Online Joint Topology Identification and Signal Estimation from Streams with Missing Data

TL;DR

This paper introduces an online algorithm for real-time topology identification and signal estimation from streaming data with missing samples, capable of handling time-varying networks efficiently.

Contribution

It presents a novel online method based on inexact proximal gradient descent for jointly estimating VAR-based topologies and signals with missing data.

Findings

Algorithm effectively tracks dynamic topologies.

Constant complexity per iteration enables scalability.

Numerical results demonstrate accurate online performance.

Abstract

Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often inferred from observed spatio-temporal data. When data are affected by noise and/or missing samples, topology identification and signal recovery (reconstruction) tasks must be performed jointly. Additional challenges arise when i) the underlying topology is time-varying, ii) data become available sequentially, and iii) no delay is tolerated. This study proposes an online algorithm to overcome these challenges in estimating VAR model-based topologies, having constant complexity per iteration, which makes it interesting for big-data scenarios. The inexact proximal online gradient descent framework is used to derive a performance guarantee for the proposed algorithm, in the form of a dynamic regret bound. Numerical tests are also presented, showing the ability of the proposed algorithm to track time-varying topologies with missing data in an online fashion.