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In addition PROOF. Let

Burges, and A. Smola (ed) Advances in Kernel Methods, support Vector Learning, MIT Press (1999). E. E. J. Williams, Learning internal representations by error propagation, Parallel distributed processing: Explorations in macrostructure of cognition, Vol. I, Badford Books, Cambridge, MA (1986) 318-362. [16] J. L. Bartlett, R. C. Williamson, and M. Anthony, Structural risk minimization over data-dependent hierarchies, IEEE Transactions on Information Theory 44(5) (1998) 1926-1940. [17] B. -R. Miiller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation 10 (1998) 1229-1319.

Roughly speaking, the "bias" of a solution / coincides with our approximation error, and its "variance" with the sample error. Quoting [3], A model which is too simple, or too inflexible, will have a large bias, while one which has too much flexibility in relation to the particular data set will have a large variance. e. the smallest error] is obtained when we have the best compromise between the conflicting requirements of small bias and small variance. 42 F. Cucker, S. Smale As described in Section 3, Chapter II in [CS], the bias-variance problem amounts to the choice of a compact subspace H of ^(X) over which £z is minimized.

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