Logistic classification with varying Gaussians

This paper is a continuation of the study of classification learning algorithms generated by regularization schemes associated with Gaussian kernels and general convex loss functions. In previous papers Xiang and Zhou (2009) [5], Xiang (2010) [7], it is assumed that the convex loss ϕϕ has a zero. This excludes some useful loss functions without zero such as the logistic loss ℓ(t)=log(1+exp(−t))ℓ(t)=log(1+exp(−t)). The main purpose of this paper is to conduct error analysis for the classification learning algorithms associated with such loss functions. The learning rates are derived by a novel application of projection operators to overcome the technical difficulty.