Topological regularization with information filtering networks

• Main Author: Aste, T. (Author)
• Format: Article
• Language: English
• Published: Elsevier Inc. 2022
• Subjects: Chow-liu tree; Chow-Liu Trees; Complex networks; Complex systems; Covariance selection; Expectation Maximization; IFN regression; Information filtering; Information filtering network; Information filtering network regression; Information filtering networks; Inverse covariance; Inverse problems; Maximum principle; Probability distributions; Regression analysis; Regularisation; Sparse expectation-maximization; Sparse inverse covariance; Topological regularization; Topology
• Online Access: View Fulltext in Publisher

 This paper introduces a novel methodology to perform topological regularization in multivariate probabilistic modeling by using sparse, complex, networks which represent the system's dependency structure and are called information filtering networks (IFN). This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with both linear and non-linear multivariate probability distributions such as the elliptical and generalized hyperbolic families. It can also be directly implemented for topological regularization of multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific expectation–maximization likelihood maximization procedure over a sparse chordal network representation is proposed for this sparse Student-t case. Examples with real data from stock prices log-returns and from artificially generated data demonstrate applicability, performances, robustness and potentials of this methodology. © 2022 The Author(s)