Most classifiers operate by selecting the maximum of an estimate of the conditional distribution $p(y|x)$ where $x$ stands for the features of the instance to be classified and $y$ denotes its label. This often results in a hubristic bias: overconfidence in the assignment of a definite label. Usually, the observations are concentrated on a small volume but the classifier provides definite predictions for the entire space. We propose constructing conformal prediction sets [vovk2005algorithmic] which contain a set of labels rather than a single label. These conformal prediction sets contain the true label with probability $1-\alpha$. Our construction is based on $p(x|y)$ rather than $p(y|x)$ which results in a classifier that is very cautious: it outputs the null set - meaning `I don't know' --- when the object does not resemble the training examples. An important property of our approach is that classes can be added or removed without having to retrain the classifier. We demonstrate the performance on the ImageNet ILSVRC dataset using high dimensional features obtained from state of the art convolutional neural networks.

本文提出了基于条件概率密度 p(x|y) 而非 p(y|x) 的符合性预测集合（conformal prediction sets）来消除分类模型中的傲慢偏差（hubristic bias），该模型在不确定时会输出空集，能很好地应对对抗攻击（adversarial attacks）。在 ImageNet ILSVRC 数据集和 CelebA、IMDB-Wiki 人脸数据集上以高维卷积神经网络为特征进行的实验结果表明它的性能优秀。

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