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Uncertainty Quantification via Stable Distribution Propagation

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arxiv 2402.08324 v1 pith:2ZYTG2T6 submitted 2024-02-13 cs.LG cs.AI

Felix Petersen , Aashwin Mishra , Hilde Kuehne , Christian Borgelt , Oliver Deussen , Mikhail Yurochkin This is my paper · ORCID
classification cs.LGcs.AI
keywords propagatingdistributionsmethoddemonstratenetworksneuralstableuncertainties
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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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Cited by 3 Pith papers

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