We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a distribution in feature space, without any assumption about the form of distribution. Our method has no trainable parameter. The method is applicable to any classification model as it is applied directly in feature space at test time and does not intervene in training process. As such, it does not impact the performance of the original model. The proposed method gives excellent qualitative result on toy datasets and can give competitive or better uncertainty estimation on standard deep learning datasets compared to strong baseline methods.

使用统计概念``镜头深度'' (LD) 和 Fermat Distance 对神经网络的``域外不确定性''进行测量，这能够准确捕捉到一个点在特征空间中相对于分布的``深度''，而不需任何有关分布形式的假设。该方法无需可训练参数，并可应用于任何分类模型，在测试时直接在特征空间中应用，不干预训练过程。该方法在玩具数据集上有出色的定性结果，并在标准深度学习数据集上相较于强基准方法提供了具有竞争力或更好的不确定性估计。

统计深度与费马距离结合的不确定性量化