Narrowing confidence interval width of SVM learning risk function by algorithmic inference

We narrow the width of the confidence intervals introduced by Vapnik for the risk function in Support Vector Machine learning [12]. We obtain this improvement by introducing both a theoretical framework for statistical inference of functions and a concept class complexity index, the detail, that is dual to the Vapnik-Chervonenkis dimension [4]. Detail of a class and maximum number of mislabelled points add up linearly to constitute the learning problem complexity. In particular, if we learn a hyperplane through a soft margin algorithm, the detail is l.e. the number of the used support vectors. The sample complexity dependency on this index is rather similar to the one on VC dimension. But in our approach we are able to identify (with some approximation) the distribution law of the random variable representing the