An efficient, accurate, and interpretable machine learning method for computing probability of failure

2026-01-28

AI Summary

This study addresses the challenge of estimating failure probabilities in complex systems under threshold conditions by proposing a novel approach that integrates Gabriel editing sets with a penalty-contour support vector machine. The method employs adaptive sampling to efficiently allocate points near the failure boundary, enabling the construction of geometrically consistent local linear surrogate models. This strategy significantly reduces the number of costly simulation calls while maintaining high accuracy, interpretability, and theoretical convergence guarantees. Empirical evaluations on four benchmark problems demonstrate superior performance compared to several state-of-the-art classifiers. Furthermore, the approach is successfully applied to estimate survival probabilities in the Lotka–Volterra competitive species model, confirming its effectiveness and practical utility in real-world scenarios.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We introduce a novel machine learning method called the Penalized Profile Support Vector Machine based on the Gabriel edited set for the computation of the probability of failure for a complex system as determined by a threshold condition on a computer model of system behavior. The method is designed to minimize the number of evaluations of the computer model while preserving the geometry of the decision boundary that determines the probability. It employs an adaptive sampling strategy designed to strategically allocate points near the boundary determining failure and builds a locally linear surrogate boundary that remains consistent with its geometry by strategic clustering of training points. We prove two convergence results and we compare the performance of the method against a number of state of the art classification methods on four test problems. We also apply the method to determine the probability of survival using the Lotka--Volterra model for competing species.

Problem

• probability of failure
• machine learning
• computer model
• decision boundary
• reliability analysis

Innovation

• Penalized Profile SVM
• adaptive sampling
• failure probability
• Gabriel edited set
• surrogate boundary