Uncertainty Quantification via Stable Distribution Propagation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910328892162048 |
|---|---|
| author | Petersen, Felix Mishra, Aashwin Kuehne, Hilde Borgelt, Christian Deussen, Oliver Yurochkin, Mikhail |
| author_facet | Petersen, Felix Mishra, Aashwin Kuehne, Hilde Borgelt, Christian Deussen, Oliver Yurochkin, Mikhail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uncertainty Quantification via Stable Distribution Propagation Petersen, Felix Mishra, Aashwin Kuehne, Hilde Borgelt, Christian Deussen, Oliver Yurochkin, Mikhail Machine Learning Artificial Intelligence 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. |
| title | Uncertainty Quantification via Stable Distribution Propagation |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2402.08324 |