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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Results from the Paper
Ranked #1 on
Recommendation Systems
on Flixster
(using extra training data)
| Task | Dataset | Model | Metric Name | Metric Value | Global Rank | Uses Extra Training Data |
Benchmark |
|---|---|---|---|---|---|---|---|
| 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 |
