# Early Stopping as Nonparametric Variational Inference

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David Duvenaud,
Dougal Maclaurin,
Ryan Adams
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Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:1070-1077, 2016.

#### Abstract

We show that unconverged stochastic gradient descent can be interpreted as sampling from a nonparametric approximate posterior distribution. This distribution is implicitly defined by the transformation of an initial distribution by a sequence of optimization steps. By tracking the change in entropy of this distribution during optimization, we give a scalable, unbiased estimate of a variational lower bound on the log marginal likelihood. This bound can be used to optimize hyperparameters instead of cross-validation. This Bayesian interpretation of SGD also suggests new overfitting-resistant optimization procedures, and gives a theoretical foundation for early stopping and ensembling. We investigate the properties of this marginal likelihood estimator on neural network models.

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