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# Latent Variable Copula Inference for Bundle Pricing from Retail Transaction Data

*Proceedings of the 31st International Conference on Machine Learning*, PMLR 32(1):217-225, 2014.

#### Abstract

Bundle discounts are used by retailers in many industries. Optimal bundle pricing requires learning the joint distribution of consumer valuations for the items in the bundle, that is, how much they are willing to pay for each of the items. We suppose that a retailer has sales transaction data, and the corresponding consumer valuations are latent variables. We develop a statistically consistent and computationally tractable inference procedure for fitting a copula model over correlated valuations, using only sales transaction data for the individual items. Simulations and data experiments demonstrate consistency, scalability, and the importance of incorporating correlations in the joint distribution.