FedPower：隐私保护的分布式特征空间估计
FedPower: Privacy-Preserving Distributed Eigenspace Estimation
AI总结：
针对分布式数据中特征空间估计面临的通信效率低和隐私泄露挑战，本文提出基于联邦学习的FedPower算法，通过交替局部幂迭代与全局聚合并引入正交普氏变换和差分隐私机制，提升了通信效率与隐私保护，并给出了收敛界与实验验证。
摘要：
特征空间估计在机器学习和统计学中是基础性的，已在PCA、降维和聚类等领域得到应用。现代机器学习社区通常假设数据来自并属于不同的组织。较低的通信能力和可能的数据隐私泄露使得特征空间的计算具有挑战性。为了应对这些挑战，我们在联邦学习（FL）框架内提出了一类名为FedPower的算法。FedPower利用著名的幂方法，通过交替进行多次局部幂迭代和一个全局聚合步骤，从而提高通信效率。在聚合中，我们提出使用正交普氏变换（OPT）对每个局部特征向量矩阵进行加权，以实现更好的对齐。为了确保强隐私保护，我们通过采用差分隐私（DP）的概念在每次迭代中添加高斯噪声。我们为FedPower提供了收敛界，这些收敛界由不同的可解释项组成，分别对应于高斯噪声、并行化以及本地机器随机采样的影响。此外，我们进行了实验以证明所提出算法的有效性。
英文摘要：
Eigenspace estimation is fundamental in machine learning and statistics, which has found applications in PCA, dimension reduction, and clustering, among others. The modern machine learning community usually assumes that data come from and belong to different organizations. The low communication power and the possible privacy breaches of data make the computation of eigenspace challenging. To address these challenges, we propose a class of algorithms called \textsf{FedPower} within the federated learning (FL) framework. \textsf{FedPower} leverages the well-known power method by alternating multiple local power iterations and a global aggregation step, thus improving communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with {\it Orthogonal Procrustes Transformation} (OPT) for better alignment. To ensure strong privacy protection, we add Gaussian noise in each iteration by adopting the notion of \emph{differential privacy} (DP). We provide convergence bounds for \textsf{FedPower} that are composed of different interpretable terms corresponding to the effects of Gaussian noise, parallelization, and random sampling of local machines. Additionally, we conduct experiments to demonstrate the effectiveness of our proposed algorithms.
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