Wasserstein-regularized Conformal Prediction under General Distribution Shift

• URL: http://arxiv.org/abs/2501.13430v1
• Date: Thu, 23 Jan 2025 07:29:44 GMT
• Title: Wasserstein-regularized Conformal Prediction under General Distribution Shift
• Authors: Rui Xu, Chao Chen, Yue Sun, Parvathinathan Venkitasubramaniam, Sihong Xie,
• Abstract summary: Conformal prediction yields a prediction set with guaranteed $1-alpha$ coverage of the true target under the i.i.d. assumption.<n>We propose a Wasserstein distance-based upper bound of the coverage gap and analyze the bound using probability measure pushforwards.<n>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.
• Score: 21.29977879431466
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conformal prediction yields a prediction set with guaranteed $1-\alpha$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-\alpha$ 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 $\alpha$. 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 $3.1\%$ across different confidence levels and outputs prediction sets 38$\%$ smaller than the worst-case approach on average.

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