  We consider the problem of kernel classification. While worst-case bounds on
the decay rate of the prediction error with the number of samples are known for
some classifiers, they often fail to accurately describe the learning curves of
real data sets. In this work, we consider the important class of data sets
satisfying the standard source and capacity conditions, comprising a number of
real data sets as we show numerically. Under the Gaussian design, we derive the
decay rates for the misclassification (prediction) error as a function of the
source and capacity coefficients. We do so for two standard kernel
classification settings, namely margin-maximizing Support Vector Machines (SVM)
and ridge classification, and contrast the two methods. We find that our rates
tightly describe the learning curves for this class of data sets, and are also
observed on real data. Our results can also be seen as an explicit prediction
of the exponents of a scaling law for kernel classification that is accurate on
some real datasets.
