  Marginal-likelihood based model-selection, even though promising, is rarely
used in deep learning due to estimation difficulties. Instead, most approaches
rely on validation data, which may not be readily available. In this work, we
present a scalable marginal-likelihood estimation method to select both
hyperparameters and network architectures, based on the training data alone.
Some hyperparameters can be estimated online during training, simplifying the
procedure. Our marginal-likelihood estimate is based on Laplace's method and
Gauss-Newton approximations to the Hessian, and it outperforms cross-validation
and manual-tuning on standard regression and image classification datasets,
especially in terms of calibration and out-of-distribution detection. Our work
shows that marginal likelihoods can improve generalization and be useful when
validation data is unavailable (e.g., in nonstationary settings).
