Abstract: Recommender systems based on collaborative filtering predict user preferences for products or services by learning past user-item relationships. A predominant approach to collaborative filtering is neighborhood based (“k-nearest neighbors“), where a user-itempreference rating is interpolated from ratings of similar items and/or users. In this work, we enhance the neighborhood-based approach leading to a substantial improvement of prediction accuracy, without a meaningful increase in running time. First, we remove certain so-called “global effects” from the data tomake the different ratings more comparable, thereby improving interpolation accuracy. Second, we show how to simultaneously derive interpolation weights for all nearest neighbors. Unlike previous approaches where each interpolation weight is computed separately, simultaneous interpolation accounts for the many interactions between neighbors by globally solving a suitable optimization problem, also leading to improved accuracy. Our method is very fast in practice, generating a prediction in about 0.2 milliseconds. Importantly, it does not require training many parameters or a lengthy preprocessing, making it very practical for large scale applications. The method was evaluated on the Netflix dataset. We could process the 2.8 million queries of the Qualifying set in 10 minutes yielding a RMSE of 0.9086. Moreover, when an extensive training is allowed, such as SVD-factorization at the preprocessing stage, our method can produce results with a RMSE of 0.8982.

Abstract: The collaborative filtering approach to recommender systems predicts user preferences for products or services by learning past useritem relationships. In this work, we propose novel algorithms for predicting user ratings of items by integrating complementary models that focus on patterns at different scales. At a local scale, we use a neighborhood-based technique that infers ratings from observed ratings by similar users or of similar items. Unlike previous local approaches, our method is based on a formal model that accounts for interactions within the neighborhood, leading to improved estimation quality. At a higher, regional, scale, we use SVD-like matrix factorization for recovering the major structural patterns in the user-item rating matrix. Unlike previous approaches that require imputations in order to fill in the unknown matrix entries, our new iterative algorithm avoids imputation. Because the models involve estimation of millions, or even billions, of parameters, shrinkage of estimated values to account for sampling variability proves crucial to prevent overfitting. Both the local and the regional approaches, and in particular their combination through a unifying model, compare favorably with other approaches and deliver substantially better results than the commercial Netflix Cinematch recommender system on a large publicly available data set.