  Federated learning platforms are gaining popularity. One of the major
benefits is to mitigate the privacy risks as the learning of algorithms can be
achieved without collecting or sharing data. While federated learning (i.e.,
many based on stochastic gradient algorithms) has shown great promise, there
are still many challenging problems in protecting privacy, especially during
the process of gradients update and exchange. This paper presents the first
gradient-free federated learning framework called GRAFFL for learning a
Bayesian generative model based on approximate Bayesian computation. Unlike
conventional federated learning algorithms based on gradients, our framework
does not require to disassemble a model (i.e., to linear components) or to
perturb data (or encryption of data for aggregation) to preserve privacy.
Instead, this framework uses implicit information derived from each
participating institution to learn posterior distributions of parameters. The
implicit information is summary statistics derived from SuffiAE that is a
neural network developed in this study to create compressed and linearly
separable representations thereby protecting sensitive information from
leakage. As a sufficient dimensionality reduction technique, this is proved to
provide sufficient summary statistics. We propose the GRAFFL-based Bayesian
Gaussian mixture model to serve as a proof-of-concept of the framework. Using
several datasets, we demonstrated the feasibility and usefulness of our model
in terms of privacy protection and prediction performance (i.e., close to an
ideal setting). The trained model as a quasi-global model can generate
informative samples involving information from other institutions and enhances
data analysis of each institution.
