Reduce the number of characteristics(indepdent variables) and depth of a decision tree. The reduced decision tree is no less efficient than the original. Irreudicble trees arise in discete decision theory. There can be many irreducible trees can be created for any given decision tree - this algorithm provides one of them.
The algorithm works by taking the characteristic that provides maximal information per level of the tree. An easy way to think of this is imagine characteristics that define a person: age, gender, height, etc. The algorithm will choose the characteristic that helps ask the least questions to always get the correct answer as asking all these characteristics. (Maybe with the given data, it is fine to only ask age, then height to always identify the right person).
The algorithm is done manually using Shannon's Entropy formula.
python3 decision_tree.py
__________Decision Tree__________
__Variables__
Independent Variables(discretized):
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
Dependent Variable(discretized):
dependent variable label
__Table__
x1: [1, 2, 0, 3, 4, 4, 4, 3, 0, 4, 4, 0]
x2: [1, 4, 1, 1, 1, 3, 2, 3, 0, 2, 2, 5]
x3: [1, 5, 2, 3, 5, 5, 5, 6, 0, 4, 5, 7]
x4: [0, 4, 4, 3, 1, 4, 4, 3, 2, 1, 1, 4]
x5: [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]
x6: [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]
x7: [1, 0, 1, 3, 4, 1, 1, 0, 2, 2, 2, 2]
x8: [1, 3, 1, 0, 2, 1, 5, 5, 5, 1, 4, 3]
x9: [1, 3, 1, 0, 1, 1, 1, 3, 3, 3, 3, 1]
x10: [2, 2, 2, 2, 4, 5, 3, 3, 1, 3, 3, 1]
x11: [1, 2, 3, 3, 3, 3, 3, 6, 5, 2, 3, 4]
dependent variable label: [0, 0, 0, 1, 1, 1, 0, 3, 0, 0, 0, 0]
frequency: [7, 2, 151, 201, 65, 102, 4, 33, 32, 43, 31, 12]
I(x1: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x1: 0, ) = 0.28550512445095166
I(x1: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x1: 1, ) = 0.010248901903367497
I(x1: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x1: 2, ) = 0.0029282576866764276
I(x1: 3, -> ER) = -1 * (
0 +
-0.18838426798846017 +
-0.39853431541633927 +
)
= 0.5869185834047994
P(x1: 3, ) = 0.34260614934114203
I(x1: 4, -> ER) = -1 * (
-0.5256995353916127 +
-0.3768976284500513 +
0 +
)
= 0.9025971638416641
P(x1: 4, ) = 0.35871156661786235
E[I(Q: x1 -> ER] = 0.524853958503559
_______________________________________________________________
I(x2: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x2: 0, ) = 0.04685212298682284
I(x2: 1, -> ER) = -1 * (
-0.5306935698325548 +
-0.4219851723360721 +
0 +
)
= 0.9526787421686269
P(x2: 1, ) = 0.6207906295754027
I(x2: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x2: 2, ) = 0.11420204978038068
I(x2: 3, -> ER) = -1 * (
0 +
-0.30553930383772004 +
-0.49681413899147003 +
)
= 0.8023534428291901
P(x2: 3, ) = 0.19765739385065886
I(x2: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x2: 4, ) = 0.0029282576866764276
I(x2: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x2: 5, ) = 0.017569546120058566
E[I(Q: x2 -> ER] = 0.750005126590686
_______________________________________________________________
I(x3: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, ) = 0.04685212298682284
I(x3: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, ) = 0.010248901903367497
I(x3: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, ) = 0.22108345534407028
I(x3: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, ) = 0.29428989751098095
I(x3: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, ) = 0.0629575402635432
I(x3: 5, -> ER) = -1 * (
-0.4467155055131088 +
-0.23635497679447573 +
0 +
)
= 0.6830704823075845
P(x3: 5, ) = 0.2986822840409956
I(x3: 6, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, ) = 0.048316251830161056
I(x3: 7, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, ) = 0.017569546120058566
E[I(Q: x3 -> ER] = 0.2040210518166138
_______________________________________________________________
I(x4: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x4: 0, ) = 0.010248901903367497
I(x4: 1, -> ER) = -1 * (
-0.4841877001798364 +
-0.5127860566919312 +
0 +
)
= 0.9969737568717676
P(x4: 1, ) = 0.20351390922401172
I(x4: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x4: 2, ) = 0.04685212298682284
I(x4: 3, -> ER) = -1 * (
0 +
-0.18838426798846017 +
-0.39853431541633927 +
)
= 0.5869185834047994
P(x4: 3, ) = 0.34260614934114203
I(x4: 4, -> ER) = -1 * (
-0.4248507869266242 +
-0.5305971119446582 +
0 +
)
= 0.9554478988712825
P(x4: 4, ) = 0.3967789165446559
E[I(Q: x4 -> ER] = 0.7830815246208145
