  Recommendation systems are emerging as an important business application with
significant economic impact. Currently popular systems include Amazon's book
recommendations, Netflix's movie recommendations, and Pandora's music
recommendations. In this paper we address the problem of estimating
probabilities associated with recommendation system data using non-parametric
kernel smoothing. In our estimation we interpret missing items as randomly
censored observations and obtain efficient computation schemes using
combinatorial properties of generating functions. We demonstrate our approach
with several case studies involving real world movie recommendation data. The
results are comparable with state-of-the-art techniques while also providing
probabilistic preference estimates outside the scope of traditional recommender
systems.
