# Online Graph Learning in Dynamic Environments

arXiv: https://arxiv.org/abs/2110.05023 · HTML: https://mlsanity.com/paper/2110.05023/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020)
- [Online Discriminative Graph Learning from Multi-Class Smooth Signals](https://mlsanity.com/paper/2101.00184/) (2021)
- [Time-Varying Graph Learning with Constraints on Graph Temporal Variation](https://mlsanity.com/paper/2001.03346/) (2020)
- [Online Topology Identification from Vector Autoregressive Time Series](https://mlsanity.com/paper/1904.01864/) (2019)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [Online Non-linear Topology Identification from Graph-connected Time Series](https://mlsanity.com/paper/2104.00030/) (2021)
- [Prediction-Correction Algorithms for Time-Varying Constrained Optimization](https://mlsanity.com/paper/1611.03681/) (2016)
- [Online Time-Varying Topology Identification via Prediction-Correction Algorithms](https://mlsanity.com/paper/2010.11634/) (2020)
- [Nonlinear Structural Vector Autoregressive Models for Inferring Effective Brain Network Connectivity](https://mlsanity.com/paper/1610.06551/) (2016)
- [Dynamic Regret Analysis for Online Tracking of Time-varying Structural Equation Model Topologies](https://mlsanity.com/paper/2003.08145/) (2020)

## Built on by (most cited first, 1 of 1)

- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)

## Abstract (arXiv)

Inferring the underlying graph topology that characterizes structured data is pivotal to many graph-based models when pre-defined graphs are not available. This paper focuses on learning graphs in the case of sequential data in dynamic environments. For sequential data, we develop an online version of classic batch graph learning method. To better track graphs in dynamic environments, we assume graphs evolve in certain patterns such that dynamic priors might be embedded in the online graph learning framework. When the information of these hidden patterns is not available, we use history data to predict the evolution of graphs. Furthermore, dynamic regret analysis of the proposed method is performed and illustrates that our online graph learning algorithms can reach sublinear dynamic regret. Experimental results support the fact that our method is superior to the state-of-art methods.