Confidence Estimates of Classification Accuracy on New Examples
Following recent results [6] showing the importance of the fat shattering dimension in explaining the beneficial effect of a large margin on generalization performance, the current paper investigates how the margin on a test example can be used to give greater certainty of correct classification in the distribution independent model. The results show that even if the classifier does not classify all of the training examples correctly, the fact that a new example has a larger margin than that on the misclassified examples, can be used to give very good estimates for the generalization performance in terms of the fat shattering dimension measured at a scale proportional to the excess margin. The estimate relies on a sufficiently large number of the correctly classified training examples having a margin roughly equal to that used to estimate generalization, indicating that the corresponding output values need to be ‘well sampled’. If this is not the case it may be better to use the estimate obtained from a smaller margin.