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Abstract: Gaussian process (GP) prediction suffers from O(n 3 ) scaling with the data set size n. By using a finite-dimensional basis to approximate the GP predictor, the computational complexity can be reduced. We derive optimal finite-dimensional predictors under a number of assumptions, and show the superiority of these predictors over the Projected Bayes Regression method (which is asymptotically optimal). We also show how to calculate the minimal model size for a given n. The calculations are... (Update)
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.... data set we can not use the direct method; i.e. inversion of the (n n) matrix K, and we need to do some approximations as proposed in [7, 35, 30]. 6 Data Sample Construction 6.1 Chaotic Mackey Glass Time Series The chaotic Mackey Glass time series is de ned by the di...
...of the system. We have to select the query points such that they x these degrees of freedom. 6 Independently, Ferrari Trecate, Williams and Opper (1999) made similar observation. They found that for small amounts of data the coecients of the eigenfunctions with small...
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BibTeX entry: (Update)
G. Ferrari Trecate, C.K.I. Williams, and M. Opper. Finite-dimensional approximation of Gaussian processes. In M.S. Kearns, S.A. Solla and D.A. Cohn, editor, Advances in Neural Information Processing Systems 11, pages 218-224. MIT Press, 1999. http://citeseer.ist.psu.edu/trecate99finitedimensional.html More
@misc{ trecate99finitedimensional,
author = "G. Trecate and C. Williams and M. Opper",
title = "Finite-dimensional approximation of Gaussian processes",
text = "G. Ferrari Trecate, C.K.I. Williams, and M. Opper. Finite-dimensional approximation
of Gaussian processes. In M.S. Kearns, S.A. Solla and D.A. Cohn, editor,
Advances in Neural Information Processing Systems 11, pages 218-224. MIT
Press, 1999.",
year = "1999",
url = "citeseer.ist.psu.edu/trecate99finitedimensional.html" }
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