Tracing the Path: New Model and Algorithms for Collaborative Filtering

Automated recommendation systems have emerged in the past decade as a useful tool to reduce the information overload faced by users at e-commerce sites. Recently Drineas et al. Kleinberg and Sandler, and others have introduced algorithms with pivvable performance guarantees. In this work we expand the mixture model introduced by Hoffman and Puzicha to include extra information often readily available to the algorithm designer. We show how this additional information leads to fast and simple algorithms with recommendation guarantees. We then begin the study of algorithms that work when the sampling step in the mixture model is done without repetition. This version of the problem often serves as a better-model for situations occurring in practice (e.g.. few of us own multiple copies of the same book), but has not been rigorously analyzed in the context of recommendation systems.