An Algorithmic Description - Design and Analysis of Learning Classifier Systems - page 191

Mixed Prediction and Prediction of Classifiers Variational Bound and Number of Classifiers

1.5 -40 7

data
pred +/- 1sd
gen. fn.
cl. 1
cl. 2

L(q)
K

-60

6

1

-80

5

0.5

-100

4

0 -120

3

-140

-0.5

2

-160

-1

1

-180

-1.5 -200 0

-1 -0.5 0 0.5 1 0 1000 2000 3000 4000 5000

Input x MCMC step

(a) (b)

Fig. 8.12. Plots similar to the ones in Fig. 8.6, where MCMC model structure search
was applied to a function with variable noise. The best discovered model structure is
given by l 1 = − 0 . 98 ,u 1 = − 0 . 06 and l 2 =0 . 08 ,u 2 =0 . 80.

Noisy Sinusoid and Available Data

f(x) mean
data

1

0.5

0

-0.5

-1

-1 -0.5 0 0.5 1

Input x

Fig. 8.13. Plot showing the mean of the noisy sinusoidal function, and the 300 obser-
vations that are available from this function

more complex function. The used function is the noisy sinusoid given over the
range (0 , 0 . 15), as shown in Fig. 8.13. Soft

interval matching is again used to clearly specify the area of the input space that
a classifier models. The data set is given by 300 samples from f ( x ).
Both GA and MCMC search are initialised as before, with the number of
classifiers sampled from

− 1 ≤ x ≤ 1by f ( x )=sin(2 πx )+ N

B (8 , 0 . 5). The GA search identified 7 classifiers with

L 155 . 68, as shown in Fig. 8.14. It is apparent that the model

can be improved by reducing the number of classifiers to 5 and moving them to

( q )+ln K ! ≈−