Estimating Probabilities in Recommendation Systems

Modeling ranked data is an essential component in a number of important applications including recommendation systems and web-search. In many cases, judges omit preference among unobserved items and between unobserved and observed items. This case of analyzing incomplete rankings is very important from a practical perspective and yet has not been fully studied due to considerable computational difficulties. We show how to avoid such computational difficulties and efficiently construct a non-parametric model for rankings with missing items. We demonstrate our approach and show how it applies in the context of collaborative filtering.