M.Sc Thesis

M.Sc StudentKeren Carmit
SubjectInfo-Gap Bayesian Classification
DepartmentDepartment of Mechanical Engineering
Supervisors PROF. Miriam Zacksenhouse
Full Thesis textFull thesis text - English Version


Decision making is an important part of all science-based professions, from project management, manufacture processes and medical applications. The Bayesian decision framework, often used in such applications, make use of  prior information and the likelihood of the data, expressed in terms of probabilities and probability density functions respectively, to arrive at a decision. In most practical applications, however, the estimated probabilities and densities are highly uncertain, due for example to inherent differences between the testing population used for their estimation and the target population used for the decision algorithm. Moreover their estimate from historical records is often poor. In decision making, improper estimation can lead to erroneous fault detection. In that case the decision algorithm is said to be non-robust. 

Info gap decision theory provides a quantitative tool for decision-making under severe uncertainty, and is applied here to evaluate the robustness of the Bayesian decision framework when applied to a two-category classification problem. Three main components constituting the theory: i. An info gap model - an unbounded class of uncertainties, by which assumptions regarding the range of the uncertainty are eliminated. ii. A performance requirement - replaces the optimization rules used in many decision algorithms. Instead of optimizing a loss function, it is restricted to a desired performance demand, allowing some degree of sub-optimality. iii. A robustness function, which is defined to be the greatest level of uncertainty at which any realization of the uncertain inputs satisfy the performance demands. The robustness function provides a quantitative tool for robustness assessment, enabling one to explore the desirability of different performance demands and decision rules.

In this work we provide a new framework for robust Bayesian decision making based info-gap theory. We provide quantitative tools for robustness assessment, trade-off analysis and robust strategy decision making, of a two category classification problem. Several potential uncertainties are considered: (i) uncertainty in the prior probabilities, (ii) uncertainty in the parameters of normally-distributed observations, and (iii) uncertainty in the shape of the probability density functions, where in the latter we explore several uncertainty structures. In addition we present a robust-satisficing (RS) rule whose robustness to uncertainty is maximized given a performance demand. We show that in some cases the RS rule is substantially more robust than the Bayesian rule at sub-optimal performance levels. In order to demonstrate the results we use a well-studied medical problem for the identifications of patients at low-risk and high-risk of heart failure.