Combining Bayesian Networks with Higher-Order Data Representations

This paper introduces Higher-Order Bayesian Networks, a probabilistic reasoning formalism which combines the efficient reasoning mechanisms of Bayesian Networks with the expressive power of higher-order logics. We discuss how the proposed graphical model is used in order to define a probability distribution semantics over particular families of higher-order terms. We give an example of the application of our method on the Mutagenesis domain, a popular dataset from the Inductive Logic Programming community, showing how we employ probabilistic inference and model learning for the construction of a probabilistic classifier based on Higher-Order Bayesian Networks.