  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.
