Simultaneous model selection via rate-distortion theory, with applications to cluster and significance analysis of gene expression data

High-dimensional data are prevalent across many application areas, and generate an everincreasing demand for statistical methods of dimension reduction, such as cluster and significance analysis. One application area that has recently received much interest is the analysis of microarray gene expression data. The results of cluster analysis are open to subjective interpretation. To facilitate the objective inference of such analyses, we use flexible parameterizations of the cluster means, paired with subset model selection, to generate sparse and easy-to-interpret representations of each cluster. Model selection in clustering is combinatorial in the numbers of clusters and experimental conditions, and thus presents a computationally challenging task. In this paper we introduce a simultaneous approach to subset model selection, applicable to both model selection in cluster and significance analysis. Our approach draws on results from rate-distortion theory, and allows us to turn the combinatorial model selection problem into a fast and simple line search. We show that simultaneous cluster model selection generates objectively interpretable models, and that the selection performance is competitive with a combinatorial search, at a fraction of the computational cost. Moreover, we show that the rate-distortion based significance analysis substantially increases the power compared with standard methods. ∗contact: [email protected], fax +1 732 445-3428, telephone +1 732 445-3145