The arboretum procedure

4

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PROC DMNEURL: Approximation to PROC NEURAL

------------ Optimization Cycle (Stage=0) --------------

------------ Activation= SQUARE (Stage=0) --------------

NOTE: ABSGCONV convergence criterion satisfied.

SQUARE: Iter=5 Crit=0.06782364: SSE=808.457819 Acc= 81.6443

------------ Activation= TANH (Stage=0) ----------------

NOTE: ABSGCONV convergence criterion satisfied.

TANH: Iter=4 Crit=0.06802595: SSE=810.869323 Acc= 81.6275

------------ Activation= ARCTAN (Stage=0) --------------

NOTE: ABSGCONV convergence criterion satisfied.

ARCTAN: Iter=5 Crit=0.06795346: SSE=810.005204 Acc= 81.6611

------------ Activation= LOGIST (Stage=0) --------------

NOTE: ABSGCONV convergence criterion satisfied.

LOGIST: Iter=11 Crit=0.06802943: SSE= 810.91085 Acc= 81.6107

------------ Activation= GAUSS (Stage=0) ---------------

NOTE: ABSGCONV convergence criterion satisfied.

GAUSS: Iter=10 Crit=0.07727582: SSE=921.127726 Acc= 80.2517

------------ Activation= SIN (Stage=0) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

SIN: Iter=5 Crit=0.06811774: SSE= 811.96345 Acc= 81.6611

------------ Activation= COS (Stage=0) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

COS: Iter=9 Crit=0.07419096: SSE=884.356261 Acc= 81.1913

------------ Activation= EXP (Stage=0) -----------------

NOTE: ABSGCONV convergence criterion satisfied.

EXP: Iter=9 Crit=0.06798656: SSE= 810.39974 Acc= 81.5436

The following approximate accuracy rates are based on the discrete values of the

predictor (

Ü

) variables:

Approximate Goodness-of-Fit Criteria (Stage 0)

Run

Activation

Criterion

SSE

Accuracy

1

SQUARE

0.067824

808.457819

81.644295

3

ARCTAN

0.067953

810.005204

81.661074

8

EXP

0.067987

810.399740

81.543624

2

TANH

0.068026

810.869323

81.627517

4

LOGIST

0.068029

810.910850

81.610738

6

SIN

0.068118

811.963450

81.661074

7

COS

0.074191

884.356261

81.191275

5

GAUSS

0.077276

921.127726

80.251678

After running through the data set we obtain the correct accuracy tables:

Classification Table for CUTOFF = 0.5000

Predicted

Activation

Accuracy

Observed

1

0

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Purpose of PROC DMNEURL

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5

SQUARE

81.610738

1

229.0

960.0

0.067548

0

136.0

4635.0

TANH

82.063758

1

254.0

935.0

0.067682

0

134.0

4637.0

ARCTAN

81.761745

1

242.0

947.0

0.067722

0

140.0

4631.0

LOGIST

81.845638

1

221.0

968.0

0.067818

0

114.0

4657.0

SIN

81.275168

1

222.0

967.0

0.067867

0

149.0

4622.0

EXP

81.543624

1

197.0

992.0

0.068101

0

108.0

4663.0

COS

81.359060

1

101.0

1088.0

0.073967

0

23.0000

4748.0

GAUSS

80.167785

1

7.0000

1182.0

0.079573

0

0

4771.0

The activation function SQUARE seems to be most appropriate for the first stage

(stage=0) of estimation. However, TANH yields an even higher accuracy rate:

Goodness-of-Fit Criteria (Ordered by SSE, Stage 0)

Run

Activation

SSE

RMSE

Accuracy

1

SQUARE

805.19026

0.367558

81.610738

3

ARCTAN

805.89106

0.367718

81.778523

8

EXP

806.66533

0.367895

81.593960

4

LOGIST

807.30313

0.368040

81.778523

2

TANH

807.72088

0.368135

81.778523

6

SIN

809.31533

0.368499

81.291946

7

COS

881.68579

0.384622

81.359060

5

GAUSS

949.21059

0.399078

80.167785

The following is the start of the second stage of estimation (stage=1). It starts with

selecting three eigenvectors which may predict the residuals best:

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

Comp

Eigval

R-Square

F Value

p-

Value

23

4763.193233

0.023292

142.109442

<.0001

21

5192.070258

0.018366

114.178467

<.0001

24

4514.317020

0.017493

110.756118

<.0001

When fitting the first order residuals the average value of the objective function

dropped from 0.068 to 0.063. For time reasons the approximate accuracy rates are

not computed after the first stage:

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