_______________________________________________________________
I(x5: 0, -> ER) = -1 * (
-0.06566833415945987 +
-0.014143494715545652 +
0 +
)
= 0.07981182887500553
P(x5: 0, ) = 0.2972181551976574
I(x5: 1, -> ER) = -1 * (
-0.453604420887072 +
-0.5299419012988664 +
-0.26554663274219203 +
)
= 1.2490929549281304
P(x5: 1, ) = 0.7027818448023426
E[I(Q: x5 -> ER] = 0.9015613757351811
_______________________________________________________________
I(x6: 0, -> ER) = -1 * (
-0.06566833415945987 +
-0.014143494715545652 +
0 +
)
= 0.07981182887500553
P(x6: 0, ) = 0.2972181551976574
I(x6: 1, -> ER) = -1 * (
-0.453604420887072 +
-0.5299419012988664 +
-0.26554663274219203 +
)
= 1.2490929549281304
P(x6: 1, ) = 0.7027818448023426
E[I(Q: x6 -> ER] = 0.9015613757351811
_______________________________________________________________
I(x7: 0, -> ER) = -1 * (
-0.2359590295397124 +
0 +
-0.0800381034387123 +
)
= 0.3159971329784247
P(x7: 0, ) = 0.05124450951683748
I(x7: 1, -> ER) = -1 * (
-0.4323338896543949 +
-0.5300788458085974 +
0 +
)
= 0.9624127354629923
P(x7: 1, ) = 0.38653001464128844
I(x7: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x7: 2, ) = 0.17276720351390923
I(x7: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x7: 3, ) = 0.29428989751098095
I(x7: 4, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x7: 4, ) = 0.0951683748169839
E[I(Q: x7 -> ER] = 0.38819452681767913
_______________________________________________________________
I(x8: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x8: 0, ) = 0.29428989751098095
I(x8: 1, -> ER) = -1 * (
-0.3927939958782128 +
-0.5287668694163314 +
0 +
)
= 0.9215608652945442
P(x8: 1, ) = 0.44363103953147875
I(x8: 2, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x8: 2, ) = 0.0951683748169839
I(x8: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x8: 3, ) = 0.020497803806734993
I(x8: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x8: 4, ) = 0.04538799414348463
I(x8: 5, -> ER) = -1 * (
-0.48970406365349045 +
0 +
-0.5089319005050813 +
)
= 0.9986359641585718
P(x8: 5, ) = 0.10102489019033675
E[I(Q: x8 -> ER] = 0.5097200932813885
_______________________________________________________________
I(x9: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x9: 0, ) = 0.29428989751098095
I(x9: 1, -> ER) = -1 * (
-0.49530525329186886 +
-0.5043907545568037 +
0 +
)
= 0.9996960078486725
P(x9: 1, ) = 0.4992679355783309
I(x9: 3, -> ER) = -1 * (
-0.29463614060578086 +
0 +
-0.4903559481583775 +
)
= 0.7849920887641584
P(x9: 3, ) = 0.20644216691068815
E[I(Q: x9 -> ER] = 0.6611716298567257
_______________________________________________________________
I(x10: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x10: 1, ) = 0.06442166910688141
I(x10: 2, -> ER) = -1 * (
-0.5203000252630731 +
-0.47037526448021255 +
0 +
)
= 0.9906752897432856
P(x10: 2, ) = 0.5285505124450952
I(x10: 3, -> ER) = -1 * (
-0.3576852658022783 +
0 +
-0.520276735592113 +
)
= 0.8779620013943912
P(x10: 3, ) = 0.16251830161054173
I(x10: 4, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x10: 4, ) = 0.0951683748169839
I(x10: 5, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x10: 5, ) = 0.1493411420204978
E[I(Q: x10 -> ER] = 0.6663068254057153
_______________________________________________________________
I(x11: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x11: 1, ) = 0.010248901903367497
I(x11: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x11: 2, ) = 0.06588579795021962
I(x11: 3, -> ER) = -1 * (
-0.5286507292762729 +
-0.39203306367711294 +
0 +
)
= 0.9206837929533858
P(x11: 3, ) = 0.8111273792093704
I(x11: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x11: 4, ) = 0.017569546120058566
I(x11: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x11: 5, ) = 0.04685212298682284
I(x11: 6, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x11: 6, ) = 0.048316251830161056
E[I(Q: x11 -> ER] = 0.7467918320588224
_______________________________________________________________
The next characteristic/level in the tree is: x3
_______________________________________________________________
I(x3: 0, x1: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x1: 0, ) = 0.04685212298682284
I(x3: 0, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x1: 1, ) = 0.0
I(x3: 0, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x1: 2, ) = 0.0
I(x3: 0, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x1: 3, ) = 0.0
I(x3: 0, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x1: 4, ) = 0.0
