# CRPS-Optimal Binning for Univariate Conformal Regression

arXiv: https://arxiv.org/abs/2603.22000 · HTML: https://mlsanity.com/paper/2603.22000/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [In-sample calibration yields conformal calibration guarantees](https://mlsanity.com/paper/2503.03841/) (2025)
- [Bin-Conditional Conformal Prediction of Fatalities from Armed Conflict](https://mlsanity.com/paper/2410.14507/) (2024)

## Built on by (most cited first, 2 of 2)

- [Marginally Useful: An Information-Gap Identity in Conformal Prediction](https://mlsanity.com/paper/2608.07479/) (2026)
- [Common-Center Geometry and Certified Radial Reconstruction for Energy-Form Full Conformal Regions](https://mlsanity.com/paper/2608.24964/) (2026)

## Abstract (arXiv)

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(n2 log n) precomputation and O(n2) storage; the globally optimal K-partition is recovered by a dynamic programme in O(n2 K) time. Minimisation of within-sample LOO-CRPS turns out to be inappropriate for selecting K as it results in in-sample optimism. We instead select K by K-fold cross-validation of test CRPS, 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. The conformal prediction is transductive and data-efficient, as all observations are used for both partitioning and p-value calculation, with no need to reserve a hold-out set. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, CQR-QRF, and conformalized isotonic distributional regression), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.