CRPS-Optimal Binning for Conformal Regression

• URL: http://arxiv.org/abs/2603.22000v1
• Date: Mon, 23 Mar 2026 14:07:09 GMT
• Title: CRPS-Optimal Binning for Conformal Regression
• Abstract summary: We propose a method for non-parametric conditional distribution estimation based on partitioning co-sorted observations into contiguous bins.<n>We form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are chosen to minimise the total leave-one-out Continuous Ranked Probability Score (LOO-CRPS), which admits a closed-form cost function with $O(n^2 \log n)$ precomputation and $O(n^2)$ storage; the globally optimal $K$-partition is recovered by a dynamic programme in $O(n^2 K)$ time. Minimisation of Within-sample LOO-CRPS turns out to be inappropriate for selecting $K$ as it results in in-sample optimism. So we instead select $K$ by evaluating test CRPS on an alternating held-out split, which yields a U-shaped criterion with a well-defined minimum. Having selected $K^*$ and fitted the full-data partition, we form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score, which carries a finite-sample marginal coverage guarantee at any prescribed level $\varepsilon$. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, and CQR-QRF), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.

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