3 0 4 0 0.0358 1.553E-7 0.00002 0 0.869
4 0 5 0 0.0358 1.44E-7 0.00002 0 1.043
5 0 6 0 0.0358 1.351E-7 0.00001 0 1.247
6 0 7 0 0.0358 1.297E-7 0.00001 0 1.415
7 0 8 0 0.0358 1.259E-7 0.00001 0 1.585
8 0 9 0 0.0358 1.235E-7 0.00001 0 1.700
9 0 10 0 0.0358 1.221E-7 0.00001 0 1.805
10 0 11 0 0.0358 1.213E-7 0.00001 0 1.864
Optimization Results: Iterations= 10 Function Calls= 12 Jacobian Calls= 11
Active Constraints= 0 Criterion= 0.035825744
Maximum Gradient Element= 0.0000127206 Lambda= 0 Rho= 1.864 Radius= 0.004365
NOTE: FCONV convergence criterion satisfied.
Optimization Results
Parameter Estimates
------------------------------------------------------------------------------
Parameter Estimate Gradient Label
------------------------------------------------------------------------------
1 X1_H1 6.020084 -4.8867E-7 X1 -> H1
2 X2_H1 0.823365 0.0000111 X2 -> H1
3 X1_H2 0.049663 -3.2277E-8 X1 -> H2
4 X2_H2 -4.986906 2.19755E-8 X2 -> H2
5 X1_H3 -5.848915 -1.8967E-6 X1 -> H3
6 X2_H3 0.767294 -0.0000127 X2 -> H3
7 BIAS_H1 -3.013469 5.59999E-7 BIAS -> H1
8 BIAS_H2 1.791192 1.32261E-7 BIAS -> H2
9 BIAS_H3 0.889276 -3.0043E-6 BIAS -> H3
10 H1_HIPL -0.262306 4.51418E-7 H1 -> HIPL
11 H2_HIPL -0.484458 1.7993E-8 H2 -> HIPL
12 H3_HIPL -0.266660 3.35605E-7 H3 -> HIPL
13 BIAS_HIP -0.490183 -3.1205E-7 BIAS -> HIPL
Value of Objective Function = 0.0358257445
PROC PRINT Report of Selected Fit Statistics for the Scored Test Data Set
Hill & Plateau Data
MLP with 3 Hidden Units
Fit Statistics for the Test Data
Test: Test: Lower Test: Upper
Average 95% Conf. 95% Conf.
Squared Limit for Limit for
Error. TASE. TASE.
0.036830 0.028999 0.045583
GCONTOUR Plot of the Predicted Values
G3D Plot of the Predicted Values
Program: 30 Hidden Units
title 'Hill & Plateau Data';
%let hidden=30;
proc neural data=sampsio.dmdsurf
dmdbcat=sampsio.dmdsurf
random=789;
input x1 x2 / id=i;
target hipl / id=o;
hidden &hidden / id=h;
prelim 10;
train maxiter=1000 outest=mlpest2;
score data=sampsio.dmtsurf out=mlpout2 outfit=mlpfit2;
title2 "MLP with &hidden Hidden Units";
run;
proc print data=mlpfit2 noobs label;
var _tase_ _tasel_ _taseu_;
where _name_ ='HIPL';
title3 'Fit Statistics for the Test Data';
run;
proc gcontour data=mlpout2;
plot x2*x1=p_hipl / pattern ctext=black coutline=gray;
pattern v=msolid;
legend frame;
title3 'Predicted Values';
footnote;
run;
proc g3d data=mlpout2;
plot x2*x1=p_hipl / grid side ctop=blue
caxis=green ctext=black
zmin=-1.5 zmax=1.5;
run;
Output: 30 Hidden Units
Preliminary Iteration History
Hill & Plateau Data
MLP with 30 Hidden Units
Iteration Pseudo-random Objective
number number seed function
0 789 0.03400
1 1095609817 0.04237
2 924680074 0.03808
3 1369944093 0.04887
4 1527099570 0.04153
5 430173087 0.03480
