Multi-output Gaussian Processes for Uncertainty-aware Recommender Systems

A database describing such user-item interactions often takes the form of a matrix, where each entry describes the interaction between one user and one item. The overall Recommender systems are often designed based rating or purchasing pattern of a user can therefore be described on a collaborative filtering approach, where user by the corresponding row in such a matrix. However, preferences are predicted by modelling interactions since there are typically large numbers of users and items between users and items. Many common approaches in the database, and each user is usually only interested in to solve the collaborative filtering task a small subset of items, this user-item matrix is often large are based on learning representations of users and and sparse. It is therefore inefficient to define the similarity items, including simple matrix factorization, Gaussian between users in the high dimensional feature space defined process latent variable models, and neuralnetwork by all items. Instead, it is more advantageous to derive abstract based embeddings. While matrix factorization feature vectors that represent users and items, which approaches fail to model nonlinear relations, inspired a large variety of low-rank matrix decomposition neural networks can potentially capture such models such as non-negative matrix decomposition [Zhang complex relations with unprecedented predictive et al., 2006], biased matrix decomposition [Koren et al., power and are highly scalable. However, neither 2009] and non-parametric decomposition [Yu et al., 2009]. of them is able to model predictive uncertainties. These methods aim at learning low dimensional representations In contrast, Gaussian Process based models can for all users and items, allowing for the prediction of generate a predictive distribution, but cannot scale the unobserved interaction between a new pair of user and to large amounts of data.