Using Bayesian Network Representations for Effective Sampling from\n Generative Network Models

Bayesian networks (BNs) are used for inference and sampling by exploiting\nconditional independence among random variables. Context specific independence\n(CSI) is a property of graphical models where additional independence relations\narise in the context of particular values of random variables (RVs).\nIdentifying and exploiting CSI properties can simplify inference. Some\ngenerative network models (models that generate social/information network\nsamples from a network distribution P(G)), with complex interactions among a\nset of RVs, can be represented with probabilistic graphical models, in\nparticular with BNs. In the present work we show one such a case. We discuss\nhow a mixed Kronecker Product Graph Model can be represented as a BN, and study\nits BN properties that can be used for efficient sampling. Specifically, we\nshow that instead of exhibiting CSI properties, the model has deterministic\ncontext-specific dependence (DCSD). Exploiting this property focuses the\nsampling method on a subset of the sampling space that improves efficiency.\n