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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 Laplaces 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).
We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by usi
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structur
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applicati
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known EM algorith
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs, which lear