Title: Federated Learning with Decoupled Probabilistic-Weighted Gradient Aggregation. Abstract:  In the federated learning paradigm, multiple mobile clients train local models independently based on datasets generated by edge devices, and the server aggregates parameters/gradients from local models to form a global model.   However, existing model aggregation approaches suffer from high bias on both data distribution   and parameter distribution for non-IID datasets,    which result in severe accuracy drop for increasing number of heterogeneous clients.    In this paper, we proposed a novel decoupled probabilistic-weighted gradient aggregation approach called FeDEC for federated learning.  The key idea is to optimize gradient parameters and statistical parameters in a decoupled way, and aggregate the parameters from local models with probabilistic weights to deal with the heterogeneity of clients.  Since the overall dataset is unaccessible by the central server,   we introduce a variational inference method to derive the optimal probabilistic weights to minimize statistical bias.   We further prove the convergence bound of the proposed approach.   Extensive experiments using mainstream convolutional neural network models based on three federated datasets  show that FeDEC significantly outperforms the state-of-the-arts in terms of model accuracy and training efficiency.