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Fried Chicken Bucket Processes Mary McGlohon Machine Learning Department Carnegie Mellon University mcglohon cmu edu Keywords Stochastic processes graphical models hierarchical models Abstract Chinese restaurant processes are useful hierarchical models however they make certain assumptions on finiteness that may not be appropriate for modeling some phenomena Therefore we introduce fried chicken bucket processes FCBP that involve different sampling methods We also introduce spork notation as a simple way of representing this model 1 Introduction Chinese restaurant processes and Indian buffet processes are useful in a number of domains for statistical modeling This work introduces a new model the Fried chicken bucket process and presents spork notation a useful representation for FCBP s and other graphical models To the author s knowledge this is the first restaurant related model that samples from continuous distributions in addition to discrete ones 2 Related work It is useful to describe work that has inspired this paper 1 2 1 Chinese restaurant processes The Chinese restaurant process CRP is a stochastic process that produces a distribution on partitions of integers 1 To visualize one imagines a Chinese restaurant with an infinite number of tables Customers arrive one at a time As each arrives he decides which table to sit at based on the following distribution similar to a Dirichlet distribution p T ablei n n i n 1 n 1 where n is the number of previous customers and n i is the number seated at table i This may be extended into hierarchies such as the customers also choosing from an infinite number of Chinese restaurants 2 This process also inspired Griffiths and Ghahramani to describe the Indian buffet process for infinite latent feature models as shown in 5 and applied again by Thibaux and Jordan in 6 p N ewT able n 2 2 Plate notation In high dimensional problems representation comes in the form of very large graphical models with many nodes Formerly researchers

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