  Hierarchical support vector regression (HSVR) models a function from data as
a linear combination of SVR models at a range of scales, starting at a coarse
scale and moving to finer scales as the hierarchy continues. In the original
formulation of HSVR, there were no rules for choosing the depth of the model.
In this paper, we observe in a number of models a phase transition in the
training error -- the error remains relatively constant as layers are added,
until a critical scale is passed, at which point the training error drops close
to zero and remains nearly constant for added layers. We introduce a method to
predict this critical scale a priori with the prediction based on the support
of either a Fourier transform of the data or the Dynamic Mode Decomposition
(DMD) spectrum. This allows us to determine the required number of layers prior
to training any models.
