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Title: Correlated random measures Authors:  Rajesh Ranganath - Princeton University (United States) [presenting]
David Blei - Columbia University (United States)
Abstract: Many hierarchical Bayesian nonparametric models are built from completely random measures, in which atom weights are independent. This leads to implicit independence assumptions in the corresponding hierarchical model, assumptions that are often misplaced in real-world settings. We address this limitation. We develop correlated random measures, a class of random measures where the measures on two disjoint sets can exhibit both positive and negative dependence. Correlated random measures model correlation within the measure by using a Gaussian process in concert with a Poisson process. With this construction, for example, we can develop a latent feature model for which we can infer both the properties of the latent features and their correlation. We develop several examples of correlated random measures and touch on correlated Poisson Kingman constructions. We show improved predictive performance on large collections of text and large collections of medical diagnostic codes.