  Federated Learning (FL) addresses the need to create models based on
proprietary data in such a way that multiple clients retain exclusive control
over their data, while all benefit from improved model accuracy due to pooled
resources. Recently proposed Neural Graphical Models (NGMs) are Probabilistic
Graphical models that utilize the expressive power of neural networks to learn
complex non-linear dependencies between the input features. They learn to
capture the underlying data distribution and have efficient algorithms for
inference and sampling. We develop a FL framework which maintains a global NGM
model that learns the averaged information from the local NGM models while
keeping the training data within the client's environment. Our design, FedNGMs,
avoids the pitfalls and shortcomings of neuron matching frameworks like
Federated Matched Averaging that suffers from model parameter explosion. Our
global model size remains constant throughout the process. In the cases where
clients have local variables that are not part of the combined global
distribution, we propose a `Stitching' algorithm, which personalizes the global
NGM models by merging the additional variables using the client's data. FedNGM
is robust to data heterogeneity, large number of participants, and limited
communication bandwidth.
