Statistical tests using hinge/ε-sensitive loss

Abstract

Statistical tests used in the literature to compare algorithms use the misclassification error which is based on the 0/1 loss and square loss for regression. Kernel-based, support vector machine classifiers (regressors) however are trained to minimize the hinge (ε-sensitive) loss and hence they should not be assessed or compared in terms of the 0/1 (square loss) but with the loss measure they are trained to minimize. We discuss how the paired t test can use the hinge (ε-sensitive) loss and show in our experiments that doing that, we can detect differences that the test on error cannot detect, indicating higher power in distinguishing between the behavior of kernel-based classifiers (regressors). Such tests can be generalized to compare L > 2 algorithms.