Early Stopping is Nonparametric Variational Inference

Abstract

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

8 pages, 5 figures

References in corpus (2)

• Gradient-based Hyperparameter Optimization through Reversible Learning
• Nested Variational Compression in Deep Gaussian Processes

Cited by in corpus (2)

• Learning to Draw Samples with Amortized Stein Variational Gradient Descent
• Known Unknowns: Uncertainty Quality in Bayesian Neural Networks