The mathematical theory of machine learning not only explains the current algorithms but
can also motivate principled approaches for the future. This self-contained textbook …

A comprehensive introduction to Support Vector Machines and related kernel methods. In
the 1990s, a new type of learning algorithm was developed, based on results from statistical …

This important work describes recent theoretical advances in the study of artificial neural
networks. It explores probabilistic models of supervised learning problems, and addresses …

We give improved constants for data dependent and variance sensitive confidence bounds,
called empirical Bernstein bounds, and extend these inequalities to hold uniformly over …

Abstract Support Vector (SV) Machines combine several techniques from statistics, machine
learning and neural networks. One of the most important ingredients are kernels, ie the …

We consider the problem of binary classification where the classifier can, for a particular
cost, choose not to classify an observation. Just as in the conventional classification …

The covering number of a ball of a reproducing kernel Hilbert space as a subset of the
continuous function space plays an important role in Learning Theory. We give estimates for …

Recently, sample complexity bounds have been derived for problems involving linear
functions such as neural networks and support vector machines. In many of these theoretical …

A family of kernels for statistical learning is introduced that exploits the geometric structure of
statistical models. The kernels are based on the heat equation on the Riemannian manifold …

Often, tasks are collected for multi-task learning (MTL) because they share similar feature
structures. Based on this observation, in this paper, we present novel algorithm-dependent …