Higher-Order Bayesian Networks: A Probabilistic Reasoning Framework for Structured Data Representations Based on Higher-Order Logics

Higher-Order Bayesian Networks: A Probabilistic Reasoning Framework for Structured Data Representations Based on Higher-Order Logics

ABSTRACT:

Bayesian Networks (BNs) are a popular formalism for performing probabilistic inference. The propositional nature of BNs restricts their application to data which can be represented as tuples of fixed length, excluding a vast field of problems which deal with multi-relational data. Basic Terms, recently introduced by John W. Lloyd, are a family of terms within a typed higher-order logic framework which are particularly suitable for representing structured individuals such as tuples, lists, trees, graphs, sets etc. I will present a proposed extension of BNs, Higher-Order Bayesian Networks, which define probability distributions over domains of Basic Terms. We can perform sampling from these distributions, and use that to calculate the answer to probabilistic inference queries. We have also developed a method for model learning given a database of observations. Finally, I will show how we have applied learning and inference on real-world classification problems.