Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
Paper derives nonasymptotic error bounds for split conformalized quantile regression under known covariate shift.
The paper derives nonasymptotic L^p bounds on interval length and conditional coverage for split conformalized quantile regression, assuming local regularity and accurate quantile estimates. The bounds are instantiated for quantile regression with sparse ReLU neural networks and extended to known covariate shift between calibration and test covariates. Matching minimax upper and lower bounds are obtained for two fixed-score calibration benchmarks, for every p in [1, infinity] in a scalar problem and for finite p in a K-threshold problem.
- Nonasymptotic L^p bounds for split conformalized quantile regression.
- Results instantiated for sparse ReLU network quantile estimators.
- Matching minimax bounds under known covariate shift.
From the original article
1 min read at arxiv.orgIn this paper, we study nonasymptotic $L^p$ error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local regularity conditions and accuracy guarantees for the estimated quantiles. We further instantiate our bounds for quantile regression with sparse ReLU neural networks.
By Rustam Isaev · arxiv.org
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