Uncertainty Quantification via Stable Distribution Propagation
Abstract
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.
Cite
Text
Petersen et al. "Uncertainty Quantification via Stable Distribution Propagation." International Conference on Learning Representations, 2024.Markdown
[Petersen et al. "Uncertainty Quantification via Stable Distribution Propagation." International Conference on Learning Representations, 2024.](https://mlanthology.org/iclr/2024/petersen2024iclr-uncertainty/)BibTeX
@inproceedings{petersen2024iclr-uncertainty,
title = {{Uncertainty Quantification via Stable Distribution Propagation}},
author = {Petersen, Felix and Mishra, Aashwin Ananda and Kuehne, Hilde and Borgelt, Christian and Deussen, Oliver and Yurochkin, Mikhail},
booktitle = {International Conference on Learning Representations},
year = {2024},
url = {https://mlanthology.org/iclr/2024/petersen2024iclr-uncertainty/}
}