I(x3: 1, x1: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x1: 0, ) = 0.0
I(x3: 1, x1: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x1: 1, ) = 0.010248901903367497
I(x3: 1, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x1: 2, ) = 0.0
I(x3: 1, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x1: 3, ) = 0.0
I(x3: 1, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x1: 4, ) = 0.0
I(x3: 2, x1: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x1: 0, ) = 0.22108345534407028
I(x3: 2, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x1: 1, ) = 0.0
I(x3: 2, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x1: 2, ) = 0.0
I(x3: 2, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x1: 3, ) = 0.0
I(x3: 2, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x1: 4, ) = 0.0
I(x3: 3, x1: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x1: 0, ) = 0.0
I(x3: 3, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x1: 1, ) = 0.0
I(x3: 3, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x1: 2, ) = 0.0
I(x3: 3, x1: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x1: 3, ) = 0.29428989751098095
I(x3: 3, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x1: 4, ) = 0.0
I(x3: 4, x1: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x1: 0, ) = 0.0
I(x3: 4, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x1: 1, ) = 0.0
I(x3: 4, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x1: 2, ) = 0.0
I(x3: 4, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x1: 3, ) = 0.0
I(x3: 4, x1: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x1: 4, ) = 0.0629575402635432
I(x3: 5, x1: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x1: 0, ) = 0.0
I(x3: 5, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x1: 1, ) = 0.0
I(x3: 5, x1: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x1: 2, ) = 0.0029282576866764276
I(x3: 5, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x1: 3, ) = 0.0
I(x3: 5, x1: 4, -> ER) = -1 * (
-0.4381806747685098 +
-0.22694406324942082 +
0 +
)
= 0.6651247380179306
P(x3: 5, x1: 4, ) = 0.2957540263543192
I(x3: 6, x1: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x1: 0, ) = 0.0
I(x3: 6, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x1: 1, ) = 0.0
I(x3: 6, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x1: 2, ) = 0.0
I(x3: 6, x1: 3, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x1: 3, ) = 0.048316251830161056
I(x3: 6, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x1: 4, ) = 0.0
I(x3: 7, x1: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x1: 0, ) = 0.017569546120058566
I(x3: 7, x1: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x1: 1, ) = 0.0
I(x3: 7, x1: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x1: 2, ) = 0.0
I(x3: 7, x1: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x1: 3, ) = 0.0
I(x3: 7, x1: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x1: 4, ) = 0.0
E[I(Q: x3, x1 -> ER] = 0.1967133192966647
_______________________________________________________________
I(x3: 0, x2: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x2: 0, ) = 0.04685212298682284
I(x3: 0, x2: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x2: 1, ) = 0.0
I(x3: 0, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x2: 2, ) = 0.0
I(x3: 0, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x2: 3, ) = 0.0
I(x3: 0, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x2: 4, ) = 0.0
I(x3: 0, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x2: 5, ) = 0.0
I(x3: 1, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x2: 0, ) = 0.0
I(x3: 1, x2: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x2: 1, ) = 0.010248901903367497
I(x3: 1, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x2: 2, ) = 0.0
I(x3: 1, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x2: 3, ) = 0.0
I(x3: 1, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x2: 4, ) = 0.0
I(x3: 1, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x2: 5, ) = 0.0
I(x3: 2, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x2: 0, ) = 0.0
I(x3: 2, x2: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x2: 1, ) = 0.22108345534407028
I(x3: 2, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x2: 2, ) = 0.0
I(x3: 2, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x2: 3, ) = 0.0
I(x3: 2, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x2: 4, ) = 0.0
I(x3: 2, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x2: 5, ) = 0.0
I(x3: 3, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x2: 0, ) = 0.0
