Generating Bayesian Networks from Probability Logic Knowledge Bases

Abstract

We present a method for dynamically gen erating Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of proba bility logic sufficient for representing the class of Bayesian networks with discrete-valued nodes. We impose constraints on the form of the sentences that guarantee that the knowl edge base contains all the probabilistic infor mation necessary to generate a network. We define the concept of d-separation for knowl edge bases and prove that a knowledge base with independence conditions defined by d separation is a complete specification of a probability distribution. We present a net work generation algorithm that, given an in ference problem in the form of a query Q and a set of evidence E, generates a network to compute P(QIE). We prove the algorithm to be correct.

Introduction of a Bayesian Network Builder Algorithm - Personalized Infectious Disease Risk Prediction

“…The Anthrax BN was built manually, neither learnt from historical datasets nor generated automatically by a specific mechanism -which this paper now presents. (Haddawy, 1994) Generating a Bayesian Network from a probabilistic knowledge-base was pioneered by Peter Haddawy (Haddawy, 1994). He used Horn clauses to form a probabilistic knowledge-base (Figure 1).…”

Model Failure and Context Switching Using Logic-Based Stochastic Models

“…One of the first attempts to explicitly use contextual information in probabilistic modeling was done in (Haddawy, 1994;. Their logic-based stochastic modeling approach utilizes explicit contextual information as a way to reduce the size of a model.…”

“…Although our research is motivated by (Haddawy, 1994;, their contextual mechanism is too simple and discrete: it cannot reflect all the complexity of internal structures of data. In this paper, we provide a formal specification of context as truth assignments to a specific set of variables that we know about.…”

“…GLL is based on earlier work by Poole (1993), Haddawy (1994), Getoor et al (2001), and Kersting and DeRaedt (2000). GLL is an extension of the basic language developed by Pless et al (2006).…”

“…Poole (1993) was one of the first to develop an approximate inference algorithm for a Turing complete probabilistic logic language where uncertainty is expressed through sets of mutually exclusive predicates annotated with probabilities. Haddawy (1994) created a first-order probabilistic logic that he used to specify a static class of (propositional) Bayesian networks (BNs) as a knowledge base. Haddawy proposed a provably correct Bayesian network generation algorithm that was later adapted to focus the knowledge base on the relevant information .…”