Labeled graph notations for graphical models
Eric Mjolsness · 2004
We introduce new diagrammatic notations for probabilistic independence networks (including Bayes nets and graphical models). These notations include new node and link types that allow for natural representation of a wide range of probabilistic data models including complex hierarchical models. The diagrammatic notations also support models defined on variable numbers of complex objects and relationships. Node types include random variable nodes, index nodes, constraint nodes, and an object supernode. Link types include conditional dependency, indexing and index limitation, variable value limitation, and gating a dependency between nodes or objects by an arbitrary graph. Examples are shown for clustering problems, information retrieval, unknown graph structures in biological regulation, and other scientific domains. The diagrams may be taken as a shorthand notation for a more detailed syntactic representation by an algebraic expression for factored probability distributions, which in turn may be specified by stochastic parameterized grammar or graph grammar models. We illustrate these ideas with previously described applications and potential new ones.