3cff0580d7873410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Statistics SeminarDepartment Seminar Series: Tamara Broderick, Feature Allocations, Paintboxes, and Probability Functions ###@###(Fri, 17 Jan 2014)Department Seminar Series: Tamara Broderick, Feature Allocations, Paintboxes, and Probability Functions ###@###(Fri, 17 Jan 2014)4448 East Hallstats1389976200000138997620000011:30 AM<p style=" text-indent: 0pt; color: black; margin-top: 0pt; font-size: 10.0pt; margin-bottom: 0pt; margin-right: 0pt; font-family: 'Times New Roman'; text-align: left;"><span style=" font-size: 14.0pt;">Abstract: &nbsp;Clustering involves placing entities into mutually exclusive categories. &nbsp;We wish to relax the requirement of mutual exclusivity, allowing objects to belong simultaneously to multiple classes, a formulation that we refer to as "feature allocation." &nbsp;The first step is a theoretical one. &nbsp;In the case of clustering the class of probability distributions over exchangeable partitions of a dataset has been characterized (via exchangeable partition probability functions and the Kingman paintbox). &nbsp;These characterizations support an elegant nonparametric Bayesian framework for clustering in which the number of clusters is not assumed to be known a priori. &nbsp;We establish an analogous characterization for feature allocation; we define notions of "exchangeable feature probability functions" and "feature paintboxes" that lead to a Bayesian framework that does not require the number of features to be fixed a priori. &nbsp;The second step is a computational one. &nbsp;Rather than appealing to Markov chain Monte Carlo for Bayesian inference, we develop a method to transform Bayesian methods for feature allocation (and other latent structure problems) into optimization problems with objective functions analogous to K-means in the clustering setting. &nbsp;These yield approximations to Bayesian inference that are scalable to large inference problems.</span></p> <p style=" text-indent: 0pt; color: black; margin-top: 0pt; font-size: 10.0pt; margin-bottom: 0pt; margin-right: 0pt; font-family: 'Times New Roman'; text-align: left;">&nbsp;</p>Nlorieannbzuniga1389643097587cbff0580d7873410VgnVCM100000c2b1d38d____once11112newnew/UMICH/stats/Home/News & Events/Statistics Seminar/Tamara Broderick Seminar Flyer WN 2014.pdfTamara Broderick, Doctoral Candidate, Department of Statistics, University of California, Berkeleyhttp://www.stat.berkeley.edu/~tab/index.html