# Accurately Predicting Probabilities of Safety-Critical Rare Events for Intelligent Systems

arXiv: https://arxiv.org/abs/2403.13869 · HTML: https://mlsanity.com/paper/2403.13869/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 20 Mar 2024.

## Builds on (most cited first, 21 of 21)

- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions](https://mlsanity.com/paper/1901.01753/) (2019)
- [Rethinking Class-Balanced Methods for Long-Tailed Visual Recognition from a Domain Adaptation Perspective](https://mlsanity.com/paper/2003.10780/) (2020)
- [Self-supervised Learning is More Robust to Dataset Imbalance](https://mlsanity.com/paper/2110.05025/) (2021)
- [Relay Backpropagation for Effective Learning of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1512.05830/) (2015)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [Striking the Right Balance with Uncertainty](https://mlsanity.com/paper/1901.07590/) (2019)
- [Imbalanced Deep Learning by Minority Class Incremental Rectification](https://mlsanity.com/paper/1804.10851/) (2018)
- ["Curse of rarity" for autonomous vehicles](https://mlsanity.com/paper/2207.02749/) (2022)
- [Deep Over-sampling Framework for Classifying Imbalanced Data](https://mlsanity.com/paper/1704.07515/) (2017)
- [Criticality Metrics for Automated Driving: A Review and Suitability Analysis of the State of the Art](https://mlsanity.com/paper/2108.02403/) (2021)
- [Testing Scenario Library Generation for Connected and Automated Vehicles, Part I: Methodology](https://mlsanity.com/paper/1905.03419/) (2019)
- [Constructing Balance from Imbalance for Long-tailed Image Recognition](https://mlsanity.com/paper/2208.02567/) (2022)
- [Testing Scenario Library Generation for Connected and Automated Vehicles, Part II: Case Studies](https://mlsanity.com/paper/1905.03428/) (2019)
- [CLIP-guided Federated Learning on Heterogeneous and Long-Tailed Data](https://mlsanity.com/paper/2312.08648/) (2023)

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

- [DiCriTest: Testing Scenario Generation for Decision-Making Agents Considering Diversity and Criticality](https://mlsanity.com/paper/2508.11514/) (2025)
- [Towards provable probabilistic safety for scalable embodied AI systems](https://mlsanity.com/paper/2506.05171/) (2025)
- [Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems](https://mlsanity.com/paper/2609.21160/) (2026)

## Abstract (arXiv)

Intelligent systems are increasingly integral to our daily lives, yet rare safety-critical events present significant latent threats to their practical deployment. Addressing this challenge hinges on accurately predicting the probability of safety-critical events occurring within a given time step from the current state, a metric we define as 'criticality'. The complexity of predicting criticality arises from the extreme data imbalance caused by rare events in high dimensional variables associated with the rare events, a challenge we refer to as the curse of rarity. Existing methods tend to be either overly conservative or prone to overlooking safety-critical events, thus struggling to achieve both high precision and recall rates, which severely limits their applicability. This study endeavors to develop a criticality prediction model that excels in both precision and recall rates for evaluating the criticality of safety-critical autonomous systems. We propose a multi-stage learning framework designed to progressively densify the dataset, mitigating the curse of rarity across stages. To validate our approach, we evaluate it in two cases: lunar lander and bipedal walker scenarios. The results demonstrate that our method surpasses traditional approaches, providing a more accurate and dependable assessment of criticality in intelligent systems.