Correlated Random Measures

Rajesh Ranganath, David M. Blei

Research output: Contribution to journalArticlepeer-review


We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process-based construction in which the atom weights are independent. Completely random measures imply strong independence assumptions in the corresponding hierarchical model, and these assumptions are often misplaced in real-world settings. Correlated random measures address this limitation. They model correlation within the measure by using a Gaussian process in concert with the Poisson process. With correlated random measures, for example, we can develop a latent feature model for which we can infer both the properties of the latent features and their dependency pattern. We develop several other examples as well. We study a correlated random measure model of pairwise count data. We derive an efficient variational inference algorithm and show improved predictive performance on large datasets of documents, web clicks, and electronic health records. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)417-430
Number of pages14
JournalJournal of the American Statistical Association
Issue number521
StatePublished - Jan 2 2018


  • Bayesian nonparametrics
  • Gaussian processes
  • Health records
  • Hierarchical models
  • Poisson processes
  • Random measures

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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