I(x3: 3, x2: 1, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x2: 1, ) = 0.29428989751098095
I(x3: 3, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x2: 2, ) = 0.0
I(x3: 3, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x2: 3, ) = 0.0
I(x3: 3, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x2: 4, ) = 0.0
I(x3: 3, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x2: 5, ) = 0.0
I(x3: 4, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x2: 0, ) = 0.0
I(x3: 4, x2: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x2: 1, ) = 0.0
I(x3: 4, x2: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x2: 2, ) = 0.0629575402635432
I(x3: 4, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x2: 3, ) = 0.0
I(x3: 4, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x2: 4, ) = 0.0
I(x3: 4, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x2: 5, ) = 0.0
I(x3: 5, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x2: 0, ) = 0.0
I(x3: 5, x2: 1, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x2: 1, ) = 0.0951683748169839
I(x3: 5, x2: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x2: 2, ) = 0.05124450951683748
I(x3: 5, x2: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x2: 3, ) = 0.1493411420204978
I(x3: 5, x2: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x2: 4, ) = 0.0029282576866764276
I(x3: 5, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x2: 5, ) = 0.0
I(x3: 6, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x2: 0, ) = 0.0
I(x3: 6, x2: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x2: 1, ) = 0.0
I(x3: 6, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x2: 2, ) = 0.0
I(x3: 6, x2: 3, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x2: 3, ) = 0.048316251830161056
I(x3: 6, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x2: 4, ) = 0.0
I(x3: 6, x2: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x2: 5, ) = 0.0
I(x3: 7, x2: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x2: 0, ) = 0.0
I(x3: 7, x2: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x2: 1, ) = 0.0
I(x3: 7, x2: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x2: 2, ) = 0.0
I(x3: 7, x2: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x2: 3, ) = 0.0
I(x3: 7, x2: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x2: 4, ) = 0.0
I(x3: 7, x2: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x2: 5, ) = 0.017569546120058566
E[I(Q: x3, x2 -> ER] = 0.0
_______________________________________________________________
I(x3: 0, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x4: 0, ) = 0.0
I(x3: 0, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x4: 1, ) = 0.0
I(x3: 0, x4: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x4: 2, ) = 0.04685212298682284
I(x3: 0, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x4: 3, ) = 0.0
I(x3: 0, x4: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x4: 4, ) = 0.0
I(x3: 1, x4: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x4: 0, ) = 0.010248901903367497
I(x3: 1, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x4: 1, ) = 0.0
I(x3: 1, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x4: 2, ) = 0.0
I(x3: 1, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x4: 3, ) = 0.0
I(x3: 1, x4: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x4: 4, ) = 0.0
I(x3: 2, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x4: 0, ) = 0.0
I(x3: 2, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x4: 1, ) = 0.0
I(x3: 2, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x4: 2, ) = 0.0
I(x3: 2, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x4: 3, ) = 0.0
I(x3: 2, x4: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x4: 4, ) = 0.22108345534407028
I(x3: 3, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x4: 0, ) = 0.0
I(x3: 3, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x4: 1, ) = 0.0
I(x3: 3, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x4: 2, ) = 0.0
I(x3: 3, x4: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x4: 3, ) = 0.29428989751098095
I(x3: 3, x4: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x4: 4, ) = 0.0
I(x3: 4, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x4: 0, ) = 0.0
I(x3: 4, x4: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x4: 1, ) = 0.0629575402635432
I(x3: 4, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x4: 2, ) = 0.0
I(x3: 4, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x4: 3, ) = 0.0
