Nonparametric choice modeling: applications to operations management

With the recent explosion of choices available to us in every walk of our life, capturing the choice behavior exhibited by individuals has become increasingly important to many businesses. At the core, capturing choice behavior boils down to being able to predict the probability of choosing a particular alternative from an offer set, given historical choice data about an individual or a group of “similar” individuals. For such predictions, one uses what is called a choice model, which models each choice occasion as follows: given an offer set, a preference list over alternatives is sampled according to a certain distribution, and the individual chooses the most preferred alternative according to the sampled preference list. Most existing literature, which dates back to at least the 1920s, considers parametric approaches to choice modeling. The goal of this thesis is to deviate from the existing approaches to propose a nonparametric approach to modeling choice. Apart from the usual advantages, the primary strength of a nonparametric model is its ability to scale with the data – certainly crucial to applications of our interest where choice behavior is highly dynamic. Given this, the main contribution of the thesis is to operationalize the nonparametric approach and demonstrate its success in several important applications. Specifically, we consider two broad setups: (1) solving decision problems using choice models, and (2) learning the choice models. In both setups, data available corresponds to marginal information about the underlying distribution over rankings. So the problems essentially boil down to designing the ‘right’ criterion to pick a model from one of the (several) distributions that are consistent with the available marginal information. First, we consider a central decision problem in operations management (OM): find an assortment of products that maximizes the revenues subject to a capacity constraint on the size of the assortment. Solving this problem requires two components: (a) predicting revenues for assortments and (b) searching over all subsets of a certain size for the optimal assortment. In order to predict revenues for an assortment, of all models consistent with the data, we use the choice model that results in the ‘worst-case’ revenue. We derive theoretical guarantees for the predictions, and