Collaborative Filtering with Graph Information: Consistency and Scalable Methods

Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space. Often, additional information about the variables is known, and it is reasonable to assume that incorporating this information will lead to better predictions. We tackle the problem of matrix completion when pairwise relationships among variables are known, via a graph. We formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods. On the theoretical front, we show that such methods generalize weighted nuclear norm formulations, and derive statistical consistency guarantees. We validate our results on both real and synthetic datasets.

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 Ranked #1 on Recommendation Systems on Flixster (using extra training data)

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Task Dataset Model Metric Name Metric Value Global Rank Uses Extra
Training Data
Recommendation Systems Douban GRALS RMSE 0.714 # 3
Recommendation Systems Douban Monti GRALS RMSE 0.8326 # 8
Recommendation Systems Flixster GRALS RMSE 0.845 # 1
Recommendation Systems Flixster Monti GRALS RMSE 1.2447 # 7
Recommendation Systems MovieLens 100K GRALS RMSE (u1 Splits) 0.945 # 14
Recommendation Systems YahooMusic GRALS RMSE 22.872 # 3
Recommendation Systems YahooMusic Monti GRALS RMSE 38.0423 # 6


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