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

TL;DR

This paper presents a novel machine learning approach called Penalized Profile Support Vector Machine, designed to efficiently and accurately estimate failure probabilities in complex systems with minimal model evaluations.

Contribution

The paper introduces a new SVM-based method with adaptive sampling and local linearization, improving efficiency and interpretability in failure probability estimation.

Findings

The method reduces the number of computer model evaluations.

It maintains decision boundary geometry for accurate failure probability.

Performance surpasses existing classification methods on test problems.

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.