Time-Varying Graph Learning for Data with Heavy-Tailed Distribution

TL;DR

This paper introduces a robust method for learning time-varying graphs from heavy-tailed data, such as financial datasets, by integrating spectral graph properties with a Student-t distribution model.

Contribution

It presents a novel stochastic approach combining VAR models and Student-t distributions for dynamic graph learning with robustness to outliers and missing data.

Findings

Effective in modeling heavy-tailed data

Handles noise and missing values well

Demonstrates success on financial datasets

Abstract

Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such networks is known as time-varying graph learning. Current methodology for learning such models often lacks robustness to outliers in the data and fails to handle heavy-tailed distributions, a common feature in many real-world datasets (e.g., financial data). This paper addresses the problem of learning time-varying graph models capable of efficiently representing heavy-tailed data. Unlike traditional approaches, we incorporate graph structures with specific spectral properties to enhance data clustering in our model. Our proposed method, which can also deal with noise and missing values in the data, is based on a stochastic approach, where a non-negative vector auto-regressive (VAR) model captures the variations in the graph and a Student-t distribution models the signal originating from this underlying time-varying graph. We propose an iterative method to learn time-varying graph topologies within a semi-online framework where only a mini-batch of data is used to update the graph. Simulations with both synthetic and real datasets demonstrate the efficacy of our model in analyzing heavy-tailed data, particularly those found in financial markets.