## Statistical Classification and Cluster Processes

author: Peter McCullagh, Department of Statistics, University of Chicago
published: July 30, 2009,   recorded: June 2009,   views: 317
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# Slides

0:00 Slides Probabilistic classification models Outline Statistical classification and discrimination Partitions The set En of partitions of [n] Probability distributions on partitions Exchangeable partition process The Ewens partition process Other interpertations of the Ewens process Characterization of the Ewens distribution The Gauss-Ewens cluster process Exchangeability of cluster process Constructive version of Gauss-Ewens process The Gauss-Ewens cluster process Constructive version of Gauss-Ewens process Ordinary Gauss-Ewens process in R2 Gauss-Ewens process with sub-clusters in R2 Constructive version of Gauss-Ewens process The Gauss-Ewens cluster process Gauss-Ewens process with sub-clusters in R2 Gauss-Ewens process with topological clusters Cluster models for classification w/o classes Explicit calculation of conditional distribution Block having maximum conditional probability A point process model for classification Point process distributions: outline for general X α -permanent: definition and properties Boson point process Boson multi-class model Classification distributions: labelled and unlabelled Example Density plot of predictive probability pr(red | data) Algorithms for approximation References (1) References (2) References (3)

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# Description

After an introduction to the notion of an exchangeable random partition, we continue with a more detailed discussion of the Ewens process and some of its antecedents. The concept of an exchangeable cluster process will be described, the main example being the Gauss-Ewens process. Some applications of cluster processes will be discussed, including problems of classification or supervised learning, and cluster analysis (unsupervised learning). A second type of probabilistic model based on point processes is also described. By contrast, which the Gauss-Ewes cluster process, the domain associated with each class is more diffuse and not localized in the feature space. For both models, the classification problem is interpreted as the problem of computing the predictive distribution for the class of a new object having a given feature vector. In one case, this is a conditional distribution given the observed features, in the other a Papangelou conditional intensity.