An empirical analysis of dropout in piecewise linear networks
Authors: David Warde-Farley, Ian Goodfellow, Aaron Courville, Yoshua Bengio
ICLR 2014

Abstract: The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.


Peer review:
[Review]:
We have addressed many of the comments kindly provided by our reviewers and apologize for not posting an updated manuscript sooner. Pending acceptance to arXiv.org, a revised version is available at http://www-etud.iro.umontreal.ca/~wardefar/iclr2014.pdf

In addition to incorporating reviewer feedback, we made one change to the experiments in Section 6 in order to be more charitable to the untied weights ensemble. Specifically, we altered the manner in which we set the hyperparameters used to train the ensemble members -- we now use a network with the same number of hidden units as the best performing dropout network but reoptimize all other hyperparameters to perform well when training via SGD without any masks. This considerably improves the untied ensemble's performance, but dropout still performs considerably better. We also provide the SGD baseline that resulted from optimizing these hyperparameters. We now employ 600 ensemble members; we hope to increase the number of ensemble members for the final copy.