Dropout with Expectation-linear Regularization

Xuezhe Ma, Yingkai Gao, Zhiting Hu, Yaoliang Yu, Yuntian Deng, Eduard Hovy

Abstract: Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout’s training and inference phases, introduced due to tractability considerations, has largely remained under-appreciated. In this work, we first formulate dropout as a tractable approximation of some latent variable model, leading to a clean view of parameter sharing and enabling further theoretical analysis. Then, we introduce (approximate) expectation-linear dropout neural networks, whose inference gap we are able to formally characterize. Algorithmically, we show that our proposed measure of the inference gap can be used to regularize the standard dropout training objective, resulting in an explicit control of the gap. Our method is as simple and efficient as standard dropout. We further prove the upper bounds on the loss in accuracy due to expectation-linearization, describe classes of input distributions that expectation-linearize easily. Experiments on three image classification benchmark datasets demonstrate that reducing the inference gap can indeed improve the performance consistently.

Conflicts: cs.cmu.edu

Keywords: Theory, Deep learning, Supervised Learning