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Activity Number: 367
Type: Invited
Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #310838
Title: Feature Allocations, Probability Functions, and Paintboxes
Author(s): Tamara Broderick*+ and Jim Pitman and Michael Jordan
Companies: University of California, Berkeley and University of California, Berkeley and University of California, Berkeley
Keywords: feature ; feature allocation ; probability function ; paintbox ; Indian buffet process ; beta process
Abstract:

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 provide analogous constructions to the clustering case by defining and studying "exchangeable feature probability functions" (EFPF) and the "feature paintbox." We demonstrate how particular Bayesian nonparametric feature models called the Indian buffet process and the beta process fit into this framework. In this manner, we bring the same level of completeness to the treatment of Bayesian nonparametric feature modeling that has previously been achieved for Bayesian nonparametric clustering.


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