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

arXiv: https://arxiv.org/abs/2104.00030 · HTML: https://mlsanity.com/paper/2104.00030/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2021.

## Built on by (most cited first, 8 of 8)

- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Structural Knowledge Informed Continual Multivariate Time Series Forecasting](https://mlsanity.com/paper/2402.12722/) (2024)
- [Time-Varying Graph Learning for Data with Heavy-Tailed Distribution](https://mlsanity.com/paper/2501.00606/) (2024)
- [Explainable nonlinear modelling of multiple time series with invertible neural networks](https://mlsanity.com/paper/2107.00391/) (2021)
- [Online Graph Learning in Dynamic Environments](https://mlsanity.com/paper/2110.05023/) (2021)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Random Feature Approximation for Online Nonlinear Graph Topology Identification](https://mlsanity.com/paper/2110.09935/) (2021)
- [Efficient Interpretable Nonlinear Modeling for Multiple Time Series](https://mlsanity.com/paper/2309.17154/) (2023)

## Abstract (arXiv)

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.