Combining Statistical Depth and Fermat Distance for Uncertainty Quantification

Hai-Vy Nguyen, Fabrice Gamboa, Reda Chhaibi, Sixin Zhang, Serge Gratton, Thierry Giaccone

Keywords: Out-of-distribution, In-distribution, Uncertainty quantification, Fermat distance, Lens depth, Novelty detection, Feature spaces, Deep learning

Abstract: 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 distributional assumption. Our method also has no trainable parameter. The method is applied directly in the 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 results on toy datasets and can give competitive or better uncertainty estimation on standard deep learning datasets compared to strong baseline methods.

Primary Area: Other (please use sparingly, only use the keyword field for more details)

Submission Number: 6359