# Nonparametric Distribution Regression Re-calibration

arXiv: https://arxiv.org/abs/2602.13362 · HTML: https://mlsanity.com/paper/2602.13362/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 54 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [Beyond calibration: estimating the grouping loss of modern neural networks](https://mlsanity.com/paper/2210.16315/) (2022)
- [Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination](https://mlsanity.com/paper/2108.03210/) (2021)
- [Local Calibration: Metrics and Recalibration](https://mlsanity.com/paper/2102.10809/) (2021)
- [Calibration tests beyond classification](https://mlsanity.com/paper/2210.13355/) (2022)
- [Calibration by Distribution Matching: Trainable Kernel Calibration Metrics](https://mlsanity.com/paper/2310.20211/) (2023)
- [Kernel Conditional Density Operators](https://mlsanity.com/paper/1905.11255/) (2019)
- [Cross-calibration of probabilistic forecasts](https://mlsanity.com/paper/1505.05314/) (2015)
- [All Models Are Miscalibrated, But Some Less So: Comparing Calibration with Conditional Mean Operators](https://mlsanity.com/paper/2502.11465/) (2025)
- [Fast and Scalable Score-Based Kernel Calibration Tests](https://mlsanity.com/paper/2510.14711/) (2025)

## Abstract (arXiv)

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration, producing narrow but overconfident predictions. However, in safety-critical settings, trustworthy uncertainty estimates are often more valuable than narrow intervals. Realizing the problem, several recent works have focused on post-hoc corrections; however, existing methods either rely on weak notions of calibration (such as PIT uniformity) or impose restrictive parametric assumptions on the nature of the error. To address these limitations, we propose a novel nonparametric re-calibration algorithm based on conditional kernel mean embeddings, capable of correcting calibration error without restrictive modeling assumptions. For efficient inference with real-valued targets, we introduce a novel characteristic kernel over distributions that can be evaluated in O(n log n) time for empirical distributions of size n. We demonstrate that our method consistently outperforms prior re-calibration approaches across a diverse set of regression benchmarks and model classes.