  In the federated learning system, parameter gradients are shared among
participants and the central modulator, while the original data never leave
their protected source domain. However, the gradient itself might carry enough
information for precise inference of the original data. By reporting their
parameter gradients to the central server, client datasets are exposed to
inference attacks from adversaries. In this paper, we propose a quantitative
metric based on mutual information for clients to evaluate the potential risk
of information leakage in their gradients. Mutual information has received
increasing attention in the machine learning and data mining community over the
past few years. However, existing mutual information estimation methods cannot
handle high-dimensional variables. In this paper, we propose a novel method to
approximate the mutual information between the high-dimensional gradients and
batched input data. Experimental results show that the proposed metric reliably
reflect the extent of information leakage in federated learning. In addition,
using the proposed metric, we investigate the influential factors of risk
level. It is proven that, the risk of information leakage is related to the
status of the task model, as well as the inherent data distribution.
