Statistical inference with probabilistic graphical models
Devavrat Shah · 2015
Abstract This chapter introduces graphical models as a powerful tool to derive efficient algorithms for inference problems. When dealing with complex interdependent variables, inference problems may become of huge complexity. In this context, the structure of the variables is of great interest. In this chapter, directed and undirected graphical models are first defined, before some crucial results are stated, such as the Hammersley–Clifford theorem of Markov random fields and the junction tree property aimed at finding groupings under which a graphical model becomes a tree. Taking advantage of the structure of the variables, belief propagation is then described, including two particular instances: the sum–product and max–sum algorithms. In the final section, the learning problem is addressed in three different contexts: parameter learning, graphical model learning, and latent graphical model learning.