Statistical Significance of the Netflix Challenge

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.Comment: Published in at http://dx.doi.org/10.1214/11-STS368 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Oii-web: An interactive online programming contest training system

In this paper we report our experience, related to the online training for the Italian and International Olympiads in Informatics. We developed an interactive online system, based on CMS, the grading system used in several major programming contests including the International Olympiads in Informatics (IOI), and used it in three distinct context: training students for the Italian Olympiads in Informatics (OII), training teachers in order to be able to assist students for the OII, and training the Italian team for the IOI. The system, that is freely available, proved to be a game changer for the whole italian olympiads in informatics ecosystem: in one year, we almost doubled the participation to OII, from 13k to 21k secondary school students. The system is developed basing on the Contest Management System (CMS, http://cms- dev.github.io/), so it is highly available to extensions supporting, for instance, the pro- duction of feedback on problems solutions submitted by trainees. The system is also freely available, with the idea of allowing for support to alternative necessities and developmen

Two-Stage Team Rent-Seeking: Experimental Analysis

This paper presents a two-stage team rent-seeking model with a contest prize that is not excludable among winning team members. When early effort is a perfect substitute for late effort, early actors can free ride on their late-moving teammates. However, when early and late efforts are complements, all team members exert positive effort levels. Asymmetries in early effort reduce effort choices for all late movers. The theory is tested with laboratory experimental methods. Although subjects overinvest relative to the Nash equilibrium in all treatments, chosen effort levels provide limited support for the model. Early movers exerted higher effort in the complement treatment, and second-stage effort choices were broadly consistent with best response functions. Surprisingly, in both single-shot and repeated play environments, early movers in the substitute treatment did not free ride, choosing effort levels similar to those of late movers. [excerpt

The use of multiplayer game theory in the modeling of biological populations

The use of game theory in modeling the natural world is widespread. However, this modeling mainly involves two player games only, or "playing the field" games where an individual plays against an entire (infinite) population. Game-theoretic models are common in economics as well, but in this case the use of multiplayer games has not been neglected. This article outlines where multiplayer games have been used in evolutionary modeling and the merits and limitations of these games. Finally, we discuss why there has been so little use of multiplayer games in the biological setting and what developments might be useful