NonparametricBayes

NonparametricBayes - Nonparametric Bayesian Models...

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Nonparametric Bayesian Models
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10/25/10 Parametric Model
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10/25/10 Nonparametric Model
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10/25/10 Example: k Nearest Neighbor (kNN) Classifier x x x x o x o o o o ? ? ?
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10/25/10 Bayesian Nonparametric Models Model is based on an infinite dimensional parameter space But utilizes only a finite subset of available parameters on any given (finite) data set i.e., model complexity is finite but unbounded Typically § Parameter space consists of functions or measures § Complexity is limited by marginalizing out over surplus dimensions nonnegative function over sets
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10/25/10 Content of most slides borrowed from Zhoubin Ghahramani and Michael
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10/25/10 What Will This Buy Us? Distributions over § Partitions E.g., for inferring topics when number of topics not known in advance E.g., for inferring clusters when number of clusters not known in advance § Directed trees of unbounded depth and breadth E.g., for inferring category structure § Sparse binary infinite dimensional matrices E.g., for inferring implicit features § Other stuff I don’t understand yet
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10/25/10 Stick Breaking
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10/25/10 Dirichlet Process Borrowed from Gharamani tutorial
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10/25/10 Dirichlet Process 2 Borrowed from Gharamani tutorial
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10/25/10 Drawing From A Dirichlet Process
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10/25/10 Chinese Restaurant Process: Informal Description Borrowed from Jordan
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10/25/10 Chinese Restaurant Process: Formal Description Borrowed from Gharamani tutorial
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