Search Algorithms and Loss Functions for Bayesian Clustering

We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the minimization of the posterior expected loss is challenging. Our approach is a stochastic search based on a series of greedy optimizations performed in a random order and is embarrassingly parallel. We consider several loss functions, including Binder loss and variation of information. We note that criticisms of Binder loss are the result of using equal penalties of misclassification and we show an efficient means to compute Binder loss with potentially unequal penalties. Furthermore, we extend the original variation of information to allow for unequal penalties and show no increased computational costs. We provide a reference implementation of our algorithm. Using a variety of examples, we show that our method produces clustering estimates that better minimize the expected loss and are obtained faster than existing methods.