One-shot Robust Federated Learning of Independent Component Analysis

2025-05-26

AI Summary

This paper addresses the highly heterogeneous independent component analysis (ICA) problem in distributed and federated learning settings, proposing the first one-shot robust aggregation framework. It tackles key challenges including extreme client-side data sparsity (up to half of clients possessing only a few observations), permutation ambiguity in estimated separation matrices, and severe statistical heterogeneity. Methodologically, it introduces a novel two-stage aggregation mechanism that jointly leverages k-means clustering and the geometric median: clustering first resolves permutation inconsistencies across clients’ separation matrices, followed by geometric-median-based robust aggregation. Theoretically, it establishes the first joint characterization of the geometric median’s estimation error bound and k-means’ maximum misclustering rate, rigorously guaranteeing convergence under extreme heterogeneity. Experiments demonstrate that the framework consistently outperforms both vanilla averaging and existing robust aggregation methods across diverse heterogeneous configurations.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Distributed Problem Solving

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• 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

Abstract

This paper investigates a general robust one-shot aggregation framework for distributed and federated Independent Component Analysis (ICA) problem. We propose a geometric median-based aggregation algorithm that leverages $k$-means clustering to resolve the permutation ambiguity in local client estimations. Our method first performs k-means to partition client-provided estimators into clusters and then aggregates estimators within each cluster using the geometric median. This approach provably remains effective even in highly heterogeneous scenarios where at most half of the clients can observe only a minimal number of samples. The key theoretical contribution lies in the combined analysis of the geometric median's error bound-aided by sample quantiles-and the maximum misclustering rates of the aforementioned solution of $k$-means. The effectiveness of the proposed approach is further supported by simulation studies conducted under various heterogeneous settings.

Problem

• Robust one-shot aggregation for federated Independent Component Analysis
• Resolving permutation ambiguity in ICA via k-means clustering
• Handling heterogeneous client data with geometric median aggregation

Innovation

• Geometric median-based aggregation algorithm
• k-means clustering resolves permutation ambiguity
• Effective in highly heterogeneous scenarios