  Federated learning is an emerging distributed machine learning framework
aiming at protecting data privacy. Data heterogeneity is one of the core
challenges in federated learning, which could severely degrade the convergence
rate and prediction performance of deep neural networks. To address this issue,
we develop a novel personalized federated learning framework for heterogeneous
data, which we refer to as FedSplit. This modeling framework is motivated by
the finding that, data in different clients contain both common knowledge and
personalized knowledge. Then the hidden elements in each neural layer can be
split into the shared and personalized groups. With this decomposition, a novel
objective function is established and optimized. We demonstrate FedSplit
enjoyers a faster convergence speed than the standard federated learning method
both theoretically and empirically. The generalization bound of the FedSplit
method is also studied. To practically implement the proposed method on real
datasets, factor analysis is introduced to facilitate the decoupling of hidden
elements. This leads to a practically implemented model for FedSplit and we
further refer to as FedFac. We demonstrated by simulation studies that, using
factor analysis can well recover the underlying shared/personalized
decomposition. The superior prediction performance of FedFac is further
verified empirically by comparison with various state-of-the-art federated
learning methods on several real datasets.
