Wasserstein-regularized Conformal Prediction under General Distribution Shift
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913721387843584 |
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| author | Xu, Rui Chen, Chao Sun, Yue Venkitasubramaniam, Parvathinathan Xie, Sihong |
| author_facet | Xu, Rui Chen, Chao Sun, Yue Venkitasubramaniam, Parvathinathan Xie, Sihong |
| contents | Conformal prediction yields a prediction set with guaranteed $1-α$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-α$ and the actual coverage. Prior studies bound the gap using total variation distance, which cannot identify the gap changes under distribution shift at a given $α$. Besides, existing methods are mostly limited to covariate shift,while general joint distribution shifts are more common in practice but less researched.In response, we first propose a Wasserstein distance-based upper bound of the coverage gap and analyze the bound using probability measure pushforwards between the shifted joint data and conformal score distributions, enabling a separation of the effect of covariate and concept shifts over the coverage gap. We exploit the separation to design an algorithm based on importance weighting and regularized representation learning (WR-CP) to reduce the Wasserstein bound with a finite-sample error bound.WR-CP achieves a controllable balance between conformal prediction accuracy and efficiency. Experiments on six datasets prove that WR-CP can reduce coverage gaps to $3.2\%$ across different confidence levels and outputs prediction sets 37$\%$ smaller than the worst-case approach on average. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wasserstein-regularized Conformal Prediction under General Distribution Shift Xu, Rui Chen, Chao Sun, Yue Venkitasubramaniam, Parvathinathan Xie, Sihong Machine Learning Conformal prediction yields a prediction set with guaranteed $1-α$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-α$ and the actual coverage. Prior studies bound the gap using total variation distance, which cannot identify the gap changes under distribution shift at a given $α$. Besides, existing methods are mostly limited to covariate shift,while general joint distribution shifts are more common in practice but less researched.In response, we first propose a Wasserstein distance-based upper bound of the coverage gap and analyze the bound using probability measure pushforwards between the shifted joint data and conformal score distributions, enabling a separation of the effect of covariate and concept shifts over the coverage gap. We exploit the separation to design an algorithm based on importance weighting and regularized representation learning (WR-CP) to reduce the Wasserstein bound with a finite-sample error bound.WR-CP achieves a controllable balance between conformal prediction accuracy and efficiency. Experiments on six datasets prove that WR-CP can reduce coverage gaps to $3.2\%$ across different confidence levels and outputs prediction sets 37$\%$ smaller than the worst-case approach on average. |
| title | Wasserstein-regularized Conformal Prediction under General Distribution Shift |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2501.13430 |