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.
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