Covariances for Free: Exploiting Mean Distributions for Federated Learning with Pre-trained Models

Dipam Goswami, Simone Magistri, Kai Wang, Bartłomiej Twardowski, Andrew D. Bagdanov, Joost van de Weijer

Keywords: Federated Learning, Transfer Learning

TL;DR: We estimate global class covariances at the server with a provably unbiased estimator requiring only local class means from clients, achieving performance competitive or superior to algorithms sharing second-order statistics

Abstract: Using pre-trained models has been found to reduce the effect of data heterogeneity and speed up federated learning algorithms. Recent works have investigated the use of first-order statistics and second-order statistics to aggregate local client data distributions at the server and achieve very high performance without any training. In this work we propose a training-free method based on an unbiased estimator of class covariance matrices. Our method, which only uses first-order statistics in the form of class means communicated by clients to the server, incurs only a fraction of the communication costs required by methods based on communicating second-order statistics. We show how these estimated class covariances can be used to initialize a linear classifier, thus exploiting the covariances without actually sharing them. When compared to state-of-the-art methods which also share only class means, our approach improves performance in the range of 4-26\% with exactly the same communication cost. Moreover, our method achieves performance competitive or superior to sharing second-order statistics with dramatically less communication overhead. Finally, using our method to initialize classifiers and then performing federated fine-tuning yields better and faster convergence.

Primary Area: transfer learning, meta learning, and lifelong learning

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Submission Number: 439