Time Varying Undirected Graphs

TL;DR

This paper introduces a method to estimate evolving undirected graphs from time-varying data, addressing the challenge of non-i.i.d. data in high-dimensional settings.

Contribution

It extends graph estimation techniques to handle non-stationary data where the underlying distribution and graph structure change over time.

Findings

Proposes a new estimation method for time-varying graphs.

Demonstrates effectiveness on simulated data.

Addresses limitations of existing i.i.d. assumptions.

Abstract

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$ penalization methods. However, current methods assume that the data are independent and identically distributed. If the distribution, and hence the graph, evolves over time then the data are not longer identically distributed. In this paper, we show how to estimate the sequence of graphs for non-identically distributed data, where the distribution evolves over time.