  Natural science datasets frequently violate assumptions of independence.
Samples may be clustered (e.g. by study site, subject, or experimental batch),
leading to spurious associations, poor model fitting, and confounded analyses.
While largely unaddressed in deep learning, this problem has been handled in
the statistics community through mixed effects models, which separate
cluster-invariant fixed effects from cluster-specific random effects. We
propose a general-purpose framework for Adversarially-Regularized Mixed Effects
Deep learning (ARMED) models through non-intrusive additions to existing neural
networks: 1) an adversarial classifier constraining the original model to learn
only cluster-invariant features, 2) a random effects subnetwork capturing
cluster-specific features, and 3) an approach to apply random effects to
clusters unseen during training. We apply ARMED to dense, convolutional, and
autoencoder neural networks on 4 applications including simulated nonlinear
data, dementia prognosis and diagnosis, and live-cell image analysis. Compared
to prior techniques, ARMED models better distinguish confounded from true
associations in simulations and learn more biologically plausible features in
clinical applications. They can also quantify inter-cluster variance and
visualize cluster effects in data. Finally, ARMED improves accuracy on data
from clusters seen during training (up to 28% vs. conventional models) and
generalization to unseen clusters (up to 9% vs. conventional models).
