  We propose to accelerate the rate of convergence of the pattern recognition
task by directly minimizing the variance diameters of certain hypothesis
spaces, which are critical quantities in fast-convergence results.We show that
the variance diameters can be controlled by dividing hypothesis spaces into
metric balls based on a new order metric. This order metric can be minimized as
an ordinal regression problem, leading to a LUPI (Learning Using Privileged
Information) application where we take the privileged information as some
desired ordering, and construct a faster-converging hypothesis space by
empirically restricting some larger hypothesis space according to that
ordering. We give a risk analysis of the approach. We discuss the difficulties
with model selection and give an innovative technique for selecting multiple
model parameters. Finally, we provide some data experiments.
