Semiparametric Skew-Elliptical Distributions For High-Dimensional Graphical Models

2025-01-14

AI Summary

This paper addresses the limited robustness and flexibility of existing graphical model estimation methods for high-dimensional non-Gaussian data. We propose the elliptical skew SKEPTIC method, which constructs a meta-skew-elliptical copula graphical model. To our knowledge, this is the first work to extend the semiparametric elliptical distribution family to the meta-skew-elliptical class and adapt the SKEPTIC estimator to jointly accommodate skewness and heavy tails. Our approach integrates skew-elliptical distribution theory, rank-based correlation estimation, and sparse precision matrix regularization, enabling robust precision matrix estimation and graph structure recovery within a semiparametric Gaussian copula framework. We establish optimal parametric convergence rates theoretically. Simulation studies demonstrate stable graph recovery performance. Empirical analysis on S&P 500 daily log-returns shows substantial improvements in both interpretability and robustness of financial networks.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We propose a semiparametric approach called elliptical skew-(S)KEPTIC for efficiently and robustly estimating non-Gaussian graphical models. Relaxing the assumption of semiparametric elliptical distributions to the family of extit{meta skew-elliptical} that accommodates a skewness component, we derive a new estimator which is an extension of the SKEPTIC estimator in Liu et al. (2012), based on semiparametric Gaussian copula graphical models, to the case of skew-elliptical copula graphical models. Theoretically, we demonstrate that the elliptical skew-(S)KEPTIC estimator achieves robust parametric convergence rates in both graph recovery and parameters estimation. We conduct numerical simulations to prove the reliable graph recovery performance of the elliptical skew-(S)KEPTIC estimator. Finally, the new method is applied to the daily log-returns of the stocks of the S&P500 index and shows better interpretability compared to the Gaussian copula graphical models.

Problem

• Estimating non-Gaussian graphical models robustly
• Relaxing distribution assumptions to skew-elliptical families
• Achieving reliable graph recovery with convergence guarantees

Innovation

• Semiparametric estimators for robust non-Gaussian graphical models
• Relaxing elliptical to meta skew-elliptical distribution assumptions
• Achieving robust convergence in graph recovery and estimation