Statistical learning for decision making : interpretability, uncertainty, and inference

Abstract

Data and predictive modeling are an increasingly important part of decision making. Here we present advances in several areas of statistical learning that are important for gaining insight from large amounts of data, and ultimately using predictive models to make better decisions. The first part of the thesis develops methods and theory for constructing interpretable models from association rules. Interpretability is important for decision makers to understand why a prediction is made. First we show how linear mixtures of rules can be used to make sequential predictions. Then we develop Bayesian Rule Lists, a method for learning small, ordered lists of rules. We apply Bayesian Rule Lists to a large database of patient medical histories and produce a simple, interpretable model that solves an important problem in healthcare, with little sacrifice to accuracy. Finally, we prove a uniform generalization bound for decision lists. In the second part of the thesis we focus on decision making from sales transaction data. We develop models and inference procedures for using transaction data to estimate quantities such as willingness-to-pay and lost sales due to stock unavailability. We develop a copula estimation procedure for making optimal bundle pricing decisions. We then develop a Bayesian hierarchical model for inferring demand and substitution behaviors from transaction data with stockouts. We show how posterior sampling can be used to directly incorporate model uncertainty into the decisions that will be made using the model. In the third part of the thesis we propose a method for aggregating relevant information from across the Internet to facilitate informed decision making. Our contributions here include an important theoretical result for Bayesian Sets, a popular method for identifying data that are similar to seed examples. We provide a generalization bound that holds for any data distribution, and moreover is independent of the dimensionality of the feature space. This result justifies the use of Bayesian Sets on high-dimensional problems, and also explains its good performance in settings where its underlying independence assumption does not hold.