Events

Seminar on

Bayesian nonparametric mixture modelling of sparse signals with cluster specific variable selection

by

Prof. Chris Holmes, University of Oxford

Abstract

We discuss a hierarchical Bayesian nonparametric mixture model for clustering when some of the covariates are assumed to be of varying relevance to the clustering problem. This can be thought of as an issue in variable selection for unsupervised learning. We demonstrate that by defining a hierarchical population based nonparametric prior on the cluster locations scaled by the inverse covariance matrices of the likelihood we arrive at a ‘sparsity prior’ representation which admits a conditionally conjugate prior. This allows us to perform full Gibbs sampling to obtain posterior distributions over parameters of interest including an explicit measure of each covariate’s relevance and a distribution over the number of potential clusters present in the data. This also allows for individual cluster specific variable selection. We demonstrate improved inference on a number of canonical problems including analysis of patterns of copy-number-variation present in colon cancer genomes.

This seminar is organised within the School on High Dimensional Design an Data Modelling organised at ECLT by Prof. Irene Poli and Prof. Phil Brown.