Accurate and scalable social recommendation using mixed-membership stochastic block models

Abstract

With increasing amounts of information available, modeling and predicting user preferences-for books or articles, for exampleare becoming more important. We present a collaborative filtering model, with an associated scalable algorithm, that makes accurate predictions of users' ratings. Like previous approaches, we assume that there are groups of users and of items and that the rating a user gives an item is determined by their respective group memberships. However, we allow each user and each item to belong simultaneously to mixtures of different groups and, unlike many popular approaches such as matrix factorization, we do not assume that users in each group prefer a single group of items. In particular, we do not assume that ratings depend linearly on a measure of similarity, but allow probability distributions of ratings to depend freely on the user's and item's groups. The resulting overlapping groups and predicted ratings can be inferred with an expectation-maximization algorithm whose running time scales linearly with the number of observed ratings. Our approach enables us to predict user preferences in large datasets and is considerably more accurate than the current algorithms for such large datasets.recommender systems | stochastic block model | collaborative filtering | social recommendation | scalable algorithm T he goal of recommender systems is to predict what movies we are going to like, what books we are going to purchase, or even who we might be interested in dating. The rapidly growing amount of data on item reviews, ratings, and purchases from a growing number of online platforms holds the promise to facilitate the development of more informed models for recommendation. At the same time, however, it poses the challenge of developing algorithms that can handle such large amounts of data accurately and efficiently.A plausible expectation when developing recommendation algorithms is that similar users relate to similar items in similar ways; e.g., they purchase similar items and give the same item similar ratings. This means that we can use the rating history of a set of users to make recommendations, even without knowing anything about the characteristics of users or items. This is the basic underlying assumption of collaborative filtering, one of the most common approaches in recommender systems (1). However, most research in recommender systems has focused on the development of scalable algorithms, often at the price of implicitly using models that are overly simplistic or unrealistic. For example, matrix factorization and latent feature approaches assume that users and items live in an abstract low-dimensional space, but whether such a space is expressive enough to accommodate the rich variety of user behaviors is rarely discussed. As a result, many current approaches have significantly lower accuracies than inference approaches based on models of user preferences that are socially more realistic (2). On the other hand, these more realistic approaches do not scale well with dataset size, whic...

Network-Based Models for Social Recommender Systems

“…We measure the predictability in terms of accuracy, that is the number of ratings predicted correctly, and the mean absolute error (MAE). Figure 5 shows the performance for the two network-based models, the simple bipartite SBM (using the approach in [14]) and the Mixed-Membership Stochastic Block Model (MMSBM) (using the approach of [15]). Moreover, Table 1: Dataset characteristics.…”

“…With respect to mathematical rigor, the Bayesian approach used by the bipartite SBM [14] is the complete and correct probabilistic treatment of the observations. However, the results of the MMSBM suggest that introducing the mixed-membership of users and items is already equivalent to sampling over different sets of simple bipartite SBMs [15].…”

“…that is 10 groups of users and 10 groups of items (recall that there is any correspondence between these groups). The performance for larger choices of K and L does not improve significantly [15]. Since iterating the EM equation of Eqs.…”

“…In this section we will consider two network-based models for recommender systems: the simple bipartite Stochastic Block Model (SBM) [14] and the Mixed-Membership Bipartite Stochastic Block Model (MMSBM) [15]. In both models, there are different groups.…”

A review of stochastic block models and extensions for graph clustering

“…The proposed model was found to perform better than the traditional approach of LDA. It can be compared with the model by Godoy-Lorite et al (2016) for recommender systems, who also applied an SBM for seemingly non-relational data that can however be represented as graphs.…”