Related papers: Uncertainty Quantification via Stable Distribution Propagation

Uncertainty Quantification via Stable Distribution Propagation

URL: http://arxiv.org/abs/2402.08324v1
Date: Tue, 13 Feb 2024 09:40:19 GMT
Title: Uncertainty Quantification via Stable Distribution Propagation
Authors: Felix Petersen, Aashwin Mishra, Hilde Kuehne, Christian Borgelt, Oliver Deussen, Mikhail Yurochkin
Abstract summary: 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.
Score: 60.065272548502
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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