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Mixed Prediction and Prediction of Classifiers
Fitness and Average Number of Classifiers
-100
10
data
pred +/- 1sd
f(x)
cl. 1
cl. 2
cl. 3
cl. 4
cl. 5
cl. 6
cl. 7
max. fitness
avg. fitness
min. fitness
avg. K
1
-150
8
0.5
-200
6
0
-250
4
-300
-0.5
2
-350
-1
-400
0
-1
-0.5
0
0.5
1
0
50
100
150
200
250
Input x
GA iteration
(a)
(b)
Fig. 8.14. Plots similar to the ones in Fig. 8.5, using GA model structure search
applied to the noisy sinusoidal function. The best discovered model structure is given
by l 1 = 0 . 98 ,u 1 = 0 . 40, l 2 = 0 . 78 ,u 2 = 0 . 32, l 3 = 0 . 22 ,u 3 =0 . 16, l 4 =
0 . 08 ,u 4 =0 . 12, l 5 =0 . 34 ,u 5 =0 . 50, l 6 =0 . 34 ,u 6 =1 . 00, and l 7 =0 . 60 ,u 2 =0 . 68.
Mixed Prediction and Prediction of Classifiers
Variational Bound and Number of Classifiers
0
data
pred +/- 1sd
gen. fn.
cl. 1
cl. 2
cl. 3
cl. 4
cl. 5
L(q)
K
10
1
-50
8
0.5
-100
6
0
-150
4
-0.5
-200
2
-1
-250
0
-1
-0.5
0
0.5
1
0
1000
2000
3000
4000
5000
Input x
MCMC step
(a)
(b)
Fig. 8.15. Plots similar to the ones in Fig. 8.6, using MCMC model structure search
applied the noisy sinusoidal function. The best discovered model structure is given by
l 1 = 1 . 00 ,u 1 = 0 . 68, l 2 = 0 . 62 ,u 2 = 0 . 30, l 3 = 0 . 24 ,u 3 =0 . 14, l 4 =0 . 34 ,u 4 =
0 . 78, and l 5 =0 . 74 ,u 5 =0 . 98.
adequate locations. However, as can be seen in Fig. 8.14(b), the GA initially was
operating with 5 classifiers, but was not able to find good interval placements, as
the low maximum fitness shows. Once it increased the number of classifiers to 7,
at around the 60th iteration, it was able to provide a fitter model structure, but
at the cost of an increased number of classifiers. It maintained this model up to
the 250th iteration without finding a better one, which indicates that the genetic
operators need to be improved and require better tuning to the representation
used in order to make the GA perform better model structure search.
That the inappropriate model can be attributed to a weak model struc-
ture search rather than a failing optimality criterion becomes apparent when
 
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