Theory of Classification: a Survey of Some Recent Advances Page 1 ESAIM: PS ESAIM:
Probability and Statistics November 2005, Vol. 9, p. 323–375 DOI: 10.1051/ps:2005018 …

For spline regressions, it is well known that the choice of knots is crucial for the performance
of the estimator. As a general learning framework covering the smoothing splines, learning …

There is increasing interest in discovering individualized treatment rules (ITRs) for patients
who have heterogeneous responses to treatment. In particular, one aims to find an optimal …

Weak Convergence Page 1 1.3 Weak Convergence In this section IDl and IE are metric spaces
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …

Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents
an accessible treatment of the two main components of support vector machines (SVMs) …

The purpose of these lecture notes is to provide an introduction to the general theory of
empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities …

Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that
can adapt over time to an evolving illness. The goal is to accommodate heterogeneity …

We prove bounds on the population risk of the maximum margin algorithm for two-class
linear classification. For linearly separable training data, the maximum margin algorithm has …

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 …

Supplementary material to “Estimation bounds and sharp oracle inequalities of regularized
procedures with Lipschitz loss functions”. Section 6 gives the proof of the main results …