Probabilistic Modeling for Frequency Vectors Using a Flexible Shifted-Scaled Dirichlet Distribution Prior

Author:

Zamzami Nuha1ORCID,Bouguila Nizar2

Affiliation:

1. Concordia Institute for Information Systems Engineering and Department of Computer Science and Artificial Intelligence, University of Jeddah, Jeddah, Saudi Arabia

2. Concordia Institute for Information Systems Engineering

Abstract

Burstiness and overdispersion phenomena of count vectors pose significant challenges in modeling such data accurately. While the dependency assumption of the multinomial distribution causes its failure to model frequency vectors in several machine learning and data mining applications, researchers found that by extending the multinomial distribution to the Dirichlet Compound multinomial (DCM), both phenomena modeling can be addressed. However, Dirichlet distribution is not the best choice, as a prior, given its negative-correlation and equal-confidence requirements. Thus, we propose to use a flexible generalization of the Dirichlet distribution, namely, the shifted-scaled Dirichlet, as a prior to the multinomial, which grants the model a capability to better fit real data, and we call the new model the Multinomial Shifted-Scaled Dirichlet (MSSD). Given that the likelihood function plays a key role in statistical inference, e.g., in maximum likelihood estimation and Fisher information matrix investigation, we propose to improve the efficiency of computing the MSSD log-likelihood by approximating its function based on Bernoulli polynomials where the log-likelihood function is computed using the proposed mesh algorithm. Moreover, given the sparsity and high-dimensionality nature of count vectors, we propose to improve its computation efficiency by approximating the novel MSSD as a member of the exponential family of distribution, which we call EMSSD. The clustering is based on mixture models, and for learning a model, selection approach is seamlessly integrated with the estimation of the parameters. The merits of the proposed approach are validated via challenging real-world applications such as hate speech detection in Twitter, real-time recognition of criminal action, and anomaly detection in crowded scenes. Results reveal that the proposed clustering frameworks offer a good compromise between other state-of-the-art techniques and outperform other approaches previously used for frequency vectors modeling. Besides, comparing to the MSSD, the approximation EMSSD has reduced the computational complexity in high-dimensional feature spaces.

Publisher

Association for Computing Machinery (ACM)

Subject

General Computer Science

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sentiment Analysis Using Smoothed Probabilistic-Based Models;2023 9th International Conference on Control, Decision and Information Technologies (CoDIT);2023-07-03

2. A Fully Bayesian Inference with Gibbs Sampling for Finite and Infinite Discrete Exponential Mixture Models;Applied Artificial Intelligence;2022-03-15

3. Sparse Generalized Dirichlet Prior Based Bayesian Multinomial Estimation;Advanced Data Mining and Applications;2022

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