The minimum number of misclassifications achievable with affine hyper_ planes on a given set of labeled points is a key quantity in both statistics and computational learning theory. However, determining this quantity exactly is essentially NP_hard_ cf_ Höfgen, Simon and van Horn (1995.) Hence,...

Support vector machines (SVMs) are special kernel based methods and have been among the most successful learning methods for more than a decade. SVMs can informally be described as kinds of regularized M-estimators for functions and have demonstrated their usefulness in many complicated...

In this paper we show that the recent notion of regression depth can be used as a data-analytic tool to measure the amount of separation between successes and failures in the binary response framework. Extending this algorithm allows us to compute the overlap in data sets which are commonly...

Cronbach’s alpha is a popular method to measure reliability, e.g. in quantifying the reliability of a score to summarize the information of several items in questionnaires. The alpha coefficient is known to be non-robust. We study the behavior of this coefficient in different settings to...

Kernel Based Regression (KBR) minimizes a convex risk over a possibly infinite dimensional reproducing kernel Hilbert space. Recently, it was shown that KBR with a least squares loss function may have some undesirable properties from a robustness point of view: even very small amounts of...