Assessment of Probability Conditions in Binary Classification Systems to Incorporate and Limit Uncertainty in Optimal Decision Regions

Abstract

The study that is discussed in this thesis involves a unique method of quantifying uncertainty with respect to a classification problem. In essence, the objective involves redefining a materials classification problem pertaining to deleterious phases with respect to material composition and temperature as more of a function with inputs and outputs where the output is a probability label of either classification label that defines the probability of deleterious phases with respect to each of the aforementioned independent variables. This helps to interpret uncertainty in predictive statements that are assessed in a classification problem. The intention behind this method is to be able to set this type of system up as an optimization problem in order to maximize the likelihood of a desired condition, or minimize the likelihood of the undesired condition.

There are two primary approaches used in this study. One involves the use of a Gaussian Process Classifier to determine the aforementioned probability and discussing how to properly implement it and how to apply workarounds needed with the process. The other involves a more direct investigation of the data in what is called Sectioning and Proportioning, which involves taking the proportion of classification labels per section of the data to best assess the overall probability trend.

Both of these methods are found to have their strengths and weaknesses, and it is useful to use both in parallel with one another in order to assess any data that is being investigated while also interpreting it and adequately projecting the probability estimation as effectively and accurately as possible.