The arboretum procedure



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PROC DMNEURL: Approximation to PROC NEURAL



Run

Activation

SSE

RMSE

Accuracy

1

SQUARE

6.68237E11

10589

33.925841

2

TANH

6.74156E11

10635

30.776431

4

LOGIST

6.74885E11

10641

30.492000

8

EXP

6.77111E11

10659

30.503925

3

ARCTAN

6.78503E11

10670

29.832932

6

SIN

6.81758E11

10695

29.402115

5

GAUSS

7.02918E11

10860

21.174016

7

COS

7.04934E11

10876

20.022492

The second stage (stage=1) starts with selecting the best principal components for

predicting the residual:

Component Selection: SS(y) and R2 (Stage=1)

Comp

Eigval

R-Square

F Value

p-Value

1

16197

0.023135

141.126005

<.0001

3

12170

0.017130

106.340108

<.0001

20

5623.081574

0.012121

76.193667

<.0001

Now a maximum of 5 iterations is needed for convergence:



------------ Optimization Cycle (Stage=1) --------------

------------ Activation= SQUARE (Stage=1) --------------

NOTE: ABSGCONV convergence criterion satisfied.

SQUARE: Iter=1 Crit=0.00675824: SSE=6.35237E11 Acc= 39.9782

------------ Activation= TANH (Stage=1) ----------------

NOTE: ABSGCONV convergence criterion satisfied.

TANH: Iter=4 Crit=0.00677155: SSE=6.36489E11 Acc= 40.1296

------------ Activation= ARCTAN (Stage=1) --------------

NOTE: ABSGCONV convergence criterion satisfied.

ARCTAN: Iter=4 Crit=0.00675928: SSE=6.35335E11 Acc= 41.0832

------------ Activation= LOGIST (Stage=1) --------------

NOTE: ABSGCONV convergence criterion satisfied.

LOGIST: Iter=5 Crit=0.00676491: SSE=6.35864E11 Acc= 41.1768

------------ Activation= GAUSS (Stage=1) ---------------

NOTE: ABSGCONV convergence criterion satisfied.

GAUSS: Iter=5 Crit=0.00701114: SSE=6.59009E11 Acc= 37.5715

------------ Activation= SIN (Stage=1) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

SIN: Iter=4 Crit=0.00676857: SSE=6.36208E11 Acc= 40.1257

------------ Activation= COS (Stage=1) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

COS: Iter=5 Crit=0.00699351: SSE=6.57351E11 Acc= 36.1925

------------ Activation= EXP (Stage=1) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

EXP: Iter=1 Crit=0.00676817: SSE= 6.3617E11 Acc= 40.3710


Purpose of PROC DMNEURL

§

17



The RMSE dropped from 10589 to 10294:

Goodness-of-Fit Criteria (Ordered by SSE, Stage 1)

Run

Activation

SSE

RMSE

Accuracy

1

SQUARE

6.31521E11

10294

41.275893

3

ARCTAN

6.32669E11

10303

40.218692

8

EXP

6.32795E11

10304

40.947613

6

SIN

6.32908E11

10305

40.499603

2

TANH

6.3331E11

10308

40.464591

4

LOGIST

6.33355E11

10309

40.566497

7

COS

6.56699E11

10497

36.381117

5

GAUSS

6.58666E11

10513

37.785522

The third stage starts with selecting the best eigenvectors for prediction of the resid-

uals of the last stage:

Component Selection: SS(y) and R2 (Stage=2)

Comp

Eigval

R-Square

F Value

p-Value

23

4811.081772

0.011805

71.186100

<.0001

28

1232.230727

0.007479

45.434565

<.0001

18

5865.674624

0.006724

41.123895

<.0001

Now, the maximum of iterations is four!



------------ Optimization Cycle (Stage=2) --------------

------------ Activation= SQUARE (Stage=2) --------------

NOTE: ABSGCONV convergence criterion satisfied.

SQUARE: Iter=1 Crit=0.00652258: SSE=6.13086E11 Acc= 42.4729

------------ Activation= TANH (Stage=2) ----------------

NOTE: ABSGCONV convergence criterion satisfied.

TANH: Iter=3 Crit=0.00650972: SSE=6.11878E11 Acc= 41.5654

------------ Activation= ARCTAN (Stage=2) --------------

NOTE: ABSGCONV convergence criterion satisfied.

ARCTAN: Iter=3 Crit=0.00650403: SSE=6.11342E11 Acc= 42.2974

------------ Activation= LOGIST (Stage=2) --------------

NOTE: ABSGCONV convergence criterion satisfied.

LOGIST: Iter=4 Crit=0.00641908: SSE=6.03358E11 Acc= 43.3779

------------ Activation= GAUSS (Stage=2) ---------------

NOTE: ABSGCONV convergence criterion satisfied.

GAUSS: Iter=2 Crit=0.00671802: SSE=6.31456E11 Acc= 41.2660

------------ Activation= SIN (Stage=2) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

SIN: Iter=4 Crit=0.00651654: SSE=6.12519E11 Acc= 41.9809

------------ Activation= COS (Stage=2) -----------------

NOTE: ABSGCONV convergence criterion satisfied.



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