I(x3: 4, x4: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x4: 4, ) = 0.0
I(x3: 5, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x4: 0, ) = 0.0
I(x3: 5, x4: 1, -> ER) = -1 * (
-0.5266015822954448 +
-0.3809234864586001 +
0 +
)
= 0.9075250687540449
P(x3: 5, x4: 1, ) = 0.14055636896046853
I(x3: 5, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x4: 2, ) = 0.0
I(x3: 5, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x4: 3, ) = 0.0
I(x3: 5, x4: 4, -> ER) = -1 * (
-0.23166250008012848 +
-0.07788092907019672 +
0 +
)
= 0.3095434291503252
P(x3: 5, x4: 4, ) = 0.1581259150805271
I(x3: 6, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x4: 0, ) = 0.0
I(x3: 6, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x4: 1, ) = 0.0
I(x3: 6, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x4: 2, ) = 0.0
I(x3: 6, x4: 3, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x4: 3, ) = 0.048316251830161056
I(x3: 6, x4: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x4: 4, ) = 0.0
I(x3: 7, x4: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x4: 0, ) = 0.0
I(x3: 7, x4: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x4: 1, ) = 0.0
I(x3: 7, x4: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x4: 2, ) = 0.0
I(x3: 7, x4: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x4: 3, ) = 0.0
I(x3: 7, x4: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x4: 4, ) = 0.017569546120058566
E[I(Q: x3, x4 -> ER] = 0.17650526639622757
_______________________________________________________________
I(x3: 0, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x5: 0, ) = 0.0
I(x3: 0, x5: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x5: 1, ) = 0.04685212298682284
I(x3: 1, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x5: 0, ) = 0.0
I(x3: 1, x5: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x5: 1, ) = 0.010248901903367497
I(x3: 2, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x5: 0, ) = 0.0
I(x3: 2, x5: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x5: 1, ) = 0.22108345534407028
I(x3: 3, x5: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x5: 0, ) = 0.29428989751098095
I(x3: 3, x5: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x5: 1, ) = 0.0
I(x3: 4, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x5: 0, ) = 0.0
I(x3: 4, x5: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x5: 1, ) = 0.0629575402635432
I(x3: 5, x5: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x5: 0, ) = 0.0029282576866764276
I(x3: 5, x5: 1, -> ER) = -1 * (
-0.4381806747685098 +
-0.22694406324942082 +
0 +
)
= 0.6651247380179306
P(x3: 5, x5: 1, ) = 0.2957540263543192
I(x3: 6, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x5: 0, ) = 0.0
I(x3: 6, x5: 1, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x5: 1, ) = 0.048316251830161056
I(x3: 7, x5: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x5: 0, ) = 0.0
I(x3: 7, x5: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x5: 1, ) = 0.017569546120058566
E[I(Q: x3, x5 -> ER] = 0.1967133192966647
_______________________________________________________________
I(x3: 0, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x6: 0, ) = 0.0
I(x3: 0, x6: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x6: 1, ) = 0.04685212298682284
I(x3: 1, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x6: 0, ) = 0.0
I(x3: 1, x6: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x6: 1, ) = 0.010248901903367497
I(x3: 2, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x6: 0, ) = 0.0
I(x3: 2, x6: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x6: 1, ) = 0.22108345534407028
I(x3: 3, x6: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x6: 0, ) = 0.29428989751098095
I(x3: 3, x6: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x6: 1, ) = 0.0
I(x3: 4, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x6: 0, ) = 0.0
I(x3: 4, x6: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x6: 1, ) = 0.0629575402635432
I(x3: 5, x6: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x6: 0, ) = 0.0029282576866764276
I(x3: 5, x6: 1, -> ER) = -1 * (
-0.4381806747685098 +
-0.22694406324942082 +
0 +
)
= 0.6651247380179306
P(x3: 5, x6: 1, ) = 0.2957540263543192
I(x3: 6, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x6: 0, ) = 0.0
I(x3: 6, x6: 1, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x6: 1, ) = 0.048316251830161056
I(x3: 7, x6: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x6: 0, ) = 0.0
