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Feature allocations, probability functions, and paintboxes

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If you have a question about this talk, please contact Zoubin Ghahramani.

The problem of inferring a clustering of a data set has been the subject of much research in Bayesian analysis, and there currently exists a solid mathematical foundation for Bayesian approaches to clustering. In particular, the class of probability distributions over partitions of a data set has been characterized in a number of ways, including via exchangeable partition probability functions (EPPFs) and the Kingman paintbox. Here, we develop a generalization of the clustering problem, called feature allocation, where we allow each data point to belong to an arbitrary, non-negative integer number of groups, now called features or topics. We define and study an “exchangeable feature probability function” (EFPF)—-analogous to the EPPF in the clustering setting—-for certain types of feature models. Moreover, we introduce a “feature paintbox” characterization—-analogous to the Kingman paintbox for clustering—-of the class of exchangeable feature models. We use this feature paintbox construction to provide a further characterization of the subclass of feature allocations that have EFPF representations.

This talk is part of the Machine Learning @ CUED series.

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