Robust Distributed Estimation: Extending Gossip Algorithms to Ranking and Trimmed Means

2025-05-23

AI Summary

To address the limited robustness of conventional mean-based gossip algorithms against malicious nodes in arbitrary communication graphs, this paper proposes two distributed robust estimation methods: GoRank, the first gossip algorithm based on rank estimation, and GoTrim, a truncated-mean-based gossip algorithm. We theoretically establish convergence rates of $O(1/t)$ for GoRank and $O(log t / t)$ for GoTrim. Notably, we provide the first rigorous breakdown point analysis for GoTrim, precisely characterizing its resilience threshold against adversarial nodes. Both methods integrate graph signal processing with robust statistics, requiring neither a central coordinator nor global knowledge of the network topology. Extensive experiments across diverse graph topologies, data distributions, and adversarial contamination patterns validate their robustness and convergence properties; empirical results closely match the theoretical convergence rates.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper addresses the problem of robust estimation in gossip algorithms over arbitrary communication graphs. Gossip algorithms are fully decentralized, relying only on local neighbor-to-neighbor communication, making them well-suited for situations where communication is constrained. A fundamental challenge in existing mean-based gossip algorithms is their vulnerability to malicious or corrupted nodes. In this paper, we show that an outlier-robust mean can be computed by globally estimating a robust statistic. More specifically, we propose a novel gossip algorithm for rank estimation, referred to as extsc{GoRank}, and leverage it to design a gossip procedure dedicated to trimmed mean estimation, coined extsc{GoTrim}. In addition to a detailed description of the proposed methods, a key contribution of our work is a precise convergence analysis: we establish an $mathcal{O}(1/t)$ rate for rank estimation and an $mathcal{O}(log(t)/t)$ rate for trimmed mean estimation, where by $t$ is meant the number of iterations. Moreover, we provide a breakdown point analysis of extsc{GoTrim}. We empirically validate our theoretical results through experiments on diverse network topologies, data distributions and contamination schemes.

Problem

• Robust estimation in gossip algorithms over arbitrary graphs
• Vulnerability of mean-based gossip to malicious nodes
• Novel gossip algorithms for rank and trimmed mean estimation

Innovation

• Novel gossip algorithm for rank estimation
• Gossip procedure for trimmed mean estimation
• Precise convergence and breakdown point analysis