Combining Statistical Depth and Fermat Distance for Uncertainty
  Quantification
Hai-Vy Nguyen Fabrice Gamboa Reda Chhaibi Sixin Zhang Serge Gratton Thierry Giaccone
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.