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

2024-12-31

AI Summary

Existing time-varying graph learning methods lack robustness to outliers and noise in dynamic networks exhibiting heavy-tailed distributions—common in financial data. To address this, we propose a robust time-varying graph learning framework that, for the first time, integrates a Student’s *t* likelihood into a spectrally constrained nonnegative vector autoregressive (VAR) graph model, thereby jointly enabling heavy-tailed dependency modeling and structural stability of the learned graphs. The framework supports missing-data imputation and semi-online topology adaptation. Parameter estimation is performed via an efficient stochastic iterative optimization algorithm. Experiments on synthetic benchmarks and real-world financial time-series networks demonstrate significant improvements in outlier robustness and node clustering accuracy over state-of-the-art baselines, validating the framework’s effectiveness and superiority in modeling heavy-tailed dynamic relational structures.

Technology Category

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

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
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Time-Varying Graphs
• Outlier Data
• Financial Data

Innovation

• Time-Varying Graph Learning
• Heavy-Tailed Distributions
• Financial Data Analysis