Bayesian Multitask Distance Metric Learning

We present a Bayesian approach for jointly learning distance metrics for a large collection of potentially related learning tasks. We assume there exists a relatively smaller set of basis distance metrics and the distance metric for each task is a sparse, positively weighted combination of these basis distance metrics. The set of basis distance metrics and the combination weights are learned from data. Moreover, taking a nonparametric Bayesian approach, the number of basis distance metrics need not be set a priori. Our proposed construction significantly reduces the number of parameters to be learned, especially when the number of tasks and/or data dimensionality is large. Several existing methods for multitask/transfer distance metric learning arise as special cases of our model. Preliminary results on real-world data show that our model outperforms various baselines. We also discuss some possible extensions of our model and future work.