# Isotonic Recalibration under a Low Signal-to-Noise Ratio

arXiv: https://arxiv.org/abs/2301.02692 · HTML: https://mlsanity.com/paper/2301.02692/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination](https://mlsanity.com/paper/2108.03210/) (2021)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [Generic Conditions for Forecast Dominance](https://mlsanity.com/paper/1805.09902/) (2018)
- [Calibrating sufficiently](https://mlsanity.com/paper/2105.07283/) (2021)
- [Honest calibration assessment for binary outcome predictions](https://mlsanity.com/paper/2203.04065/) (2022)
- [Distributional (Single) Index Models](https://mlsanity.com/paper/2006.09219/) (2020)
- [Model selection with Gini indices under auto-calibration](https://mlsanity.com/paper/2207.14372/) (2022)

## Built on by (most cited first, 8 of 8)

- [Smoothness and monotonicity constraints for neural networks using ICEnet](https://mlsanity.com/paper/2305.08807/) (2023)
- [From Point to probabilistic gradient boosting for claim frequency and severity prediction](https://mlsanity.com/paper/2412.14916/) (2024)
- [Calibration Bands for Mean Estimates within the Exponential Dispersion Family](https://mlsanity.com/paper/2503.18896/) (2025)
- [Assessing model calibration with boosting trees](https://mlsanity.com/paper/2606.08084/) (2026)
- [Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance](https://mlsanity.com/paper/2503.21321/) (2025)
- [Gini Score under Ties and Case Weights](https://mlsanity.com/paper/2511.15446/) (2025)
- [CAIRO: Decoupling Order from Scale in Regression](https://mlsanity.com/paper/2602.14440/) (2026)
- [Scaling Laws, Tabular Data and Actuarial Ratemaking Models](https://mlsanity.com/paper/2609.03106/) (2026)

## Abstract (arXiv)

Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to ensure auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to explainable pricing systems because the resulting isotonically recalibrated regression functions have a low complexity.