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Dropout as a Bayesian Approximation: Appendix

We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an explanation to some of dropout's key properties, such as its robustness to over-fitting. Our interpretation allows us to reason about uncertainty in deep learning, and allows the introduction of the Bayesian machinery into existing deep learning frameworks in a principled way. This document is an appendix for the main paper "Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning" by Gal and Ghahramani, 2015.