Estimating Network Structures using Model Selection

This chapter continues discussing the estimation of pairwise Markov random fields—undirected network models in which edges indicate the strength of conditional associations—introduced in Chapter 6. While Chapter 6 was concerned with the interpretation and saturated estimation (i.e., network structures estimated with all edges included) of such models, this chapter is concerned with unsaturated estimation and model search strategies: how to select which edges should be included in the network model. The chapter discusses four methods of estimating the model structure: thresholding (removing edges that do not meet some criterion), pruning (thresholding followed by re-estimation of non-zero edge-weights), extensive model search strategies (searching through the model space for an optimal model), and finally regularization (penalized likelihood estimation resulting in a sparse model). The chapter ends with recommendations for which estimation strategy should be used in which setting.