I(x3: 7, x6: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x6: 1, ) = 0.017569546120058566
E[I(Q: x3, x6 -> ER] = 0.1967133192966647
_______________________________________________________________
I(x3: 0, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x7: 0, ) = 0.0
I(x3: 0, x7: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x7: 1, ) = 0.0
I(x3: 0, x7: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x7: 2, ) = 0.04685212298682284
I(x3: 0, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x7: 3, ) = 0.0
I(x3: 0, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x7: 4, ) = 0.0
I(x3: 1, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x7: 0, ) = 0.0
I(x3: 1, x7: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x7: 1, ) = 0.010248901903367497
I(x3: 1, x7: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x7: 2, ) = 0.0
I(x3: 1, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x7: 3, ) = 0.0
I(x3: 1, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x7: 4, ) = 0.0
I(x3: 2, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x7: 0, ) = 0.0
I(x3: 2, x7: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x7: 1, ) = 0.22108345534407028
I(x3: 2, x7: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x7: 2, ) = 0.0
I(x3: 2, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x7: 3, ) = 0.0
I(x3: 2, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x7: 4, ) = 0.0
I(x3: 3, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x7: 0, ) = 0.0
I(x3: 3, x7: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x7: 1, ) = 0.0
I(x3: 3, x7: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x7: 2, ) = 0.0
I(x3: 3, x7: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x7: 3, ) = 0.29428989751098095
I(x3: 3, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x7: 4, ) = 0.0
I(x3: 4, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x7: 0, ) = 0.0
I(x3: 4, x7: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x7: 1, ) = 0.0
I(x3: 4, x7: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x7: 2, ) = 0.0629575402635432
I(x3: 4, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x7: 3, ) = 0.0
I(x3: 4, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x7: 4, ) = 0.0
I(x3: 5, x7: 0, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x7: 0, ) = 0.0029282576866764276
I(x3: 5, x7: 1, -> ER) = -1 * (
-0.17841209262502639 +
-0.05340095739956382 +
0 +
)
= 0.2318130500245902
P(x3: 5, x7: 1, ) = 0.15519765739385066
I(x3: 5, x7: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x7: 2, ) = 0.04538799414348463
I(x3: 5, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x7: 3, ) = 0.0
I(x3: 5, x7: 4, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x7: 4, ) = 0.0951683748169839
I(x3: 6, x7: 0, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x7: 0, ) = 0.048316251830161056
I(x3: 6, x7: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x7: 1, ) = 0.0
I(x3: 6, x7: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x7: 2, ) = 0.0
I(x3: 6, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x7: 3, ) = 0.0
I(x3: 6, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x7: 4, ) = 0.0
I(x3: 7, x7: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x7: 0, ) = 0.0
I(x3: 7, x7: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x7: 1, ) = 0.0
I(x3: 7, x7: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x7: 2, ) = 0.017569546120058566
I(x3: 7, x7: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x7: 3, ) = 0.0
I(x3: 7, x7: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x7: 4, ) = 0.0
E[I(Q: x3, x7 -> ER] = 0.035976842317139913
_______________________________________________________________
I(x3: 0, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x8: 0, ) = 0.0
I(x3: 0, x8: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x8: 1, ) = 0.0
I(x3: 0, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x8: 2, ) = 0.0
I(x3: 0, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x8: 3, ) = 0.0
I(x3: 0, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x8: 4, ) = 0.0
I(x3: 0, x8: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x8: 5, ) = 0.04685212298682284
I(x3: 1, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x8: 0, ) = 0.0
I(x3: 1, x8: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x8: 1, ) = 0.010248901903367497
I(x3: 1, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x8: 2, ) = 0.0
I(x3: 1, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x8: 3, ) = 0.0
