  Deep learning is a form of machine learning for nonlinear high dimensional
pattern matching and prediction. By taking a Bayesian probabilistic
perspective, we provide a number of insights into more efficient algorithms for
optimisation and hyper-parameter tuning. Traditional high-dimensional data
reduction techniques, such as principal component analysis (PCA), partial least
squares (PLS), reduced rank regression (RRR), projection pursuit regression
(PPR) are all shown to be shallow learners. Their deep learning counterparts
exploit multiple deep layers of data reduction which provide predictive
performance gains. Stochastic gradient descent (SGD) training optimisation and
Dropout (DO) regularization provide estimation and variable selection. Bayesian
regularization is central to finding weights and connections in networks to
optimize the predictive bias-variance trade-off. To illustrate our methodology,
we provide an analysis of international bookings on Airbnb. Finally, we
conclude with directions for future research.
