A Federated Distributionally Robust Support Vector Machine with Mixture of Wasserstein Balls Ambiguity Set for Distributed Fault Diagnosis

2024-10-04

arXiv.org

AI Summary

This paper addresses the federated classification problem in remote industrial equipment fault diagnosis, where multi-client data are decentralized, privacy-sensitive, and exhibit uncertainty in both labels and features. We propose a federated distributionally robust support vector machine (SVM) framework. Its core innovation is a novel mixed Wasserstein ball (MoWB) ambiguity set, which simultaneously captures local data heterogeneity and ensures global optimization decomposability, with theoretically guaranteed generalization bounds. The method integrates distributionally robust optimization, Wasserstein distance, federated learning, and ADMM-based subgradient coordination to enable joint client-server training without sharing raw data. Experiments on synthetic and real-world industrial datasets demonstrate that the proposed approach achieves strong robustness against label noise, distributional shifts, and feature perturbations, exhibits stable convergence, and incurs significantly lower communication overhead compared to state-of-the-art baselines.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The training of classification models for fault diagnosis tasks using geographically dispersed data is a crucial task for original equipment manufacturers (OEMs) seeking to provide long-term service contracts (LTSCs) to their customers. Due to privacy and bandwidth constraints, such models must be trained in a federated fashion. Moreover, due to harsh industrial settings the data often suffers from feature and label uncertainty. Therefore, we study the problem of training a distributionally robust (DR) support vector machine (SVM) in a federated fashion over a network comprised of a central server and $G$ clients without sharing data. We consider the setting where the local data of each client $g$ is sampled from a unique true distribution $mathbb{P}_g$, and the clients can only communicate with the central server. We propose a novel Mixture of Wasserstein Balls (MoWB) ambiguity set that relies on local Wasserstein balls centered at the empirical distribution of the data at each client. We study theoretical aspects of the proposed ambiguity set, deriving its out-of-sample performance guarantees and demonstrating that it naturally allows for the separability of the DR problem. Subsequently, we propose two distributed optimization algorithms for training the global FDR-SVM: i) a subgradient method-based algorithm, and ii) an alternating direction method of multipliers (ADMM)-based algorithm. We derive the optimization problems to be solved by each client and provide closed-form expressions for the computations performed by the central server during each iteration for both algorithms. Finally, we thoroughly examine the performance of the proposed algorithms in a series of numerical experiments utilizing both simulation data and popular real-world datasets.

Problem

• Federated classification with private and uncertain client data
• Robustifying SVM against perturbations in local distributions
• Handling data heterogeneity via Wasserstein balls mixture

Innovation

• Federated Distributionally Robust SVM
• Mixture of Wasserstein Balls ambiguity
• Theoretical guarantees with performance bounds