# Towards Safe Machine Learning for CPS: Infer Uncertainty from Training Data

arXiv: https://arxiv.org/abs/1909.04886 · HTML: https://mlsanity.com/paper/1909.04886/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

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

- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Out of Distribution Reasoning by Weakly-Supervised Disentangled Logic Variational Autoencoder](https://mlsanity.com/paper/2210.09959/) (2022)
- [Verifying the Generalization of Deep Learning to Out-of-Distribution Domains](https://mlsanity.com/paper/2406.02024/) (2024)
- [Towards Robust Training Datasets for Machine Learning with Ontologies: A Case Study for Emergency Road Vehicle Detection](https://mlsanity.com/paper/2406.15268/) (2024)
- [Operational Range Bounding in Spectroscopy: A Safety Cage Framework for Machine Learning Models](https://mlsanity.com/paper/2609.13514/) (2026)

## Abstract (arXiv)

Machine learning (ML) techniques are increasingly applied to decision-making and control problems in Cyber-Physical Systems among which many are safety-critical, e.g., chemical plants, robotics, autonomous vehicles. Despite the significant benefits brought by ML techniques, they also raise additional safety issues because 1) most expressive and powerful ML models are not transparent and behave as a black box and 2) the training data which plays a crucial role in ML safety is usually incomplete. An important technique to achieve safety for ML models is "Safe Fail", i.e., a model selects a reject option and applies the backup solution, a traditional controller or a human operator for example, when it has low confidence in a prediction. Data-driven models produced by ML algorithms learn from training data, and hence they are only as good as the examples they have learnt. As pointed in [17], ML models work well in the "training space" (i.e., feature space with sufficient training data), but they could not extrapolate beyond the training space. As observed in many previous studies, a feature space that lacks training data generally has a much higher error rate than the one that contains sufficient training samples [31]. Therefore, it is essential to identify the training space and avoid extrapolating beyond the training space. In this paper, we propose an efficient Feature Space Partitioning Tree (FSPT) to address this problem. Using experiments, we also show that, a strong relationship exists between model performance and FSPT score.