Abstract
The Bayesian analysis of neural networks is difficult because the prior over functions has a complex form, leading to implementations that either make approximations or use Monte Carlo integration techniques. In this paper I investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis to be carried out exactly using matrix operations. The method has been tested on two challenging problems and has produced excellent results.
Keywords
- Gaussian Process
- Hide Unit
- Hierarchical Bayesian Approach
- Automatic Relevance Determination
- Boston Housing Data
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References
N. A. C. Cressie, Statistics for Spatial Data, Wiley (1993).
F. Girosi, M. Jones, and T. Poggio, Regularization Theory and Neural Networks Architectures, Neural Computation, Vol. 7(2) (1995), pp219–269.
A. G. Journel and Ch. J. Huijbregts, Mining Geostatistics, Academic Press (1978).
D. J. C. MacKay, A Practical Bayesian Framework for Back-propagation Networks, Neural Computation, Vol. 4(3) (1992), pp448–472.
D. J. C. MacKay, Bayesian Methods for Backpropagation Networks, In J. L. van Hemmen, E. Domany, and K. Schulten, editors, Models of Neural Networks II, Springer (1993).
R. M. Neal, Bayesian Learning via Stochastic Dynamics, in: S. J. Hanson, J. D. Cowan, and C. L. Giles, eds., Neural Information Processing Systems, Vol. 5 (1993), pp475–482. Morgan Kaufmann, San Mateo, CA,.
R. M. Neal, Bayesian Learning for Neural Networks, PhD thesis, Dept. of Computer Science, University of Toronto (1995).
T. Poggio and F. Girosi, Networks for approximation and learning, Proceedings of IEEE, Vol. 78 (1990), pp1481–1497.
J. R. Quinlan, Combining Instance-Based and Model-Based Learning, in: P. E. Utgoff, ed., Proc. ML’93, Morgan Kaufmann, San Mateo, CA (1993).
G. Wahba, Spline Models for Observational Data, Society for Industrial and Applied Mathematics, CBMS-NSF Regional Conference series in applied mathematics (1990).
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© 1997 Springer Science+Business Media New York
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Williams, C.K.I. (1997). Regression with Gaussian Processes. In: Ellacott, S.W., Mason, J.C., Anderson, I.J. (eds) Mathematics of Neural Networks. Operations Research/Computer Science Interfaces Series, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6099-9_66
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DOI: https://doi.org/10.1007/978-1-4615-6099-9_66
Publisher Name: Springer, Boston, MA
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