  Shapley Value is commonly adopted to measure and incentivize client
participation in federated learning. In this paper, we show -- theoretically
and through simulations -- that Shapley Value underestimates the contribution
of a common type of client: the Maverick. Mavericks are clients that differ
both in data distribution and data quantity and can be the sole owners of
certain types of data. Selecting the right clients at the right moment is
important for federated learning to reduce convergence times and improve
accuracy. We propose FedEMD, an adaptive client selection strategy based on the
Wasserstein distance between the local and global data distributions. As FedEMD
adapts the selection probability such that Mavericks are preferably selected
when the model benefits from improvement on rare classes, it consistently
ensures the fast convergence in the presence of different types of Mavericks.
Compared to existing strategies, including Shapley Value-based ones, FedEMD
improves the convergence of neural network classifiers by at least 26.9% for
FedAvg aggregation compared with the state of the art.
