  Deep learning applies hierarchical layers of hidden variables to construct
nonlinear high dimensional predictors. Our goal is to develop and train deep
learning architectures for spatio-temporal modeling. Training a deep
architecture is achieved by stochastic gradient descent (SGD) and drop-out (DO)
for parameter regularization with a goal of minimizing out-of-sample predictive
mean squared error. To illustrate our methodology, we predict the sharp
discontinuities in traffic flow data, and secondly, we develop a classification
rule to predict short-term futures market prices as a function of the order
book depth. Finally, we conclude with directions for future research.
