Decision Theoretic Bayesian Computation

Purdue University, West Lafayette IN

Investigators

Abstract

Decision-makers, whether in business, policy-making, or engineering systems, face the problem of taking action without complete knowledge of the state of the world. Examples of such situations include controlling industrial plants, maneuvering autonomous vehicles, developing new drugs, making investment decisions or staffing decisions in service systems. Modern decision-makers typically use sophisticated probabilistic models to capture uncertainty, and take optimal actions within the framework of such models. In general, the models themselves involve unknown parameters which must be estimated from data. While large datasets improve the estimation of the parameters, leading to more accurate decisions, these big-data settings also raise computational challenges that call for approximations in the estimation. Current methodology typically proceeds in two steps: (1) use the vast statistical and machine learning literature to approximately estimate model parameters, and (2) use the resulting approximations to compute the best possible action. This two-stage procedure can result in sub-optimality of actions, as the approximations computed in the first stage are not tailored to the decision-making problem in the second stage. The objective of this project is to develop and study a methodological framework for approximate computation that puts decision-making at its center, recognizing that the ultimate goal of most big-data analyses is to help decide among actions in the face of uncertainty. The project will provide tools and theory to accurately account for trade-offs between statistical accuracy, decision-theoretic utility and computational complexity, and will integrate decision-making into the computational revolution that has driven much of modern data-science. The tools and theory potentially impact a large range of data-driven decision-making problems. This project works in the overarching framework of Bayesian statistics, where the primary object of interest is the posterior distribution over the unknown parameters and variables. The research focuses on theoretical and methodological challenges arising from approximate computation for Bayesian decision theory. The investigators consider two complementary problems, (a) Decision-theoretic variational Bayes, and (b) Robust decision-making. The former task analyzes and extends variational methods, developed in the machine learning community to approximate intractable Bayesian posterior distributions, from a decision-theoretic viewpoint. The investigators will theoretically study the optimality of such algorithms with respect to decision-making rather than prediction, and develop novel `loss-calibrated' algorithms that search for approximations using decision-theoretic, rather than inferential criteria. Task (b) recognizes that a model is always an approximation to reality, and is therefore misspecified. As a consequence, a Bayesian posterior distribution, even if calculated exactly, might not actually characterize the distribution over future observations. The investigators explore connections with approximations from the first task, and move from uncertainty about parameters and variables under a specified model, to uncertainty about the choice of model itself. They develop and analyze methodology that allows robust and principled decisions in the face of such `Knightian' uncertainty. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.