The research objective of this award is to establish theoretical foundations and build algorithms for the problem of learning non-parametric models of customer choice from limited data. Existing tools for this task posit parametric models of choice which are subsequently fit to data. In contrast, the starting point for this research will be a characterization of the set of all possible choice models consistent with any data that might be available. Given such a characterization, the research will produce methodologies for, and establish the merits of, several distinct criteria for selecting an appropriate choice model from this set. In the spirit of Occam's razor, one criterion that will be considered is finding the "sparsest" model from this set. The study of this criterion will establish the limits to choice model identification, a key component of any theory of learning. This will be accomplished via the use and development of tools from the area of compressive sensing. A second criterion for model selection will be derived from a certain function of the choice model sought that arises in numerous revenue optimization applications. Algorithms that utilize this criterion to select a choice model will require new optimization techniques for robust optimization.
If successful, this research will advance the fundamental techniques used in obtaining choice models from available partial data. Choice models are probabilistic descriptions of how consumers choose from options presented to them. This research will make possible a "black box" approach to the problem of learning such choice models that will be valuable in applications where expert input is difficult or expensive to obtain. Applications in this genre include problems of inventory and assortment optimization faced by large auto companies and online retailers alike. This research will provide a viable methodology for such problems wherein the complex nature of consumer demand is explicitly accounted for. The implementation of such methodologies will lead to increased revenues and efficiencies. At the same time, this investigation represents a promising direction within the statistical inference, signal processing and machine learning communities, which have recently begun to explore the methodological challenges herein under the umbrella of compressive sensing. In that sense, this work will advance the theory of compressed sensing and non-parametric learning.
