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 φ has a zero. This excludes some useful loss functions without zero such as the logistic loss 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.