Bayesian estimation of the inverted Beta-Liouville mixture models with extended variational inference

Wenbo Guan; Shilin Wang; Xiongtao Ma; Yongfa Ling; Huirui Cao; Fan Yang

doi:10.1117/12.2605311

28 October 2021 Bayesian estimation of the inverted Beta-Liouville mixture models with extended variational inference

Wenbo Guan, Shilin Wang, Xiongtao Ma, Yongfa Ling, Huirui Cao, Fan Yang

Proceedings Volume 11884, International Symposium on Artificial Intelligence and Robotics 2021; 1188417 (2021) https://doi.org/10.1117/12.2605311
Event: International Symposium on Artificial Intelligence and Robotics 2021, 2021, Fukuoka, Japan

Abstract

This paper addresses the problem of the Bayesian estimation of the inverted Beta-Liouville mixture model (IBLMM), which has a fairly flexible positive data modeling capability. This problem does not usually admit an analytically tractable solution. Sampling approaches (e.g., Markov chain Monte Carlo (MCMC)) can be used to address this problem. However, these approaches are usually computationally demanding, and as a result, they may be impractical for real-world applications. Therefore, we adopt the recently proposed extended variational inference (EVI) framework to address this problem in an elegant way. First, some lower bound approximations are introduced to the evidence lower bound (ELBO) (i.e., the original objective function) in the conventional variational inference (VI) framework, which yields a computationally tractable lower bound. Then, we can derive a form-closed analytical solution by taking this bound as the new objective function and optimizing it with respect to individual variational factors. We verify the effectiveness of this method by using it in two real applications, namely, text categorization and face detection.

Citation Download Citation

Wenbo Guan, Shilin Wang, Xiongtao Ma, Yongfa Ling, Huirui Cao, and Fan Yang "Bayesian estimation of the inverted Beta-Liouville mixture models with extended variational inference", Proc. SPIE 11884, International Symposium on Artificial Intelligence and Robotics 2021, 1188417 (28 October 2021); https://doi.org/10.1117/12.2605311

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KEYWORDS

Data modeling

Facial recognition systems

Neodymium

Expectation maximization algorithms

Machine learning

Process modeling

Statistical analysis

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