One-shot Robust Federated Learning of Independent Component Analysis

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arXiv:2505.20532v2 Announce Type: replace Abstract: 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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