Stochastic Wasserstein Gradient Flows using Streaming Data with an Application in Predictive Maintenance

TL;DR

This paper introduces a stochastic Wasserstein gradient flow method for real-time estimation in streaming data scenarios, with applications in predictive maintenance, demonstrating improved robustness over traditional methods.

Contribution

It proposes a novel stochastic projected Wasserstein gradient flow algorithm that effectively handles streaming data for estimation tasks in safety-critical applications.

Findings

Convergence of the proposed algorithm is established.

The method outperforms classical least squares in predictive maintenance tasks.

Enhanced robustness in decision-making processes is demonstrated.

Abstract

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that keeps track of the belief of the estimated quantity and can consume samples from online data. We show the convergence properties of our algorithm. Our analysis combines recent advances in the Wasserstein space and its differential structure with more classical stochastic gradient descent. We apply our methodology for predictive maintenance of safety-critical processes: Our approach is shown to lead to superior performance when compared to classical least squares, enabling, among others, improved robustness for decision-making.