We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the classification problem at hand. We demonstrate that such techniques tend to introduce biased estimates for instances whose predictions are supposed to be highly confident. We argue that this deficiency is an artifact of the dynamics of training with SGD-like optimizers, and it has some properties similar to overfitting. Based on this observation, we develop an uncertainty estimation algorithm that selectively estimates the uncertainty of highly confident points, using earlier snapshots of the trained model, before their estimates are jittered (and way before they are ready for actual classification). We present extensive experiments indicating that the proposed algorithm provides uncertainty estimates that are consistently better than all known methods.
The most common, and well-known approach for obtaining confidence scores for DNNs is by measuring the classification margin. When softmax is in use at the last layer, its values correspond to the distance from the decision boundary, where large values tend to reflect high confidence levels. This concept is widely used in the context of classification with a reject option in linear models and in particular, in SVMs . In the context of neural networks, @cite_5 @cite_4 were the first to propose this approach and, for DNNs, it has been recently shown to outperform the MC-dropout on ImageNet .
@cite_5 @cite_4
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Criteria for evaluating the classification reliability of a neural classifier and for accordingly making a reject option are proposed. Such an option, implemented by means of two rules which can be applied independently of topology, size, and training algorithms of the neural classifier, allows one to improve the classification reliability. It is assumed that a performance function P is defined which, taking into account the requirements of the particular application, evaluates the quality of the classification in terms of recognition, misclassification, and reject rates. Under this assumption the optimal reject threshold value, determining the best trade-off between reject rate and misclassification rate, is the one for which the function P reaches its absolute maximum. No constraints are imposed on the form of P, but the ones necessary in order that P actually measures the quality of the classification process. The reject threshold is evaluated on the basis of some statistical distributions characterizing the behavior of the classifier when operating without reject option; these distributions are computed once the training phase of the net has been completed. The method has been tested with a neural classifier devised for handprinted and multifont printed characters, by using a database of about 300000 samples. Experimental results are discussed. > A method defining a reject option that is applicable to a given 0-reject classifier is proposed. The reject option is based on an estimate of the classification reliability, measured by a reliability evaluator spl Psi . Trivially, once a reject threshold spl sigma has been fixed, a sample is rejected if the corresponding value of spl Psi is below spl sigma . Obviously, as spl sigma represents the least tolerable classification reliability level, when its value varies the reject option becomes more or less severe. In order to adapt the behavior of the reject option to the requirements of the considered application domain, a function P characterizing the reject option's adequacy to the domain has been introduced. It is shown that P can be expressed as a function of spl sigma and, consequently, the optimal value for spl sigma is defined as the one which maximizes the function P. The method for determining the optimal threshold value is independent of the specific 0-reject classifier, while the definition of the reliability evaluators is related to the classifier's architecture. General criteria for defining appropriate reliability evaluators within a classification paradigm are illustrated in the paper and are based on the localization, in the feature space, of the samples that could be classified with a low reliability. The definition of the reliability evaluators for three popular architectures of neural networks (backpropagation, learning vector quantization and probabilistic network) is presented. Finally, the method has been tested with reference to a complex classification problem with data generated according to a distribution-of-distributions model.