Sparsistent Estimation of Time-Varying Discrete Markov Random Fields

In recent years, we have witnessed fast advancement of data-acquisition techniques in many areas, including biological domains, engineering and social sciences. As a result, new statistical and machine learning techniques are needed to help us develop a better understanding of complexities underlying large, noisy data sets. Networks have been commonly used to abstract noisy data and provide an insight into regularities and dependencies between observed variables. For example, in a biological study, nodes of the network can represent genes in one organism and edges can represent associations or regulatory dependencies among genes. In a social domain, nodes of a network can represent actors and edges can represent interactions between actors. Recent popular techniques for modeling and exploring networks are based on the structure estimation in the probabilistic graphical models, specifically, Markov Random Fields (MRFs).