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

Yang Cheng1, Dehua Li1,*, 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.

Keywords

Beta process, joint distribution, beta Bernoulli process, exact inference

Cite This Article

Cheng, Y., Li, D., Jiang, W. (2019). The Exact Inference of Beta Process and Beta Bernoulli Process From Finite Observations. CMES-Computer Modeling in Engineering & Sciences, 121(1), 49–82.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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