Deep Learning for Spatio-Temporal Modeling: Dynamic Traffic Flows and High Frequency Trading

Deep learning applies layers of hierarchical hidden variables to capture these interactions and nonlinearities. The theoretical roots lie in the Kolmogorov-Arnold representation theorem (Arnold, 1957; Kolmogorov, 1957) of multivariate functions, which states that any continuous multivariate function can be expressed as a superposition of continuous univariate semi-affine functions. This remarkable result has direct consequences for statistical modeling as a nonparametric pattern matching algorithm. Deep learning relies on pattern matching via its layers of univariate semi-affine functions and can be applied to both regression and classification problems. Deep learners provide a nonlinear predictor in complex settings where the input space can be very high dimensional.