Preconditioning |

The numerical value of is meaningless before we learn to express the idea in a unitless (dimensionless) manner. Without pretending we are doing physics, let us use some of the language of thermodynamics, a physical field that does deal with equilibria and random fluctuations. Define an energy ratio and a volume ratio that can be used to bring to unitless form. Naturally, the square roots arise, because we are minimizing quadratic functions of residuals.

Can we really think of ``volume'' as related to the number of components in the model space? Perhaps. Likewise the data space? Less likely. And, is the energy measure really an appropriate one? Maybe. What is the goal of these speculative thoughts? The goal is to give you a starting numerical value for , say . Your final guide is your own experimental experience. Try either one of these next two regressions:

(13) | |||

(14) |

Preconditioning |

2015-05-07