Adversarially-regularized mixed effects deep learning (ARMED) models for improved interpretability, performance, and generalization on clustered data

Data in the natural sciences frequently violate assumptions of independence. Such datasets have samples with inherent clustering (eg by study site, subject, 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. These models separate cluster-invariant, population-level fixed effects from cluster-specific random effects. We propose a general-purpose framework for Adversarially-Regularized Mixed Effects Deep learning (ARMED) models through three non-intrusive additions to existing neural networks: 1) a domain 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 feedforward neural networks, convolutional neural networks, and autoencoders on 4 applications including classification of synthesized nonlinear data, dementia prognosis and diagnosis, and live-cell microscopy image analysis. We compare to conventional models, domain adversarial-only models, and the inclusion of cluster membership as an input covariate. ARMED models better distinguish confounded from true associations in synthetic data and emphasize more biologically plausible features in clinical applications. They also quantify inter-cluster variance in clinical data and can visualize batch effects in cell images. 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). By incorporating powerful mixed effects modeling into deep learning, ARMED increases interpretability, performance, and generalization on clustered data.