Robust time-varying undirected graphs

Abstract

Undirected graphs are useful tools for the analysis of sparse and highdimensional data sets. In this setting the sparsity helps in reducing the complexity of the model. However, sparse graphs are usually estimated under the Gaussian paradigm thereby leading to estimates that are very sensitive to the presence of outlying observations. In this paper we deal with sparse time-varying undirected graphs, namely sparse graphs whose structure evolves over time. Our contribution is to provide a robustification of these models, in particular we propose a robust estimator which minimises the γ -divergence. We provide an algorithm for the parameter estimation and we investigate the rate of convergence of the proposed estimator.