  This paper presents a method for solving the supervised learning problem in
which the output is highly nonlinear and discontinuous. It is proposed to solve
this problem in three stages: (i) cluster the pairs of input-output data
points, resulting in a label for each point; (ii) classify the data, where the
corresponding label is the output; and finally (iii) perform one separate
regression for each class, where the training data corresponds to the subset of
the original input-output pairs which have that label according to the
classifier. It has not yet been proposed to combine these 3 fundamental
building blocks of machine learning in this simple and powerful fashion. This
can be viewed as a form of deep learning, where any of the intermediate layers
can itself be deep. The utility and robustness of the methodology is
illustrated on some toy problems, including one example problem arising from
simulation of plasma fusion in a tokamak.
