Open Access

ARTICLE

The Exact Inference of Beta Process and Beta Bernoulli Process From Finite Observations

Yang Cheng¹, Dehua Li^1,*, Wenbin Jiang ²

1 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China.
2 School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China.
* Corresponding Author: Dehua Li. Email: lidehua1946@sina.com.

Computer Modeling in Engineering & Sciences 2019, 121(1), 49-82. https://doi.org/10.32604/cmes.2019.07657

Abstract

Beta Process is a typical nonparametric Bayesian model. and the Beta Bernoulli Process provides a Bayesian nonparametric prior for models involving collections of binary valued features. Some previous studies considered the Beta Process inference problem by giving the Stick-Breaking sampling method. This paper focuses on analyzing the form of precise probability distribution based on a Stick-Breaking approach, that is, the joint probability distribution is derived from any finite number of observable samples: It not only determines the probability distribution function of the Beta Process with finite observation (represented as a group of number between [0,1]), but also gives the distribution function of the Beta Bernoulli Process with the same finite dimension (represented as a matrix with element value of 0 or, 1) by using this distribution as a prior.

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Keywords

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