# Probabilistic Safety Regions Via Finite Families of Scalable Classifiers

arXiv: https://arxiv.org/abs/2309.04627 · HTML: https://mlsanity.com/paper/2309.04627/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Trustworthy AI: From Principles to Practices](https://mlsanity.com/paper/2110.01167/) (2021)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Review of Uncertainty Estimation and its Application in Medical Imaging](https://mlsanity.com/paper/2302.08119/) (2023)
- [Robust Machine Learning Systems: Challenges, Current Trends, Perspectives, and the Road Ahead](https://mlsanity.com/paper/2101.02559/) (2021)
- [Engineering Safety in Machine Learning](https://mlsanity.com/paper/1601.04126/) (2016)
- [Extensible Machine Learning for Encrypted Network Traffic Application Labeling via Uncertainty Quantification](https://mlsanity.com/paper/2205.05628/) (2022)
- [Robust Machine Learning via Privacy/Rate-Distortion Theory](https://mlsanity.com/paper/2007.11693/) (2020)
- [Prediction error quantification through probabilistic scaling -- EXTENDED VERSION](https://mlsanity.com/paper/2105.14187/) (2021)
- [Chance constrained sets approximation: A probabilistic scaling approach -- EXTENDED VERSION](https://mlsanity.com/paper/2101.06052/) (2021)

## Built on by (most cited first, 2 of 2)

- [Conformal Predictions for Probabilistically Robust Scalable Machine Learning Classification](https://mlsanity.com/paper/2403.10368/) (2024)
- [Safe and Efficient Social Navigation through Explainable Safety Regions Based on Topological Features](https://mlsanity.com/paper/2503.16441/) (2025)

## Abstract (arXiv)

Supervised classification recognizes patterns in the data to separate classes of behaviours. Canonical solutions contain misclassification errors that are intrinsic to the numerical approximating nature of machine learning. The data analyst may minimize the classification error on a class at the expense of increasing the error of the other classes. The error control of such a design phase is often done in a heuristic manner. In this context, it is key to develop theoretical foundations capable of providing probabilistic certifications to the obtained classifiers. In this perspective, we introduce the concept of probabilistic safety region to describe a subset of the input space in which the number of misclassified instances is probabilistically controlled. The notion of scalable classifiers is then exploited to link the tuning of machine learning with error control. Several tests corroborate the approach. They are provided through synthetic data in order to highlight all the steps involved, as well as through a smart mobility application.