Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

One-shot Robust Federated Learning of Independent Component Analysis

Dian Jin, Xin Bing, Yuqian Zhang

TL;DR

The paper tackles robust one-shot aggregation for federated ICA where each client contributes an estimator of the mixing matrix $A^*$ up to signed permutations. It introduces RF-ICA, a two-stage method that first resolves sign ambiguity against a benchmark and then clusters the $Kr$ estimator columns into $r$ groups, applying a geometric-median aggregator within each cluster to overcome heterogeneity. Theoretical guarantees couple k-means misclustering bounds with the robustness of the geometric median to obtain consistency and explicit error rates under ICA models with sub-Gaussian sources and orthonormal or near-orthonormal mixing matrices. Empirical results on simulated heterogeneous data demonstrate that RF-ICA outperforms standard one-shot baselines and remains robust as the fraction of unreliable clients grows, highlighting its practical value for cross-silo federated ICA with minimal communication rounds.

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.

One-shot Robust Federated Learning of Independent Component Analysis

TL;DR

The paper tackles robust one-shot aggregation for federated ICA where each client contributes an estimator of the mixing matrix up to signed permutations. It introduces RF-ICA, a two-stage method that first resolves sign ambiguity against a benchmark and then clusters the estimator columns into groups, applying a geometric-median aggregator within each cluster to overcome heterogeneity. Theoretical guarantees couple k-means misclustering bounds with the robustness of the geometric median to obtain consistency and explicit error rates under ICA models with sub-Gaussian sources and orthonormal or near-orthonormal mixing matrices. Empirical results on simulated heterogeneous data demonstrate that RF-ICA outperforms standard one-shot baselines and remains robust as the fraction of unreliable clients grows, highlighting its practical value for cross-silo federated ICA with minimal communication rounds.

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 -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 -means. The effectiveness of the proposed approach is further supported by simulation studies conducted under various heterogeneous settings.

Paper Structure

This paper contains 19 sections, 8 theorems, 57 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation and the proposed method
  3. Resolve the signed permutation ambiguity
  4. Geometric median for robust aggregation
  5. Review on the FastICA algorithm
  6. Theoretical results
  7. Analysis of the $k$-means clustering
  8. Analysis of the robust aggregation via geometric median
  9. Theoretical guarantees for \ref{['alg:1']}
  10. Explicit error rates under the ICA model
  11. Experimental results
  12. Extension to approximation $k$-means solution
  13. Proofs
  14. Proof of \ref{['lem:k_means']}
  15. Proof of \ref{['lem:mis_class']}
  16. ...and 4 more sections

Key Result

Lemma 1

Let $(\bar{\boldsymbol \theta}_1, \ldots, \bar{\boldsymbol \theta}_r)$ and $\bar{\sigma}$ be obtained from kmeans. If $8 \sqrt{7\epsilon / \Delta } \le 1$ then Moreover, for any $a \in [r]$,

Figures (2)

  • Figure 1: The averaged estimation error of our algorithm (RF-ICA) with three competing methods.
  • Figure 2: The averaged estimation error of four competing methods.

Theorems & Definitions (17)

  • Remark 1: Choice of the benchmark client
  • Remark 2: Comparison with the $k$-median
  • Lemma 1
  • Definition 1: Sample quantile
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Corollary 1: Error rate under ICA
  • Theorem 2
  • proof
  • ...and 7 more