Soft computing for the posterior of a matrix t graphical network

• Published in: International journal of approximate reasoning Vol. 180; p. 109397
• Main Authors: Pillay, Jason, Bekker, Andriette, Ferreira, Johannes, Arashi, Mohammad
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2025
• Subjects: Adjacency matrix; Bayesian network; Gaussian graphical model; Matrix variate gamma distribution; Matrix variate t; Precision matrix; Stock price data; Matrix variate t; Precision matrix; Stock price data; Matrix variate gamma distribution; Adjacency matrix; Gaussian graphical model; Bayesian network
• ISSN: 0888-613X
• DOI: 10.1016/j.ijar.2025.109397

Modeling noisy data in a network context remains an unavoidable obstacle; fortunately, random matrix theory may comprehensively describe network environments. Noisy data necessitates the probabilistic characterization of these networks using matrix variate models. Denoising network data using a Bayesian approach is not common in surveyed literature. Therefore, this paper adopts the Bayesian viewpoint and introduces a new version of the matrix variate t graphical network. This model's prior beliefs rely on the matrix variate gamma distribution to handle the noise process flexibly; from a statistical learning viewpoint, such a theoretical consideration benefits the comprehension of structures and processes that cause network-based noise in data as part of machine learning and offers real-world interpretation. A proposed Gibbs algorithm is provided for computing and approximating the resulting posterior probability distribution of interest to assess the considered model's network centrality measures. Experiments with synthetic and real-world stock price data are performed to validate the proposed algorithm's capabilities and show that this model has wider flexibility than the model proposed by [13]. •Expanding the framework for denoising financial data inside the realm of graphical network theory, where the assumption of normality in the model is inadequate to account for the variation.•Introduction of the matrix variate gamma and inverse matrix variate gamma as priors for the covariance matrices; the univariate scale parameter β may be fixed or subject to a prior.•Following Bayesian inference with more flexible priors, there is an improvement based on relevant accuracy measures.•Experimental results indicate that our proposed framework and results outperform those of [13].