Uncertainty Quantification via Stable Distribution Propagation Article Swipe

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Felix Petersen , Aashwin Mishra , Hilde Kuehne , Christian Borgelt , Oliver Deußen , Mikhail Yurochkin ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2402.08324

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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Distribution (mathematics) Computer science Mathematics Econometrics Statistical physics Statistics Physics Mathematical analysis

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2402.08324
PDF: https://arxiv.org/pdf/2402.08324
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4391833640

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DOI: https://doi.org/10.48550/arxiv.2402.08324

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Title: Uncertainty Quantification via Stable Distribution Propagation

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-02-13

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Authors: Felix Petersen, Aashwin Mishra, Hilde Kuehne, Christian Borgelt, Oliver Deußen, Mikhail Yurochkin

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Landing page: https://arxiv.org/abs/2402.08324

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Concepts: Distribution (mathematics), Computer science, Mathematics, Econometrics, Statistical physics, Statistics, Physics, Mathematical analysis

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