  Federated Learning (FL) wherein multiple institutions collaboratively train a
machine learning model without sharing data is becoming popular. Participating
institutions might not contribute equally, some contribute more data, some
better quality data or some more diverse data. To fairly rank the contribution
of different institutions, Shapley value (SV) has emerged as the method of
choice. Exact SV computation is impossibly expensive, especially when there are
hundreds of contributors. Existing SV computation techniques use
approximations. However, in healthcare where the number of contributing
institutions are likely not of a colossal scale, computing exact SVs is still
exorbitantly expensive, but not impossible. For such settings, we propose an
efficient SV computation technique called SaFE (Shapley Value for Federated
Learning using Ensembling). We empirically show that SaFE computes values that
are close to exact SVs, and that it performs better than current SV
approximations. This is particularly relevant in medical imaging setting where
widespread heterogeneity across institutions is rampant and fast accurate data
valuation is required to determine the contribution of each participant in
multi-institutional collaborative learning.
