test cases

In the following standard settings are:

A sample is a training or test sample that is a pair of input vector and output vector. In TMVA it is also called event since this data often comes from a simulation or measurement. During learning or testing, this pair defines the input and target value.

Input, input value, input vector, input sample is the vector in the domain. Output value, output vector, output point, output sample is the actual vector in the codomain.

Target, target value, target vector is the intended vector in the codomain that should be produced.

Epsilon is the deviation from the target value, i.e. epsilon = actual – target.

Convergence of the algorithm means calculating the RMS over all test samples after the training.

Training iteration or epoch is the step in the training indicating how far the algorithm run in order to minimize the error function (maximizing the fitness function) of the net.

gauss + randomUniform

test case: (in1,in2)=(out1,out2)=(gauss1+noise1,gauss1^k+noise2): gauss=N(0, 0.4), noise=random[-0.1, 0.1]

k=1 http://www.vamosi.org/files/dev/N(0,0.4),random[-0.1,0.1]/nn_N(0,0.4),random[-0.1,0.1]1.pdf

k=2 http://www.vamosi.org/files/dev/N(0,0.4),random[-0.1,0.1]/nn_N(0,0.4),random[-0.1,0.1]2.pdf

k=3 http://www.vamosi.org/files/dev/N(0,0.4),random[-0.1,0.1]/nn_N(0,0.4),random[-0.1,0.1]3.pdf

gauss + randomGauss

(in1,in2)=(out1,out2)=(gauss1+gauss2,gauss1^k+gauss3): gauss1=N(0, 0.4), gauss2/3=N(0, 0.1), all gauss uncorrelated

k=1

Perceptron=2:10:1:5:2 (convergence warnings)

rmsIn1= 0.412901
rmsIn2= 0.411148
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.582692
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.399552
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.565053
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.407056
rmsOut2= 0.405025
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.57423
rmsEpsilon1= 0.0719919
rmsEpsilon2= 0.0693656
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.0999721

Perceptron=2:10:10:10:1:5:2

rmsIn1= 0.412901
rmsIn2= 0.411148
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.582692
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.399552
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.565053
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.406587
rmsOut2= 0.404947
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.573842
rmsEpsilon1= 0.0719385
rmsEpsilon2= 0.0694588
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.0999984

Divergence with 2:20:20:20:1:5:2 !!

2:10:1:5:2

Plot http://www.vamosi.org/files/dev/N(0,0.4),N(0,0.1)/N(0,0.4),N(0,0.1);N(0,0.4),N(0,0.1)1.pdf

ROOT http://www.vamosi.org/files/dev/N(0,0.4),N(0,0.1)/N(0,0.4),N(0,0.1);N(0,0.4),N(0,0.1)1.root

k=2

Perceptron=2:10:10:1:5:2

rmsIn1= 0.412901
rmsIn2= 0.297292
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.508792
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.279628
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.487682
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.409966
rmsOut2= 0.284026
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.498741
rmsEpsilon1= 0.0540769
rmsEpsilon2= 0.0837956
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.0997297

divergence with 10:10:10:1:5

rmsIn1= 0.412901
rmsIn2= 0.297292
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.508792
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.279628
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.487682
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.415005
rmsOut2= 0.306197
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.515738
rmsEpsilon1= 0.0644636
rmsEpsilon2= 0.0978475
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.117174

Plot with 2:10:10:1:5:2

http://www.vamosi.org/files/dev/N(0,0.4),N(0,0.1)/N(0,0.4),N(0,0.1);N(0,0.4),N(0,0.1)2.pdf

k=3

Perceptron=2:10:10:1:5:2

rmsIn1= 0.412901
rmsIn2= 0.272219
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.494561
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.253653
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.473268
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.41379
rmsOut2= 0.239281
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.477993
rmsEpsilon1= 0.0137421
rmsEpsilon2= 0.11327
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.114101

Perceptron=2:10:10:10:1:5:2

rmsIn1= 0.412901
rmsIn2= 0.272219
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.494561
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.253653
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.473268
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.390539
rmsOut2= 0.218751
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.44763
rmsEpsilon1= 0.0811195
rmsEpsilon2= 0.292942
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.303966

DIVERGENCE with 2:10:10:10:10:1:5:2 !

rmsIn1= 0.412901
rmsIn2= 0.272219
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.494561
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.253653
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.473268
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.00297916
rmsOut2= 0.00748708
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.00805802
rmsEpsilon1= 0.411944
rmsEpsilon2= 0.272141
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.493719

DIVERGENCE with 2:20:20:20:1:5:2

rmsIn1= 0.412901
rmsIn2= 0.272219
rmsIn=(rmsIn1^2+rmsIn2^2)^1/2= 0.494561
rmsInNoNoise1= 0.399552
rmsInNoNoise2= 0.253653
rmsInNoNoise=(rmsInNoNoise1^2+rmsInNoNoise2^2)^1/2= 0.473268
rmsNoise1= 0.0999885
rmsNoise2= 0.0996634
rmsNoise=(rmsNoise1^2+rmsNoise2^2)^1/2= 0.141175

rmsOut1= 0.0582925
rmsOut2= 0.1551
rmsOut=(rmsOut1^2+rmsOut2^2)^1/2= 0.165692
rmsEpsilon1= 0.394749
rmsEpsilon2= 0.24723
rmsEpsilon=(rmsEpsilon1^2+rmsEpsilon2^2)^1/2= 0.465778

Plot with 2:10:10:1:5:2

http://www.vamosi.org/files/dev/N(0,0.4),N(0,0.1)/N(0,0.4),N(0,0.1);N(0,0.4),N(0,0.1)3.pdf