Variational Bayesian Matching

Matching of samples refers to the problem of inferring unknown co-occurrence or alignment between observations in two data sets. Given two sets of equally many samples, the task is to find for each sample a representative sample in the other set, without prior knowledge on a distance measure between the sets. Recently a few alternative solutions have been suggested, based on maximization of joint likelihood or various measures of between-data statistical dependency. In this work we present an variational Bayesian solution for the problem, learning a Bayesian canonical correlation analysis model with a permutation parameter for re-ordering the samples in one of the sets. We approximate the posterior over the permutations, and demonstrate that the resulting matching algorithm clearly outperforms all of the earlier solutions.