A Market Discovery Algorithm to Estimate a General Class of Nonparametric Choice Models

W propose an approach for estimating customer preferences for a set of substitutable products using only sales transactions and product availability data. The underlying demand framework combines a general, nonparametric discrete choice model with a Bernoulli process of arrivals over time. The choice model is defined by a discrete probability mass function (pmf) on a set of possible preference rankings of alternatives, and it is compatible with any random utility model. An arriving customer is assumed to purchase the available option that ranks highest in her preference list. The problem we address is how to jointly estimate the arrival rate and the pmf of the rank-based choice model under a maximum likelihood criterion. Since the potential number of customer types is factorial, we propose a market discovery algorithm that starts with a parsimonious set of types and enlarge it by automatically generating new types that increase the likelihood value. Numerical experiments confirm the potential of our proposal. For a realistic data set in the hospitality industry, our approach improves the root mean square errors between predicted and observed purchases computed under independent demand model estimates by 67%–93%.