Bayesian object matching

Matching of object refers to the problem of inferring unknown co-occurrence or alignment between observations or samples 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. Given a distance measure, the problem would correspond to a linear assignment problem, the problem of finding a permutation that re-orders samples in one set to minimize the total distance. When no such measure is available, we need to consider more complex solutions. Typical approaches maximize statistical dependency between the two sets, whereas in this work we present a Bayesian solution that builds a joint model for the two sources. We learn a Bayesian canonical correlation analysis model that includes a permutation parameter for re-ordering the samples in one of the sets. We provide both variational and sampling-based inference for approximative Bayesian analysis, and demonstrate on three data sets that the resulting methods outperform the earlier solutions.