Early Stopping as Nonparametric Variational Inference
David Duvenaud, Dougal Maclaurin, Ryan Adams
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.
BibTeX
@InProceedings{pmlr-v51-duvenaud16,
title = {Early Stopping as Nonparametric Variational Inference},
author = {Duvenaud, David and Maclaurin, Dougal and Adams, Ryan},
booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
pages = {1070--1077},
year = {2016},
editor = {Gretton, Arthur and Robert, Christian C.},
volume = {51},
series = {Proceedings of Machine Learning Research},
address = {Cadiz, Spain},
month = {09--11 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v51/duvenaud16.pdf},
url = {https://proceedings.mlr.press/v51/duvenaud16.html},
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.}
}