required features. In particular, we define the Indian buffet process and the beta process, and shed light on their role as priors in Bayesian nonparametric latent feature models. To emphasize the usefulness of taking this approach, we consider two main applications. In the first, we show how a binary Gaussian latent feature model using an Indian buffet process prior can be used to explain why the people of certain countries are happier than others. The second is an application in audio source separation in which we use a Bayesian nonparametric model (BP-NMF) to successfully separate two audio signals.