  Inspired by the legacy of the Netflix contest, we provide an overview of what
has been learned---from our own efforts, and those of others---concerning the
problems of collaborative filtering and recommender systems. The data set
consists of about 100 million movie ratings (from 1 to 5 stars) involving some
480 thousand users and some 18 thousand movies; the associated ratings matrix
is about 99% sparse. The goal is to predict ratings that users will give to
movies; systems which can do this accurately have significant commercial
applications, particularly on the world wide web. We discuss, in some detail,
approaches to "baseline" modeling, singular value decomposition (SVD), as well
as kNN (nearest neighbor) and neural network models; temporal effects,
cross-validation issues, ensemble methods and other considerations are
discussed as well. We compare existing models in a search for new models, and
also discuss the mission-critical issues of penalization and parameter
shrinkage which arise when the dimensions of a parameter space reaches into the
millions. Although much work on such problems has been carried out by the
computer science and machine learning communities, our goal here is to address
a statistical audience, and to provide a primarily statistical treatment of the
lessons that have been learned from this remarkable set of data.
