# Conformal Thresholded Intervals for Efficient Regression

arXiv: https://arxiv.org/abs/2407.14495 · HTML: https://mlsanity.com/paper/2407.14495/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [TorchCP: A Python Library for Conformal Prediction](https://mlsanity.com/paper/2402.12683/) (2024)
- [On training locally adaptive CP](https://mlsanity.com/paper/2306.04648/) (2023)

## Built on by (most cited first, 11 of 11)

- [Conformalized Interval Arithmetic with Symmetric Calibration](https://mlsanity.com/paper/2408.10939/) (2024)
- [Conditional Conformal Risk Adaptation](https://mlsanity.com/paper/2504.07611/) (2025)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability](https://mlsanity.com/paper/2506.07804/) (2025)
- [Adaptive Conformal Inference by Particle Filtering under Hidden Markov Models](https://mlsanity.com/paper/2411.01558/) (2024)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Fast Conformal Prediction using Conditional Interquantile Intervals](https://mlsanity.com/paper/2601.02769/) (2026)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [Geometry of tail allocation in conformal prediction intervals](https://mlsanity.com/paper/2604.25202/) (2026)
- [Super-Level-Set Regression: Conditional Quantiles via Volume Minimization](https://mlsanity.com/paper/2605.06210/) (2026)

## Abstract (arXiv)

This paper introduces Conformal Thresholded Intervals (CTI), a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. Unlike existing methods that rely on nested conformal frameworks and full conditional distribution estimation, CTI estimates the conditional probability density for a new response to fall into each interquantile interval using off-the-shelf multi-output quantile regression. By leveraging the inverse relationship between interval length and probability density, CTI constructs prediction sets by thresholding the estimated conditional interquantile intervals based on their length. The optimal threshold is determined using a calibration set to ensure marginal coverage, effectively balancing the trade-off between prediction set size and coverage. CTI's approach is computationally efficient and avoids the complexity of estimating the full conditional distribution. The method is theoretically grounded, with provable guarantees for marginal coverage and achieving the smallest prediction size given by Neyman-Pearson . Extensive experimental results demonstrate that CTI achieves superior performance compared to state-of-the-art conformal regression methods across various datasets, consistently producing smaller prediction sets while maintaining the desired coverage level. The proposed method offers a simple yet effective solution for reliable uncertainty quantification in regression tasks, making it an attractive choice for practitioners seeking accurate and efficient conformal prediction.