Inspired by "Google™ Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe a very simple algorithm for solving it. Our algorithm uses a model based concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly using a single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from Each Movie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia. We compare to Google™ Sets and show that Bayesian Sets gives very reasonable set completions.
Ghahramani, Z; Heller, KA
Start / End Page
International Standard Serial Number (ISSN)