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The parameter epsilon
strikes the balance between
our data-fitting goal and our model-styling goal.
These two regression systems typically have differing physical units;
therefore, the numerical value of
is accidental,
for example comparing milliseconds to meters.
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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:
Next: THE PRECONDITIONED SOLVER
Up: PRECONDITIONING THE REGULARIZATION
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2015-05-07