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Quantification of Uncertainty in predictions is a challenging problem. In theclassification settings, although deep learning based models generalize well,class probabilities often lack reliability. Calibration errors are used toquantify uncertainty, and several methods exist to minimize calibration error.We argue that between the choice of having a minimum calibration error onoriginal distribution which increases across distortions or having a (possiblyslightly higher) calibration error which is constant across distortions, weprefer the latter  We hypothesize that the reason for unreliability of deep networks is - Theway neural networks are currently trained, the probabilities do not generalizeacross small distortions. We observe that quantile based approaches canpotentially solve this problem. We propose an innovative approach to decouplethe construction of quantile representations from the loss function allowing usto compute quantile based probabilities without disturbing the originalnetwork. We achieve this by establishing a novel duality property betweenquantiles and probabilities, and an ability to obtain quantile probabilitiesfrom any pre-trained classifier.  While post-hoc calibration techniques successfully minimize calibrationerrors, they do not preserve robustness to distortions. We show that, Quantileprobabilities (QuantProb), obtained from Quantile representations, preserve thecalibration errors across distortions, since quantile probabilities generalizebetter than the naive Softmax probabilities.

QuantProb: Generalizing Probabilities along with Predictions for a Pre-trained Classifier