[2603.22000] CRPS-Optimal Binning for Conformal Regression

Computer Science > Machine Learning arXiv:2603.22000 (cs) [Submitted on 23 Mar 2026] Title:CRPS-Optimal Binning for Conformal Regression Authors:Paolo Toccaceli View a PDF of the paper titled CRPS-Optimal Binning for Conformal Regression, by Paolo Toccaceli View PDF HTML (experimental) 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 p...