Gaussian beta process

This thesis presents a new framework for constituting a group of dependent completely random measures, unifying and extending methods in the literature. The dependent completely random measures are constructed based on a shared completely random measure, which is extended to the covariate space, and further differentiated by the covariate information associated with the data for which the completely random measures serve as priors. As a concrete example of the flexibility provided by the framework, a group of dependent feature learning measures are constructed based on a shared beta process, with Gaussian processes applied to build adaptive dependencies learnt from the practical data, denoted as the Gaussian beta process. Experiment results are presented for gene-expression series data (time as covariate), as well as digital image data (spatial location as covariate).