Learning Customer Preferences from Bundle Sales Data

Abstract

This paper studies estimation problem of customer preferences from bundle sales data. Product bundling is a common selling mechanism used in retails. To set profitable bundle selection and prices, the seller needs to learn the distribution of consumers' valuations for individual products from the transaction data. When customers purchase bundles or multiple products, classical methods such as discrete choice models cannot be used to estimate customers' valuations. In this paper, we propose an approach to learn the distribution of consumers' valuations toward the products using bundle sales data. Our approach is to define a utility model for customer choices and estimate the parameters of a valuation distribution that maximizes the likelihood of observing the transaction data. Our approach reduces this problem to an estimation problem where the samples are censored by polyhedral regions on the valuation space of customers. Using the EM algorithm and Monte Carlo simulation, our approach can recover the distribution of consumers' valuations. We extend the framework to allow for unobserved no-purchases and clustered market segments. In addition, we provide theoretical results on the identifiability of the probability model and the convergence of the EM algorithm. Moreover, the performance of the approach is also demonstrated numerically with synthetic and real datasets. This study demonstrates the need and challenge for retailers to leverage the transaction data of bundle sales to learn customers' preferences. The proposed algorithm can be used efficiently in practice to achieve the goal.

Keywords: EM algorithm, bundle, estimation, censored demand, clustering

JEL Classification: C38, C49, C53, C55