# Time-Varying Graph Learning for Data with Heavy-Tailed Distribution

arXiv: https://arxiv.org/abs/2501.00606 · HTML: https://mlsanity.com/paper/2501.00606/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 64 references that are in the map.
- First posted on arXiv 31 Dec 2024.

## Builds on (most cited first, 17 of 17)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [A Class of Prediction-Correction Methods for Time-Varying Convex Optimization](https://mlsanity.com/paper/1509.05196/) (2015)
- [Learning Undirected Graphs in Financial Markets](https://mlsanity.com/paper/2005.09958/) (2020)
- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Time-Varying Graph Learning with Constraints on Graph Temporal Variation](https://mlsanity.com/paper/2001.03346/) (2020)
- [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)
- [Tracking Switched Dynamic Network Topologies from Information Cascades](https://mlsanity.com/paper/1606.08882/) (2016)
- [Does the ℓ1-norm Learn a Sparse Graph under Laplacian Constrained Graphical Models?](https://mlsanity.com/paper/2006.14925/) (2020)
- [Online Time-Varying Topology Identification via Prediction-Correction Algorithms](https://mlsanity.com/paper/2010.11634/) (2020)
- [Joint Signal Recovery and Graph Learning from Incomplete Time-Series](https://mlsanity.com/paper/2312.16940/) (2023)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning Time-Varying Graphs from Incomplete Graph Signals](https://mlsanity.com/paper/2510.17903/) (2025)
- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (2025)

## Abstract (arXiv)

Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such networks is known as time-varying graph learning. Current methodology for learning such models often lacks robustness to outliers in the data and fails to handle heavy-tailed distributions, a common feature in many real-world datasets (e.g., financial data). This paper addresses the problem of learning time-varying graph models capable of efficiently representing heavy-tailed data. Unlike traditional approaches, we incorporate graph structures with specific spectral properties to enhance data clustering in our model. Our proposed method, which can also deal with noise and missing values in the data, is based on a stochastic approach, where a non-negative vector auto-regressive (VAR) model captures the variations in the graph and a Student-t distribution models the signal originating from this underlying time-varying graph. We propose an iterative method to learn time-varying graph topologies within a semi-online framework where only a mini-batch of data is used to update the graph. Simulations with both synthetic and real datasets demonstrate the efficacy of our model in analyzing heavy-tailed data, particularly those found in financial markets.