Online Non-linear Topology Identification from Graph-connected Time Series

TL;DR

This paper introduces an online kernel-based method for identifying causal topologies in non-linear, non-stationary time series, effectively handling streaming data and outperforming existing batch methods.

Contribution

It presents a novel online algorithm for topology estimation in non-linear time series, addressing the limitations of batch-based approaches and enabling real-time analysis.

Findings

Outperforms state-of-the-art topology estimation methods

Effective on both real and synthetic datasets

Handles streaming sensor signals efficiently

Abstract

Estimating the unknown causal dependencies among graph-connected time series plays an important role in many applications, such as sensor network analysis, signal processing over cyber-physical systems, and finance engineering. Inference of such causal dependencies, often know as topology identification, is not well studied for non-linear non-stationary systems, and most of the existing methods are batch-based which are not capable of handling streaming sensor signals. In this paper, we propose an online kernel-based algorithm for topology estimation of non-linear vector autoregressive time series by solving a sparse online optimization framework using the composite objective mirror descent method. Experiments conducted on real and synthetic data sets show that the proposed algorithm outperforms the state-of-the-art methods for topology estimation.