Correlated Random Measures
This addresses the problem of misplaced independence assumptions in real-world hierarchical models for researchers in Bayesian nonparametrics, though it is incremental as it builds on existing Poisson-process frameworks.
The paper tackles the limitation of strong independence assumptions in hierarchical Bayesian nonparametric models by introducing correlated random measures, which allow for flexible dependence among atom weights using a Gaussian process. It demonstrates improved predictive performance on large datasets like documents, web clicks, and electronic health records.
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 data sets of documents, web clicks, and electronic health records.