A poly-time algorithm achieves O(β)^{o(d)} volume approximation for minimum-volume β-conditioned ellipsoids with O(α/γ) coverage loss, plus a matching hardness result.
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Super-level-set regression directly optimizes conditional level-set boundaries via volume minimization to achieve minimum-volume prediction regions with conditional coverage.
Tomographic Quantile Forests estimate multivariate conditional distributions nonparametrically by training one model on directional quantiles and reconstructing via sliced Wasserstein minimization.
Multivariate standardized residuals via Mahalanobis distance from a learned local covariance yield asymptotic conditional coverage for conformal prediction under a derived sufficient condition on the data distribution.
A new kernel nonconformity score for multivariate conformal prediction that adapts to residual geometry, provides finite-sample coverage, and achieves convergence rates based on effective kernel rank rather than ambient dimension.
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Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery
A poly-time algorithm achieves O(β)^{o(d)} volume approximation for minimum-volume β-conditioned ellipsoids with O(α/γ) coverage loss, plus a matching hardness result.
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Super-Level-Set Regression: Conditional Quantiles via Volume Minimization
Super-level-set regression directly optimizes conditional level-set boundaries via volume minimization to achieve minimum-volume prediction regions with conditional coverage.
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Multivariate Uncertainty Quantification with Tomographic Quantile Forests
Tomographic Quantile Forests estimate multivariate conditional distributions nonparametrically by training one model on directional quantiles and reconstructing via sliced Wasserstein minimization.
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Multivariate Standardized Residuals for Conformal Prediction
Multivariate standardized residuals via Mahalanobis distance from a learned local covariance yield asymptotic conditional coverage for conformal prediction under a derived sufficient condition on the data distribution.
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A Kernel Nonconformity Score for Multivariate Conformal Prediction
A new kernel nonconformity score for multivariate conformal prediction that adapts to residual geometry, provides finite-sample coverage, and achieves convergence rates based on effective kernel rank rather than ambient dimension.