Combining Statistical Depth and Fermat Distance for Uncertainty Quantification
This provides a parameter-free method for uncertainty estimation in classification models without affecting model performance, though it appears incremental as it builds on existing statistical depth and distance concepts.
The paper tackles the problem of out-of-domain uncertainty quantification in neural network predictions by combining Lens Depth and Fermat Distance to measure point depth in feature space without distributional assumptions, achieving competitive or better results compared to strong baselines on standard datasets.
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.