Investigating the Relationship Between Dropout Regularization and Model Complexity in Neural Networks

Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random combinations of the dropout rate and the number of hidden units in each dense layer, on each of the three data sets we selected. The generated figures, with binary cross entropy loss and binary accuracy on the z-axis, question the common assumption that adding depth to a dense layer while increasing the dropout rate will certainly enhance performance. We also discover a complex correlation between the two hyperparameters that we proceed to quantify by building additional machine learning and Deep Learning models which predict the optimal dropout rate given some hidden units in each dense layer. Linear regression and polynomial logistic regression require the use of arbitrary thresholds to select the cost data points included in the regression and to assign the cost data points a binary classification, respectively. These machine learning models have mediocre performance because their naive nature prevented the modeling of complex decision boundaries. Turning to Deep Learning models, we build neural networks that predict the optimal dropout rate given the number of hidden units in each dense layer, the desired cost, and the desired accuracy of the model. Though, this attempt encounters a mathematical error that can be attributed to the failure of the vertical line test. The ultimate Deep Learning model is a neural network whose decision boundary represents the 2,000 previously generated data points. This final model leads us to devise a promising method for tuning hyperparameters to minimize computational expense yet maximize performance. The strategy can be applied to any model hyperparameters, with the prospect of more efficient tuning in industrial models.