Take a look at the new version of this page: [ beta version ]. Tell us what you think.

ABSTRACT

A popular approach to collaborative filtering is matrix factorization. In this paper we develop a non-linear probabilistic matrix factorization using Gaussian process latent variable models. We use stochastic gradient descent (SGD) to optimize the model. SGD allows us to apply Gaussian processes to data sets with millions of observations without approximate methods. We apply our approach to benchmark movie recommender data sets. The results show better than previous state-of-the-art performance.

REFERENCES

• 1: Robert M. Bell , Yehuda Koren, Lessons from the Netflix prize challenge, ACM SIGKDD Explorations Newsletter, v.9 n.2, December 2007 [doi>10.1145/1345448.1345465]
• 2: Bell, R. M., Koren, Y., & Volinsky, C. (2008). The BellKor 2008 solution to the netflix prize. Available from http://www.research.att.com/~volinsky/netflix/.
• 3: Christopher M. Bishop, Bayesian PCA, Proceedings of the 1998 conference on Advances in neural information processing systems II, p.382-388, July 1999
• 4: Bishop, C. M. (1999b). Variational principal components. Proceedings Ninth International Conference on Artificial Neural Networks, ICANN'99 (pp. 509--514).
• 5: Dennis DeCoste, Collaborative prediction using ensembles of Maximum Margin Matrix Factorizations, Proceedings of the 23rd international conference on Machine learning, p.249-256, June 25-29, 2006, Pittsburgh, Pennsylvania [doi>10.1145/1143844.1143876]
• 6: Yehuda Koren, Factorization meets the neighborhood: a multifaceted collaborative filtering model, Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, August 24-27, 2008, Las Vegas, Nevada, USA [doi>10.1145/1401890.1401944]
• 7: Neil Lawrence, Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models, The Journal of Machine Learning Research, 6, p.1783-1816, 12/1/2005
• 8: Marlin, B. (2004a). Collaborative filtering: A machine learning perspective. Master's thesis, University of Toronto.
• 9: Marlin, B. (2004b). Modeling user rating profiles for collaborative filtering. Advances in Neural Information Processing Systems (pp. 627--634). Cambridge, MA: MIT Press.
• 10: Minka, T. P. (2001). Automatic choice of dimensionality for PCA. Advances in Neural Information Processing Systems (pp. 598--604). Cambridge, MA: MIT Press.
• 11: Seung-Taek Park , David M. Pennock, Applying collaborative filtering techniques to movie search for better ranking and browsing, Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, August 12-15, 2007, San Jose, California, USA [doi>10.1145/1281192.1281252]
• 12: Carl Edward Rasmussen , Christopher K. I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), The MIT Press, 2005
• 13: Jasson D. M. Rennie , Nathan Srebro, Fast maximum margin matrix factorization for collaborative prediction, Proceedings of the 22nd international conference on Machine learning, p.713-719, August 07-11, 2005, Bonn, Germany [doi>10.1145/1102351.1102441]
• 14: Ruslan Salakhutdinov , Andriy Mnih, Bayesian probabilistic matrix factorization using Markov chain Monte Carlo, Proceedings of the 25th international conference on Machine learning, p.880-887, July 05-09, 2008, Helsinki, Finland [doi>10.1145/1390156.1390267]
• 15: Salakhutdinov, R., & Mnih, A. (2008b). Probabilistic matrix factorization. Advances in Neural Information Processing Systems (pp. 1257--1264). Cambridge, MA: MIT Press.
• 16: Schölkopf, B., & Smola, A. J. (2001). Learning with kernels. Cambridge, MA: MIT Press.
• 17: Tipping, M. E., & Bishop, C. M. (1999). Probabilistic principal component analysis. Journal of the Royal Statistical Society, B, 6, 611--622.

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Gradient methods; Stochastic programming
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo)

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.4 Model Validation and Analysis
      I.6.5 Model Development
          Subjects: Modeling methodologies

General Terms:
Algorithms, Design, Performance, Theory