spread exceeds the thresholds. The count is this example is represented as a
fraction, which is obtained by dividing it by the total number of sample
points. Then we construct the cost function corresponding to these counts.
Strictly speaking, a constrained minimization would need to be performed
on the cost function by anchoring the count fraction at zero to be at the
value 0.5. This is to recognize the assumption of symmetry of the spread
about its mean; that is, the total count fractions above and below the mean
are likely to be at 0.5. However, we will do just the unconstrained version
here.
The cost function just shown is then minimized using various values of
lto obtain estimates of the count fraction function. A plot of the fit error
against values of lin a log scale is shown in Figure 8.5. Note that the fit
error remains relatively constant, close to zero for small values of l. For
these small values of l, the fit error dominates the cost function. After a par-
ticular threshold value, further increases in lare accompanied by fit error in-
creases. Let us call this threshold value the heel of the curve. This is the point
after which the regularization cost measure takes control. Increases in llead
Trading Design 133
FIGURE 8.5 Lamda Plot.Log (λ)–6 –4 –2 0 2 4604812Cost