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]:
The authors attempt a further understanding of dropout through a set of empirical analyses that test a number of questions: 1, how close is the weight-scaling approximation to the geometric mean; 2., how good is the geometric mean compared to the arithmetic mean for classification; 3., Is the role of weight-tying in dropout important; and 4., is the ensemble aspect of dropout important compared to the benefit of using masking noise.

The conclusions of the authors are convincing, and the paper is a illuminating companion to some of the more theoretical analyses of dropout that have been presented recently. The dropout bagging vs dropout boosting is especially interesting. Standard dropout, which most resembles ensemble bagging, is compared to a version of weight-tied boosting. This comparison is constructed to try to determine whether there is a benefit to the bag ensemble, where each sub-model is independently tested and trained, compared the weight-tied boosting, where each sub-model is trained based on the performance of the entire ensemble. In weight-tied boosting, the benefit of weight-tying and masking noise are preserved, but not the independent sub-model training. The results seem to show that the independent ensemble/bagging aspect of dropout is important, rather than just the noise or the weight-tying.

The submission is relevant to the ICLR community. The experiments are carefully chosen and the conclusions are not overstated. The only significant barrier to publication is the lack of analysis of the empirical data and the figures, which are poorly chosen and not well explained. Figures 1 and 2 are difficult to read/interpret. A single summary/analysis for each of the 2 sets of data points would be very helpful. Figure 3 only goes to 120 ensemble members, but the text describes results at 360. It would be valuable to plot the full results, even if it is flat after 120.