Statistical Significance of the Netflix Challenge
Statistical Science 2012, Vol. 27, No. 2, 202–231 DOI: 10.1214/11-STS368 c Institute of Mathematical Statistics, 2012 Statistical Significance of the Netflix Challenge Andrey Feuerverger, Yu He and Shashi Khatri Abstract. 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 rec- ommender 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, ap- proaches 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 considera- tions 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 pa- rameter 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. Key words and phrases: Collaborative filtering, cross-validation, ef- fective number of degrees of freedom, empirical Bayes, ensemble meth- ods, gradient descent, latent factors, nearest neighbors, Netflix contest, neural networks, penalization, prediction error, recommender systems, restricted Boltzmann machines, shrinkage, singular value decomposi- tion.
[Show full text]