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Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning
Alexander Immer · Matthias Bauer · Vincent Fortuin · Gunnar Ratsch · Khan Emtiyaz

Tue Jul 20 06:20 AM -- 06:25 AM (PDT) @

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).

Author Information

Alexander Immer (ETH-Z, MPI-IS)
Matthias Bauer (DeepMind)
Vincent Fortuin (ETH Zürich)

I am doing my PhD in machine learning at ETH Zürich.

Gunnar Ratsch (ETH Zurich)
Khan Emtiyaz (RIKEN)

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