Inferring Dynamic Hidden Graph Structure in Heterogeneous Correlated Time Series

2025-12-01

AI Summary

This paper addresses the problem of inferring dynamic hidden graph structures from heterogeneous, multivariate time series exhibiting distinct periodicities and generative mechanisms. To this end, we propose Windowed Variance–Correlation (WVC), a novel metric that directly estimates time-varying weighted adjacency matrices within a unified dynamical graph model framework, operating over specified temporal windows. WVC jointly accounts for local signal volatility and cross-series covariation, enabling robust detection of nonstationary and asynchronous dependencies—patterns often missed by conventional approaches such as sliding-window correlation or Granger causality. In extensive synthetic experiments, WVC demonstrates significantly improved accuracy and robustness in modeling dynamic inter-series dependencies, particularly under challenging conditions including large inter-series periodic disparities, low signal-to-noise ratios, and divergent underlying generative processes.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• 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: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and evaluate a windowed variance-correlation metric (WVC) designed to quantify time-varying correlations between signals. This method directly recovers hidden relationships in an specified time interval as a weighted adjacency matrix, consequently inferring hidden dynamic graph structure. On simulated data, our method captures correlations that other methods miss. The proposed method expands the ability to learn dynamic graph structure between significantly different signals within a single cohesive dynamical graph model.

Problem

• Infer hidden dynamic relationships in heterogeneous time series
• Quantify time-varying correlations using a windowed variance-correlation metric
• Recover hidden dynamic graph structure as weighted adjacency matrices

Innovation

• Windowed variance-correlation metric quantifies time-varying correlations
• Recovers hidden relationships as weighted adjacency matrix
• Learns dynamic graph structure between different signals