# The Penalized Inverse Probability Measure for Conformal Classification

arXiv: https://arxiv.org/abs/2406.08884 · HTML: https://mlsanity.com/paper/2406.08884/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 13 Jun 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [Challenges in Deploying Machine Learning: a Survey of Case Studies](https://mlsanity.com/paper/2011.09926/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Fair Conformal Predictors for Applications in Medical Imaging](https://mlsanity.com/paper/2109.04392/) (2021)
- [Improving Expert Predictions with Conformal Prediction](https://mlsanity.com/paper/2201.12006/) (2022)
- [Confident Object Detection via Conformal Prediction and Conformal Risk Control: an Application to Railway Signaling](https://mlsanity.com/paper/2304.06052/) (2023)
- [Group-Conditional Conformal Prediction via Quantile Regression Calibration for Crop and Weed Classification](https://mlsanity.com/paper/2308.15094/) (2023)
- [Deep learning powered real-time identification of insects using citizen science data](https://mlsanity.com/paper/2306.02507/) (2023)
- [Responsible and Regulatory Conform Machine Learning for Medicine: A Survey of Challenges and Solutions](https://mlsanity.com/paper/2107.09546/) (2021)
- [How Nonconformity Functions and Difficulty of Datasets Impact the Efficiency of Conformal Classifiers](https://mlsanity.com/paper/2108.05677/) (2021)

## Built on by (most cited first, 3 of 3)

- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Conformal Object Detection by Sequential Risk Control](https://mlsanity.com/paper/2505.24038/) (2025)
- [Uncertainty Guarantees on Automated Precision Weeding using Conformal Prediction](https://mlsanity.com/paper/2501.07185/) (2025)

## Abstract (arXiv)

The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction framework offers such formal guarantees by transforming any point into a set predictor with valid, finite-set, guarantees on the coverage of the true at a chosen level of confidence. Central to this methodology is the notion of the nonconformity score function that assigns to each example a measure of ''strangeness'' in comparison with the previously seen observations. While the coverage guarantees are maintained regardless of the nonconformity measure, the point predictor and the dataset, previous research has shown that the performance of a conformal model, as measured by its efficiency (the average size of the predicted sets) and its informativeness (the proportion of prediction sets that are singletons), is influenced by the choice of the nonconformity score function. The current work introduces the Penalized Inverse Probability (PIP) nonconformity score, and its regularized version RePIP, that allow the joint optimization of both efficiency and informativeness. Through toy examples and empirical results on the task of crop and weed image classification in agricultural robotics, the current work shows how PIP-based conformal classifiers exhibit precisely the desired behavior in comparison with other nonconformity measures and strike a good balance between informativeness and efficiency.