Online Time-Varying Topology Identification via Prediction-Correction Algorithms

TL;DR

This paper introduces an online prediction-correction algorithm for identifying time-varying graph topologies from data, addressing the challenges of non-stationarity and ill-posedness in dynamic environments.

Contribution

It develops a general-purpose online method for dynamic topology identification based on recent time-varying optimization techniques, with a specialized case study on Gaussian graphical models.

Findings

Effective in non-stationary environments

Intrinsic temporal regularization of topology

Validated on Gaussian graphical model case study

Abstract

Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the topology has to be learned from data. Topology identification is a challenging task, as the problem is often ill-posed, and becomes even harder when the graph structure is time-varying. In this paper, we address the problem of dynamic topology identification by building on recent results from time-varying optimization, devising a general-purpose online algorithm operating in non-stationary environments. Because of its iteration-constrained nature, the proposed approach exhibits an intrinsic temporal-regularization of the graph topology without explicitly enforcing it. As a case-study, we specialize our method to the Gaussian graphical model (GGM) problem and corroborate its performance.