I(x3: 1, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x8: 4, ) = 0.0
I(x3: 1, x8: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x8: 5, ) = 0.0
I(x3: 2, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x8: 0, ) = 0.0
I(x3: 2, x8: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x8: 1, ) = 0.22108345534407028
I(x3: 2, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x8: 2, ) = 0.0
I(x3: 2, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x8: 3, ) = 0.0
I(x3: 2, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x8: 4, ) = 0.0
I(x3: 2, x8: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x8: 5, ) = 0.0
I(x3: 3, x8: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x8: 0, ) = 0.29428989751098095
I(x3: 3, x8: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x8: 1, ) = 0.0
I(x3: 3, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x8: 2, ) = 0.0
I(x3: 3, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x8: 3, ) = 0.0
I(x3: 3, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x8: 4, ) = 0.0
I(x3: 3, x8: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x8: 5, ) = 0.0
I(x3: 4, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x8: 0, ) = 0.0
I(x3: 4, x8: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x8: 1, ) = 0.0629575402635432
I(x3: 4, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x8: 2, ) = 0.0
I(x3: 4, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x8: 3, ) = 0.0
I(x3: 4, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x8: 4, ) = 0.0
I(x3: 4, x8: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x8: 5, ) = 0.0
I(x3: 5, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x8: 0, ) = 0.0
I(x3: 5, x8: 1, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x8: 1, ) = 0.1493411420204978
I(x3: 5, x8: 2, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x8: 2, ) = 0.0951683748169839
I(x3: 5, x8: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x8: 3, ) = 0.0029282576866764276
I(x3: 5, x8: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x8: 4, ) = 0.04538799414348463
I(x3: 5, x8: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x8: 5, ) = 0.005856515373352855
I(x3: 6, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x8: 0, ) = 0.0
I(x3: 6, x8: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x8: 1, ) = 0.0
I(x3: 6, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x8: 2, ) = 0.0
I(x3: 6, x8: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x8: 3, ) = 0.0
I(x3: 6, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x8: 4, ) = 0.0
I(x3: 6, x8: 5, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x8: 5, ) = 0.048316251830161056
I(x3: 7, x8: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x8: 0, ) = 0.0
I(x3: 7, x8: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x8: 1, ) = 0.0
I(x3: 7, x8: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x8: 2, ) = 0.0
I(x3: 7, x8: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x8: 3, ) = 0.017569546120058566
I(x3: 7, x8: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x8: 4, ) = 0.0
I(x3: 7, x8: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x8: 5, ) = 0.0
E[I(Q: x3, x8 -> ER] = 0.0
_______________________________________________________________
I(x3: 0, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x9: 0, ) = 0.0
I(x3: 0, x9: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x9: 1, ) = 0.0
I(x3: 0, x9: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x9: 3, ) = 0.04685212298682284
I(x3: 1, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x9: 0, ) = 0.0
I(x3: 1, x9: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x9: 1, ) = 0.010248901903367497
I(x3: 1, x9: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x9: 3, ) = 0.0
I(x3: 2, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x9: 0, ) = 0.0
I(x3: 2, x9: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x9: 1, ) = 0.22108345534407028
I(x3: 2, x9: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x9: 3, ) = 0.0
I(x3: 3, x9: 0, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x9: 0, ) = 0.29428989751098095
I(x3: 3, x9: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x9: 1, ) = 0.0
I(x3: 3, x9: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x9: 3, ) = 0.0
I(x3: 4, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x9: 0, ) = 0.0
I(x3: 4, x9: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x9: 1, ) = 0.0
I(x3: 4, x9: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x9: 3, ) = 0.0629575402635432
