The arboretum procedure



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PROC DMNEURL: Approximation to PROC NEURAL



COS: Iter=4 Crit=0.00671738: SSE=6.31396E11 Acc= 41.2783

------------ Activation= EXP (Stage=2) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

EXP: Iter=0 Crit=0.00656615: SSE=6.17182E11 Acc= 41.6251

The RMSE dropped from 10294 to 10035:



Goodness-of-Fit Criteria (Ordered by SSE, Stage 2)

Run

Activation

SSE

RMSE

Accuracy

4

LOGIST

6.00171E11

10035

44.076324

3

ARCTAN

6.11611E11

10130

42.722853

2

TANH

6.12574E11

10138

42.454925

6

SIN

6.12902E11

10141

42.618536

1

SQUARE

6.14545E11

10154

43.452922

8

EXP

6.17964E11

10183

42.588823

7

COS

6.31415E11

10293

41.153349

5

GAUSS

6.31533E11

10294

41.028769

In stage 3 components are selected w.r.t. the residuals from stage 2:



Component Selection: SS(y) and R2 (Stage=3)

Comp

Eigval

R-Square

F Value p-Value

5

8108.233368

0.008115

48.751302

<.0001

7

7678.598513

0.004569

27.574638

<.0001

27

3496.302840

0.003929

23.802006

<.0001

------------ Optimization Cycle (Stage=3) --------------

------------ Activation= SQUARE (Stage=3) --------------

NOTE: ABSGCONV convergence criterion satisfied.

SQUARE: Iter=1 Crit=0.00627437: SSE=5.89756E11 Acc= 46.5664

------------ Activation= TANH (Stage=3) ----------------

NOTE: ABSGCONV convergence criterion satisfied.

TANH: Iter=2 Crit=0.00628152: SSE=5.90428E11 Acc= 46.2812

------------ Activation= ARCTAN (Stage=3) --------------

NOTE: ABSGCONV convergence criterion satisfied.

ARCTAN: Iter=2 Crit=0.00628195: SSE=5.90469E11 Acc= 46.2125

------------ Activation= LOGIST (Stage=3) --------------

NOTE: ABSGCONV convergence criterion satisfied.

LOGIST: Iter=5 Crit=0.00628127: SSE=5.90404E11 Acc= 45.8040

------------ Activation= GAUSS (Stage=3) ---------------

NOTE: ABSGCONV convergence criterion satisfied.

GAUSS: Iter=2 Crit=0.00637032: SSE=5.98775E11 Acc= 45.3250

------------ Activation= SIN (Stage=3) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

SIN: Iter=6 Crit=0.00627884: SSE=5.90176E11 Acc= 46.0972


Purpose of PROC DMNEURL

§

19



------------ Activation= COS (Stage=3) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

COS: Iter=5 Crit=0.00637738: SSE=5.99438E11 Acc= 44.6439

------------ Activation= EXP (Stage=3) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

EXP: Iter=1 Crit=0.00628498: SSE=5.90753E11 Acc= 46.4650

The RMSE dropped from 10035 to 9939:



Goodness-of-Fit Criteria (Ordered by SSE, Stage 3)

Run

Activation

SSE

RMSE

Accuracy

1

SQUARE

5.88794E11

9939.361833

46.874168

6

SIN

5.89308E11

9943.696786

46.045231

4

LOGIST

5.89532E11

9945.590341

45.936035

2

TANH

5.89658E11

9946.655850

46.521683

3

ARCTAN

5.89714E11

9947.122017

46.462470

8

EXP

5.89994E11

9949.489480

46.590155

5

GAUSS

5.98777E11

10023

45.338954

7

COS

5.99432E11

10029

44.563112

Again, the new stage 4 starts with component selection w.r.t. the residuals of the last

stage3:

Component Selection: SS(y) and R2 (Stage=4)

Comp

Eigval

R-Square

F Value

p-Value

14

5977.581155

0.004044

24.196310

<.0001

24

4589.938565

0.002803

16.817296

<.0001

8

7098.575517

0.002425

14.583721

0.0001

A maximum of 7 iterations is needed for convergence:



------------ Optimization Cycle (Stage=4) --------------

------------ Activation= SQUARE (Stage=4) --------------

NOTE: ABSGCONV convergence criterion satisfied.

SQUARE: Iter=1 Crit=0.00618628: SSE=5.81476E11 Acc= 46.9112

------------ Activation= TANH (Stage=4) ----------------

NOTE: ABSGCONV convergence criterion satisfied.

TANH: Iter=5 Crit= 0.0061812: SSE=5.80998E11 Acc= 45.5545

------------ Activation= ARCTAN (Stage=4) --------------

NOTE: ABSGCONV convergence criterion satisfied.

ARCTAN: Iter=3 Crit=0.00618984: SSE= 5.8181E11 Acc= 45.7876

------------ Activation= LOGIST (Stage=4) --------------

NOTE: ABSGCONV convergence criterion satisfied.

LOGIST: Iter=2 Crit= 0.0062313: SSE=5.85708E11 Acc= 47.2978



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