A Fundamental Accuracy--Robustness Trade-off in Regression and Classification
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912455172554752 |
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| author | Bahmani, Sohail |
| author_facet | Bahmani, Sohail |
| contents | We derive a fundamental trade-off between standard and adversarial risk in a rather general situation that formalizes the following simple intuition: "If no (nearly) optimal predictor is smooth, adversarial robustness comes at the cost of accuracy." As a concrete example, we evaluate the derived trade-off in regression with polynomial ridge functions under mild regularity conditions. Generalizing our analysis of this example, we formulate a necessary condition under which adversarial robustness can be achieved without significant degradation of the accuracy. This necessary condition is expressed in terms of a quantity that resembles the Poincaré constant of the data distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fundamental Accuracy--Robustness Trade-off in Regression and Classification Bahmani, Sohail Machine Learning We derive a fundamental trade-off between standard and adversarial risk in a rather general situation that formalizes the following simple intuition: "If no (nearly) optimal predictor is smooth, adversarial robustness comes at the cost of accuracy." As a concrete example, we evaluate the derived trade-off in regression with polynomial ridge functions under mild regularity conditions. Generalizing our analysis of this example, we formulate a necessary condition under which adversarial robustness can be achieved without significant degradation of the accuracy. This necessary condition is expressed in terms of a quantity that resembles the Poincaré constant of the data distribution. |
| title | A Fundamental Accuracy--Robustness Trade-off in Regression and Classification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.05853 |