Efficient Retrieval of Recommendations in a Matrix Factorization Framework Noam KoenigsteinParikshit RamYuval Shavitt School of Electrical Engineering Tel Aviv University Computational Science & Engineering Georgia Institute of Technology School of Electrical Engineering Tel Aviv University

Motivation In the field of Recommender System, Matrix Factorization (MF) models have shown superior accuracy for recommendation tasks. E.g., The Netflix Prize, KDD-Cup’11, etc. Training is fast. Computing test scores is fast. But… Retrieval of Recommendations (RoR) is s--l--o--w ! This problem is well known in the industry, yet never been approached before in academia!

I T E M S USERSUSERS Yahoo! Music: 1M Users 625K Items 6 Tera elements ~300 multiplications ~5 days CPU Naïve Multithreading: High latency + wasteful Yahoo! Music: 1M Users 625K Items 6 Tera elements ~300 multiplications ~5 days CPU

Reduction to Inner Product

Best Matches Algorithms Metric Space Cosine Similarity Locality Sensitive Hashing

Metric Trees R R

Branch-and-bound Algorithm

Bounding Inner Product Similarity

Approximate Solution Users vectors can be normalized  Users can be clustered based on their spherical angle!

Relative Error Bound What is the error when recommendations are retrieved based on an approximate user vector?

Adaptive Approximate Solution

Experimentations Set-up MovieLensNetflixYahoo! Music Ratings1,000,206100,480,507252,800,275 Users6,040480,1891,000,990 Items3,95217,770624,961 Sparsity95.81%98.82%99.96% Yahoo! Music Recommendations: Modeling Music Ratings with Temporal Dynamics and Item Taxonomy Gideon Dror, Noam Koenigstein, Yehuda Koren (RecSys-11`)

Exact Alg. Speedup

Approximate Alg. Speedup

Speedup vs. Precision

Speedup vs. MedianRank

Conclusions We introduce a new and relevant research problem An exact solution with limited speedup An approximate solution with a tradeoff between accuracy and speedup Much room for further research…

Basic Model

Reduction to Inner Product