We present a discrete choice, random utility model and a new estimation technique for analyzing consumer demand for large numbers of products. In our model each product has an associated unobservable vector of attributes from which the consumer derives utility. We allow the consumer to purchase multiple products at once in a consumption bundle.

Because the number of bundles available is massive, a new estimation technique, which is based on the practice of negative sampling in NLP, is needed to sidestep an intractable likelihood function. We prove consistency of our estimator, validate the consistency result through simulation exercises, and estimate our model using supermarket scanner data.