Empirical confidence estimates for classification by deep neural networks

How well can we estimate the probability that the classification predicted by a deep neural network is correct (or in the Top 5)? It is well-known that the softmax values of the network are not estimates of the probabilities of class labels. However, there is a misconception that these values are not informative. We define the notion of implied loss and prove that if an uncertainty measure is an implied loss, then low uncertainty means high probability of correct (or Top-k) classification on the test set. We demonstrate empirically that these values can be used to measure the confidence that the classification is correct. Our method is simple to use on existing networks: we proposed confidence measures for Top-k which can be evaluated by binning values on the test set.