Structure Learning with Side Information: Sample Complexity

The vertices represent the RVs, and the edges signify the conditional dependencies among the RVs. Structure learning is the process of inferring the edges by observing realizations of the RVs, and it has applications in a wide range of technological, social, and biological networks. Learning the structure of graphs when the vertices are treated in isolation from inferential information known about them is well-investigated. In a wide range of domains, however, often there exist additional inferred knowledge about the structure, which can serve as valuable side information. For instance, the gene networks that represent different subtypes of the same cancer share similar edges across all subtypes and also have exclusive edges corresponding to each subtype, rendering partially similar graphical models for gene expression in different cancer subtypes.