We consider the task of discriminating speech and non-speech in noisy environments. Previously, Mesgarani et. al [1] achieved state-of-the-art performance using a cortical representation of sound in conjunction with a feature reduction algorithm and a nonlinear support vector machine classifier. In the present work, we show that we can achieve the same or better accuracy by using a linear regularized least squares classifier directly on the high-dimensional cortical representation; the new system is substantially simpler conceptually and computationally. We select the regularization constant automatically, yielding a parameter-free learning system. Intriguingly, we find that optimal classifiers for noisy data can be trained on clean data using heavy regularization.