A Nonparametric Approach to Modeling Choice with Limited Data

A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model of choice to use. Thus motivated, we visit the following problem: For a `generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal information about these distributions), how may one predict revenues from offering a particular assortment of choices? We present a framework to answer such questions and design a number of tractable algorithms from a data and computational standpoint for the same. This paper thus takes a significant step towards `automating' the crucial task of choice model selection in the context of operational decision problems.