A Nonparametric Approach to Modeling Choice with Limited Data

Vivek F. Farias, Srikanth Jagabathula, and Devavrat Shah, A Nonparametric Approach to Modeling Choice with Limited Data, Management Science, February 2013, Vol. 59, No. 2, pp. 305-322. 

Choice models today are ubiquitous across a range of applications in operations and marketing. Real-world implementations of many of these models face the formidable stumbling block of simply identifying the “right” model of choice to use. Because models of choice are inherently high-dimensional objects, the typical approach to dealing with this problem is positing, a priori, a parametric model that one believes adequately captures choice behavior. This approach can be substantially suboptimal in scenarios where one cares about using the choice model learned to make fine-grained predictions; one must contend with the risks of mis-specification and overfitting/underfitting. 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? An outcome of our investigation is a nonparametric approach in which the data automatically select the right choice model for revenue predictions. The approach is practical. Using a data set consisting of automobile sales transaction data from a major U.S. automaker, our method demonstrates a 20% improvement in prediction accuracy over state-of-the-art benchmark models; this improvement can translate into a 10% increase in revenues from optimizing the offer set. We also address a number of theoretical issues, among them a qualitative examination of the choice models implicitly learned by the approach. We believe that this paper takes a step toward “automating” the crucial task of choice model selection.

The authors formulated the minimum revenue problem under consumer choices as a linear programming with exponential growing of decision variables in terms of product number. Based on duality, they developed polynomial-time algorithms by using constraint sampling and efficient representation of purchase permutations. Profs. Farias and Shah then founded the company Celect and was later acquired by Nike. Once again, it demonstrates the positive cycle of advanced research and academic-industrial collaboration.