Mathematical modeling of group product recommendation with partial information: How many ratings do we need?

Product recommendation is one of the most important services in the Internet. In this paper, we consider a product recommendation system which recommends products to a group of users. The recommendation system only has partial preference information on this group of users: a user only indicates his preference to a small subset of products in the form of ratings. This partial preference information makes it a challenge to produce an accurate recommendation. In this work, we explore a number of fundamental questions. What is the desired number of ratings per product so to guarantee an accurate recommendation? What are some effective voting rules in summarizing ratings? How users’ misbehavior such as cheating, in product rating may affect the recommendation accuracy? What are some efficient rating schemes? To answer these questions, we present a formal mathematical model of a group recommendation system. We formally analyze the model. Through this analysis we gain the insight to develop a randomized algorithm which is both computationally efficient and asymptotically accurate in evaluating the recommendation accuracy under a very general setting. We propose a novel and efficient heterogeneous rating scheme which requires equal or less rating workload, but can improve over a homogeneous rating scheme by as much as 30%. We carry out experiments on both synthetic data and real-world data from TripAdvisor. Not only we validate our model, but also we obtain a number of interesting observations, i.e., a small of misbehaving users can decrease the recommendation accuracy remarkably. For TripAdvisor, one hundred ratings per product is sufficient to guarantee a high accuracy recommendation. We believe our model and methodology are important building blocks to refine and improve applications of group recommendation systems.