Global analytic solution for variational Bayesian matrix factorization

Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Volumn , Issue , 2010, Pages

  Nakajima, Shinichi ^a   Sugiyama, Masashi ^b   Tomioka, Ryota ^c  

^a NIKON CORPORATION   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BARIUM COMPOUNDS; BAYESIAN NETWORKS; MATRIX FACTORIZATION; OPTIMAL SYSTEMS;

ANALYTIC SOLUTION; BAYESIAN MATRIX FACTORIZATIONS; BAYESIAN METHODS; GLOBAL OPTIMAL SOLUTIONS; ITERATED CONDITIONAL MODES; LOCAL OPTIMAL SOLUTION; MATRIX FACTORIZATIONS; OPTIMIZATION PROBLEMS; QUARTIC EQUATION; VARIATIONAL BAYESIAN;

SINGULAR VALUE DECOMPOSITION;

EID: 85161979138     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. Y. Amit, M. Fink, N. Srebro, and S. Ullman. Uncovering shared structures in multiclass classification. In Proceedings of International Conference on Machine Learning, pages 17-24, 2007.
2. A. Asuncion and D.J. Newman. UCI machine learning repository, 2007.
3. H. Attias. Inferring parameters and structure of latent variable models by variational Bayes. In Proceedings of the Fifteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-99), pages 21-30, San Francisco, CA, 1999. Morgan Kaufmann.
4. J. Besag. On the Statistical Analysis of Dirty Pictures. J. Royal Stat. Soc. B, 48:259-302, 1986.
5. C. M. Bishop. Pattern Recognition and Machine Learning. Springer, New York, NY, USA, 2006.
6. J.-F. Cai, E. J. Candes, and Z. Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4):1956-1982, 2008.
7. O. Chapelle and Z. Harchaoui. A Machine Learning Approach to Conjoint Analysis. In Advances in neural information processing systems, volume 17, pages 257-264, 2005.
8. D. R. Hardoon, S. R. Szedmak, and J. R. Shawe-Taylor. Canonical correlation analysis: An overview with application to learning methods. Neural Computation, 16(12):2639-2664, 2004.
9. M. Hazewinkel, editor. Encyclopaedia of Mathematics. Springer, 2002.
10. W. James and C. Stein. Estimation with quadratic loss. In Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, volume 1, pages 361-379. University of California Press, 1961.
11. H. Jeffreys. An Invariant Form for the Prior Probability in Estimation Problems. In Proceedings of the Royal Society of London. Series A, volume 186, pages 453-461, 1946.
12. S. Ji and J. Ye. An accelerated gradient method for trace norm minimization. In Proceedings of International Conference on Machine Learning, pages 457-464, 2009.
13. Y. J. Lim and T. W. Teh. Variational Bayesian Approach to Movie Rating Prediction. In Proceedings of KDD Cup and Workshop, 2007.
14. S. Nakajima. Matlab Code for VBMF, http://sites.google.com/site/ shinnkj23/, 2010.
15. S. Nakajima and M. Sugiyama. Implicit regularization in variational Bayesian matrix factorization. In Proceedings of 27th International Conference on Machine Learning (ICML2010), 2010.
16. R. M. Neal. Bayesian Learning for Neural Networks. Springer, 1996.
17. A. Paterek. Improving Regularized Singular Value Decomposition for Collaborative Filtering. In Proceedings of KDD Cup and Workshop, 2007.
18. T. Raiko, A. Ilin, and J. Karhunen. Principal Component Analysis for Large Sale Problems with Lots of Missing Values. In Proc. of ECML, volume 4701, pages 691-698, 2007.
19. G. R. Reinsel and R. P. Velu. Multivariate reduced-rank Regression: Theory and Applications. Springer, New York, 1998.
20. J. D. M. Rennie and N. Srebro. Fast maximum margin matrix factorization for collaborative prediction. In Proceedings of the 22nd International Conference on Machine learning, pages 713-719, 2005.
21. R. Rosipal and N. Krämer. Overview and recent advances in partial least squares. In Subspace, Latent Structure and Feature Selection Techniques, volume 3940, pages 34-51. Springer, 2006.
22. R. Salakhutdinov and A. Mnih. Probabilistic matrix factorization. In J.C. Platt, D. Koller, Y. Singer, and S. Roweis, editors, Advances in Neural Information Processing Systems 20, pages 1257-1264, 2008.
23. N. Srebro, J. Rennie, and T. Jaakkola. Maximum Margin Matrix Factorization. In Advances in NIPS, volume 17, 2005.
24. M.E. Tipping and C.M. Bishop. Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society: Series B, 61(3):611-622, 1999.
25. R. Tomioka, T. Suzuki, M. Sugiyama, and H. Kashima. An efficient and general augmented Lagrangian algorithm for learning low-rank matrices. In Proceedings of International Conference on Machine Learning, 2010.
26. S. Watanabe. Algebraic Geometry and Statistical Learning. Cambridge University Press, Cambridge, UK, 2009.
27. K. J.Worsley, J-B. Poline, K. J. Friston, and A. C. Evanss. Characterizing the Response of PET and fMRI Data Using Multivariate Linear Models. NeuroImage, 6(4):305-319, 1997.
28. I-Cheng Yeh. Modeling slump flow of concrete using second-order regressions and artificial neural networks. Cement and Concrete Composites, 29(6):474-480, 2007.
29. K. Yu, V. Tresp, and A. Schwaighofer. Learning Gaussian Processes from Multiple Tasks. In Proc. of ICML, page 1019, 2005.