Corpus ID: 15476562

Generalization Bounds andLearning Rates forRegularized Principal

  title={Generalization Bounds andLearning Rates forRegularized Principal},
  author={ManifoldsAlex and Jake Smola and Robert C. Williamson},
We derive uniform convergence bounds and learning rates for regularized principal manifolds. This builds on previous work of Kegl et al., however we are able to obtain stronger bounds taking advantage of the decomposition of the principal manifold in terms of kernel functions. In particular, we are able to give bounds on the covering numbers which are independent of the number of basis functions (line elements) used. Finally we are able to obtain a nearly optimal learning rate of order O(m ? 1… Expand


The connection between regularization operators and support vector kernels
It is proved that the Green's Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties and it is shown that a large number of radial basis functions, namely conditionally positive definite functions, may be used as support vector kernel. Expand
Learning and Design of Principal Curves
This work defines principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution, making it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction. Expand
Entropy, Compactness and the Approximation of Operators
1. Entropy quantities 2. Approximation quantities 3. Inequalities of Bernstein-Jackson type 3. Inequalities of Berstein-Jackson type 4. A refined Riesz theory 5. Operators with values in C(X) 6.Expand
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