解决联邦ICA中局部估计不一致的聚合难题，实现抗干扰的一次性全局矩阵恢复。
One-shot Robust Federated Learning of Independent Component Analysis
- 通过构造符号不变的亲和矩阵，用谱聚类消除排列歧义。
- 即使部分客户端数据质量差，只要每组多数可靠，仍能准确恢复全局混合矩阵。
- 适合高异构性、存在异常客户端的联邦学习场景，尤其适用于信号分离任务。
本文研究分布式与联邦独立成分分析（ICA）中的一次性鲁棒聚合问题。每个客户端计算局部ICA估计器，服务器需在不访问原始数据的情况下恢复共同的全局混合矩阵。主要挑战在于局部估计器仅在符号排列意义下可识别，且估计质量差异大。本文提出谱鲁棒联邦ICA（SRF-ICA）方法：从所有局部原子构建符号不变亲和矩阵，进行谱k-means以消除排列模糊性，对每组估计值内符号对齐，最后使用几何中位数实现鲁棒聚合。理论证明谱聚类步骤控制了组内误分率，且最终估计器在大量低质量客户端存在时仍保持精度，只要每组包含多数可靠原子。分析结合谱扰动界、k-means误分保证及几何中位数的分位数鲁棒性。因篇幅限制，模拟实验展示该方法在异质样本量与污染水平下的有效性留于附录。
原文摘要 · Abstract (English)
This paper studies robust one-shot aggregation for distributed and federated Independent Component Analysis (ICA). In this setting, each client computes a local ICA estimator, while the server aims to recover a common global mixing matrix without accessing raw data. The main difficulty is that local ICA estimators are identifiable only up to signed permutations and may have highly heterogeneous estimation quality. We propose Spectral-Robust-Federated ICA (SRF-ICA), a one-shot aggregation method that constructs a sign-invariant affinity matrix from all local atoms, performs spectral k-means to resolve the permutation ambiguity, aligns signs within each estimated cluster, and then applies the geometric median for robust aggregation. We prove that the spectral clustering step controls the cluster-wise misclustering rate, and that the final estimator remains accurate even when a substantial fraction of local atoms are produced from low-quality clients, as long as each cluster contains a majority of reliable atoms. The analysis combines spectral perturbation bounds, k-means misclustering guarantees, and quantile-based robustness of the geometric median. Due to space constraints, simulation studies demonstrating the effectiveness of the proposed approach under heterogeneous sample sizes and corruption levels are deferred to the appendix.
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