Soft computing for the posterior of a matrix t graphical network

Abstract

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].

HIGHLIGHTS • 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].