93,194 research outputs found
A theory of cross-validation error
This paper presents a theory of error in cross-validation testing of algorithms for predicting
real-valued attributes. The theory justifies the claim that predicting real-valued
attributes requires balancing the conflicting demands of simplicity and accuracy. Furthermore,
the theory indicates precisely how these conflicting demands must be balanced, in
order to minimize cross-validation error. A general theory is presented, then it is
developed in detail for linear regression and instance-based learning
Learning Sets with Separating Kernels
We consider the problem of learning a set from random samples. We show how
relevant geometric and topological properties of a set can be studied
analytically using concepts from the theory of reproducing kernel Hilbert
spaces. A new kind of reproducing kernel, that we call separating kernel, plays
a crucial role in our study and is analyzed in detail. We prove a new analytic
characterization of the support of a distribution, that naturally leads to a
family of provably consistent regularized learning algorithms and we discuss
the stability of these methods with respect to random sampling. Numerical
experiments show that the approach is competitive, and often better, than other
state of the art techniques.Comment: final versio
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