6 739241177 0.03857
7 321367798 0.02955
8 58127801 0.04378
9 1974465768 0.02971
Optimization Start
Parameter Estimates
-------------------------------------------------------
Parameter Estimate Gradient Label
-------------------------------------------------------
1 X1_H1 -0.467800 0.0000599 X1 -> H1
2 X2_H1 -0.406536 0.0002672 X2 -> H1
3 X1_H2 -1.507694 0.0002234 X1 -> H2
4 X2_H2 0.547571 -0.0003621 X2 -> H2
5 X1_H3 0.565220 0.0000279 X1 -> H3
6 X2_H3 0.339673 0.0008228 X2 -> H3
7 X1_H4 -0.832673 0.0000150 X1 -> H4
8 X2_H4 0.282776 -0.0004894 X2 -> H4
9 X1_H5 -0.129020 0.0000243 X1 -> H5
10 X2_H5 -0.031309 0.0001306 X2 -> H5
11 X1_H6 -0.060165 0.0002855 X1 -> H6
12 X2_H6 1.691299 0.0001026 X2 -> H6
13 X1_H7 0.787984 0.0001247 X1 -> H7
14 X2_H7 0.062126 0.0007617 X2 -> H7
15 X1_H8 -0.150388 0.0000205 X1 -> H8
16 X2_H8 -0.118346 0.0002827 X2 -> H8
17 X1_H9 -1.319054 -0.00112 X1 -> H9
18 X2_H9 -0.856195 0.00424 X2 -> H9
19 X1_H10 0.369538 -0.0003333 X1 -> H10
20 X2_H10 0.149047 0.0004931 X2 -> H10
21 X1_H11 -0.227129 0.0002816 X1 -> H11
22 X2_H11 -0.867869 0.00100 X2 -> H11
23 X1_H12 -1.208871 0.0000539 X1 -> H12
24 X2_H12 0.229684 -0.0008334 X2 -> H12
25 X1_H13 -0.774966 0.0004976 X1 -> H13
26 X2_H13 0.479537 -0.00141 X2 -> H13
27 X1_H14 0.092770 -0.0006323 X1 -> H14
28 X2_H14 -1.080409 -0.0004827 X2 -> H14
29 X1_H15 -0.622859 0.00147 X1 -> H15
30 X2_H15 -0.772737 0.00172 X2 -> H15
31 X1_H16 -0.138595 -0.00141 X1 -> H16
32 X2_H16 0.822709 0.00251 X2 -> H16
33 X1_H17 -0.262409 0.0001737 X1 -> H17
34 X2_H17 -1.162618 0.0004185 X2 -> H17
35 X1_H18 0.030999 -0.00369 X1 -> H18
36 X2_H18 -2.728742 0.00228 X2 -> H18
37 X1_H19 0.021237 -0.00180 X1 -> H19
38 X2_H19 1.362841 -0.00108 X2 -> H19
39 X1_H20 -0.429323 2.98698E-6 X1 -> H20
40 X2_H20 0.299725 -2.3418E-6 X2 -> H20
41 X1_H21 0.155524 0.0004407 X1 -> H21
42 X2_H21 -0.563073 0.0002520 X2 -> H21
43 X1_H22 -0.110919 5.39502E-6 X1 -> H22
44 X2_H22 -0.338627 -8.6108E-6 X2 -> H22
45 X1_H23 1.805185 -0.00197 X1 -> H23
46 X2_H23 0.230073 -0.0007495 X2 -> H23
47 X1_H24 -1.368753 -0.0001878 X1 -> H24
48 X2_H24 -0.299062 -0.00261 X2 -> H24
49 X1_H25 0.234343 -0.0000412 X1 -> H25
50 X2_H25 -0.209074 -0.0000807 X2 -> H25
Optimization Start
Parameter Estimates
-------------------------------------------------------
Parameter Estimate Gradient Label
-------------------------------------------------------
51 X1_H26 -0.055756 -0.0000101 X1 -> H26
52 X2_H26 -0.331826 0.0001698 X2 -> H26
53 X1_H27 -0.799268 0.0001618 X1 -> H27
54 X2_H27 -0.195293 0.0005865 X2 -> H27
55 X1_H28 -1.130014 0.0006003 X1 -> H28
56 X2_H28 0.540507 -0.00117 X2 -> H28
57 X1_H29 -0.808714 0.0000157 X1 -> H29
58 X2_H29 0.442020 -0.0003948 X2 -> H29
59 X1_H30 -1.075334 -0.0008229 X1 -> H30