# Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learning

arXiv: https://arxiv.org/abs/2302.00872 · HTML: https://mlsanity.com/paper/2302.00872/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 51 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A review of deep learning in medical imaging: Imaging traits, technology trends, case studies with progress highlights, and future promises](https://mlsanity.com/paper/2008.09104/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Understanding Softmax Confidence and Uncertainty](https://mlsanity.com/paper/2106.04972/) (2021)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Stochastic Configuration Networks: Fundamentals and Algorithms](https://mlsanity.com/paper/1702.03180/) (2017)
- [Optimized conformal classification using gradient descent approximation](https://mlsanity.com/paper/2105.11255/) (2021)
- [CLTune: A Generic Auto-Tuner for OpenCL Kernels](https://mlsanity.com/paper/1703.06503/) (2017)
- [Giving Commands to a Self-Driving Car: How to Deal with Uncertain Situations?](https://mlsanity.com/paper/2106.04232/) (2021)

## Built on by (most cited first, 5 of 5)

- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Multi-Modal Conformal Prediction Regions with Simple Structures by Optimizing Convex Shape Templates](https://mlsanity.com/paper/2312.07434/) (2023)
- [Conformal Prediction and Trustworthy AI](https://mlsanity.com/paper/2508.06885/) (2025)
- [SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors](https://mlsanity.com/paper/2606.10734/) (2026)
- [Threshold-Aware Conformal Routing](https://mlsanity.com/paper/2610.02487/) (2026)

## Abstract (arXiv)

By generating prediction intervals (PIs) to quantify the uncertainty of each prediction in deep learning regression, the risk of wrong predictions can be effectively controlled. High-quality PIs need to be as narrow as possible, whilst covering a preset proportion of real labels. At present, many approaches to improve the quality of PIs can effectively reduce the width of PIs, but they do not ensure that enough real labels are captured. Inductive Conformal Predictor (ICP) is an algorithm that can generate effective PIs which is theoretically guaranteed to cover a preset proportion of data. However, typically ICP is not directly optimized to yield minimal PI width. However, in this study, we use Directly Optimized Inductive Conformal Regression (DOICR) that takes only the average width of PIs as the loss function and increases the quality of PIs through an optimized scheme under the validity condition that sufficient real labels are captured in the PIs. Benchmark experiments show that DOICR outperforms current state-of-the-art algorithms for regression problems using underlying Deep Neural Network structures for both tabular and image data.