High Dimensional Preference Learning: Topological Data Analysis Informed Sampling for Engineering Decision Making

Engineering design-decisions often involve many attributes which can differ in the levels of their importance to the decision maker (DM), while also exhibiting complex statistical relationships. Learning a decision-making policy which accurately represents the DM’s actions has long been the goal of decision analysts. To circumvent elicitation and modeling issues, this process is often oversimplified in how many factors are considered and how complicated the relationships considered between them are. Without these simplifications, the classical lottery-based preference elicitation is overly expensive, and the responses degrade rapidly in quality as the number of attributes increase. In this paper, we investigate the ability of deep preference machine learning to model high-dimensional decision-making policies utilizing rankings elicited from decision makers. To aid in the training of this machine learner, we propose a topological data analysis (TDA)-based algorithm to select the group of elicitations which would best fill the experimental space. Finally, we apply the proposed method on a vehicle design selection problem involving 19 attributes, discuss the results, and identify avenues for future work.