  Modern approaches to supervised learning like deep neural networks (DNNs)
typically implicitly assume that observed responses are statistically
independent. In contrast, correlated data are prevalent in real-life
large-scale applications, with typical sources of correlation including
spatial, temporal and clustering structures. These correlations are either
ignored by DNNs, or ad-hoc solutions are developed for specific use cases. We
propose to use the mixed models framework to handle correlated data in DNNs. By
treating the effects underlying the correlation structure as random effects,
mixed models are able to avoid overfitted parameter estimates and ultimately
yield better predictive performance. The key to combining mixed models and DNNs
is using the Gaussian negative log-likelihood (NLL) as a natural loss function
that is minimized with DNN machinery including stochastic gradient descent
(SGD). Since NLL does not decompose like standard DNN loss functions, the use
of SGD with NLL presents some theoretical and implementation challenges, which
we address. Our approach which we call LMMNN is demonstrated to improve
performance over natural competitors in various correlation scenarios on
diverse simulated and real datasets. Our focus is on a regression setting and
tabular datasets, but we also show some results for classification. Our code is
available at https://github.com/gsimchoni/lmmnn.
