Assessing approximate inference for binary gaussian process classification

Journal of Machine Learning Research

Volumn 6, Issue , 2005, Pages

  Kuss, Malte ^a   Rasmussen, Carl Edward ^a  

^a MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

Author keywords

Evidence; Expectation propagation; Gaussian process priors; Laplace's approximation; Marginal likelihood; MCMC; Probabilistic classification

Indexed keywords

APPROXIMATION THEORY; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PROBABILITY DISTRIBUTIONS;

EVIDENCE; EXPECTATION PROPAGATION; GAUSSIAN PROCESS PRIORS; LAPLACE'S APPROXIMATION; MARGINAL LIKELIHOOD; MCMC; PROBABILISTIC CLASSIFICATION;

RANDOM PROCESSES;

EID: 25444528713     PISSN: 15337928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (29)

1. P. Abrahamsen. A review of Gaussian random fields and correlation functions. Technical Report 917, Norwegian Computing Center, Oslo, 1997.
2. C.-C. Chang and C.-J. Lin. LIBSVM: A library for Support Vector Machines, 2001. http://www.csie.ntu.edu.tw/~cjlin/libsvm.
3. O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee. Choosing multiple parameters for support vector machines. Machine Learning, 46(1):131-159, 2002.
4. W. Chu and Z. Ghahramani. Gaussian processes for ordinal regression. Journal of Machine Learning Research, 6:1019-1041, 2005.
5. L. Csató and M. Opper. Sparse online Gaussian processes. Neural Computation, 14(2):641-669, 2002.
6. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Hybrid Monte Carlo. Physics Letters B, 195(2):216-222, 1987.
7. A. Gelman and X.-L. Meng. Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statistical Science, 13(2): 163-185, 1998.
8. M. N. Gibbs and D. J. C. MacKay. Variational Gaussian process classifiers. IEEE Transactions on Neural Networks, 11(6):1458-1464, 2000.
9. G. H. Golub and C. F. Van Loan. Matrix Computations. John Hopkins University Press, Baltimore, second edition, 1989.
10. S. Hettich, C. L. Blake, and C. J. Merz. UCI repository of machine learning databases, 1998. http://www.ics.uci.edu/~mlearn/MLRepository.html.
11. R. E. Kass and A. E. Raftery. Bayes factors. Journal of the American Statistical Association, 90 (430):773-795, 1995.
12. N. Lawrence, M. Seeger, and R. Herbrich. Fast sparse Gaussian process methods: The informative vector machine. In S. Becker, S. Thrun, and K. Obermayer, editors, Advances in Neural Information Processing Systems 15, pages 609-616, Cambridge, MA, 2003. The MIT Press.
13. J. S. Liu. Monte Carlo Strategies in Scientific Computing. Springer, New York, 2001.
14. D. J. C. MacKay. Comparison of approximate methods for handling hyperparameters. Neural Computation, 11(5):1035-1068, 1999.
15. D. J. C. MacKay. Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge, UK, 2003.
16. T. P. Minka. A Family of Algorithms for Approximate Bayesian Inference. PhD thesis, Department of Electrical Engineering and Computer Science, MIT, 2001.
17. R. M. Neal. Probabilistic inference using Markov chain Monte Carlo methods. Technical Report CRG-TR-93-1, Department of Computer Science, University of Toronto, 1993.
18. R. M. Neal. Regression and classification using Gaussian process priors. In J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics 6, pages 475-501. Oxford University Press, 1998.
19. R. M. Neal. Annealed importance sampling. Statistics and Computing, 11:125-139, 2001.
20. A. O'Hagan. Curve fitting and optimal design for prediction. Journal of the Royal Statistical Society, Series B, 40(1):1-42, 1978.
21. M. Opper and O. Winther. Gaussian processes for classification: Mean-field algorithms. Neural Computation, 12(11):2655-2684, 2000.
22. J. C. Platt. Probabilities for SV machines. In A. J. Smola, P. L. Bartlett, B. Schölkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 61-73. The MIT Press, Cambridge, MA, 2000.
23. C. E. Rasmussen and C. K. I Williams. Gaussian Processes for Machine Learning. The MIT Press, Cambridge, MA, 2006. In press.
24. B. D. Ripley. Pattern Recognition and Neural Newtorks. Cambridge University Press, Cambridge, UK, 1996.
25. B. Schölkopf and A. J. Smola. Learning with Kernels. The MIT Press, Cambridge, MA, 2002.
26. M. Seeger. PAC-Bayesian generalisation error bounds for Gaussian process classification. Journal of Machine Learning Research, 3:233-269, 2002.
27. M. Seeger. Bayesian Gaussian Process Models: PAC-Bayesian Generalisation Error Bounds and Sparse Approximations. PhD thesis, University of Edinburgh, 2003.
28. M. Seeger. Expectation propagation for exponential families, 2005. Note obtainable from http://www.kyb.tuebingen.mpg.de/~seeger.
29. C. K. I. Williams and D. Barber. Bayesian classification with Gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(12):1342-1351, 1998.