Local Dependent Components

Abstract

We introduce a mixture of probabilistic canonical correlation analyzers model for analyzing local correlations, or more generally mutual statistical dependencies, in cooccurring data pairs. The model extends the traditional canonical correlation analysis and its probabilistic interpretation in three main ways. First, a full Bayesian treatment enables analysis of small samples (large p, small n, a crucial problem in bioinformatics, for instance), and rigorous estimation of the degree of dependency and independency. Secondly, the mixture formulation generalizes the method from global linearity to the more reasonable assumption of different kinds of dependencies for different kinds of data. As a third novel extension the method decomposes the variation in the data into shared and data set-specific components.