A Bayesian Rule Generation Framework for 'Omic' Biomedical Data Analysis

High-dimensional biomedical 'omic' datasets are accumulating rapidly from studies aimed at early detection and better management of human disease. These datasets pose tremendous challenges for analysis due to their large number of variables that represent measurements of biochemical molecules, such as proteins and mRNA, from bodily fluids or tissues extracted from a rather small cohort of samples. Machine learning methods have been applied to modeling these datasets including rule learning methods, which have been successful in generating models that are easily interpretable by the scientists. Rule learning methods have typically relied on a frequentist measure of certainty within IF-THEN (propositional) rules. In this dissertation, a Bayesian Rule Generation Framework (BRGF) is developed and tested that can produce rules with probabilities, thereby enabling a mathematically rigorous representation of uncertainty in rule models. The BRGF includes a novel Bayesian Discretization method combined with one or more search strategies for building constrained Bayesian Networks from data and converting them into probabilistic rules. Both global and local structures are built using different Bayesian Network generation algorithms and the rule models generated from the network are tested on public and private 'omic' datasets. We show that using a specific type of structure (Bayesian decision graphs) in tandem with a specific type of search method (parallel greedy) allows us to achieve statistically significant higher overall performance over current state of the art rule learning methods. Not only does using the BRGF boost performance on average on 'omic' biomedical data to a statistically significant point, but also provides the ability to incorporate prior information in a mathematically rigorous fashion for modeling purposes