I(x3: 5, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x9: 0, ) = 0.0
I(x3: 5, x9: 1, -> ER) = -1 * (
-0.12673339216107363 +
-0.033349433583498365 +
0 +
)
= 0.160082825744572
P(x3: 5, x9: 1, ) = 0.25036603221083453
I(x3: 5, x9: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x9: 3, ) = 0.048316251830161056
I(x3: 6, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x9: 0, ) = 0.0
I(x3: 6, x9: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x9: 1, ) = 0.0
I(x3: 6, x9: 3, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x9: 3, ) = 0.048316251830161056
I(x3: 7, x9: 0, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x9: 0, ) = 0.0
I(x3: 7, x9: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x9: 1, ) = 0.017569546120058566
I(x3: 7, x9: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x9: 3, ) = 0.0
E[I(Q: x3, x9 -> ER] = 0.04007930190676692
_______________________________________________________________
I(x3: 0, x10: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x10: 1, ) = 0.04685212298682284
I(x3: 0, x10: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x10: 2, ) = 0.0
I(x3: 0, x10: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x10: 3, ) = 0.0
I(x3: 0, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x10: 4, ) = 0.0
I(x3: 0, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x10: 5, ) = 0.0
I(x3: 1, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x10: 1, ) = 0.0
I(x3: 1, x10: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x10: 2, ) = 0.010248901903367497
I(x3: 1, x10: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x10: 3, ) = 0.0
I(x3: 1, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x10: 4, ) = 0.0
I(x3: 1, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x10: 5, ) = 0.0
I(x3: 2, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x10: 1, ) = 0.0
I(x3: 2, x10: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x10: 2, ) = 0.22108345534407028
I(x3: 2, x10: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x10: 3, ) = 0.0
I(x3: 2, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x10: 4, ) = 0.0
I(x3: 2, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x10: 5, ) = 0.0
I(x3: 3, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x10: 1, ) = 0.0
I(x3: 3, x10: 2, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x10: 2, ) = 0.29428989751098095
I(x3: 3, x10: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x10: 3, ) = 0.0
I(x3: 3, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x10: 4, ) = 0.0
I(x3: 3, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x10: 5, ) = 0.0
I(x3: 4, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x10: 1, ) = 0.0
I(x3: 4, x10: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x10: 2, ) = 0.0
I(x3: 4, x10: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x10: 3, ) = 0.0629575402635432
I(x3: 4, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x10: 4, ) = 0.0
I(x3: 4, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x10: 5, ) = 0.0
I(x3: 5, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x10: 1, ) = 0.0
I(x3: 5, x10: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x10: 2, ) = 0.0029282576866764276
I(x3: 5, x10: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x10: 3, ) = 0.05124450951683748
I(x3: 5, x10: 4, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x10: 4, ) = 0.0951683748169839
I(x3: 5, x10: 5, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 5, x10: 5, ) = 0.1493411420204978
I(x3: 6, x10: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x10: 1, ) = 0.0
I(x3: 6, x10: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x10: 2, ) = 0.0
I(x3: 6, x10: 3, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x10: 3, ) = 0.048316251830161056
I(x3: 6, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x10: 4, ) = 0.0
I(x3: 6, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x10: 5, ) = 0.0
I(x3: 7, x10: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x10: 1, ) = 0.017569546120058566
I(x3: 7, x10: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x10: 2, ) = 0.0
I(x3: 7, x10: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x10: 3, ) = 0.0
I(x3: 7, x10: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x10: 4, ) = 0.0
I(x3: 7, x10: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x10: 5, ) = 0.0
E[I(Q: x3, x10 -> ER] = 0.0
_______________________________________________________________
I(x3: 0, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x11: 1, ) = 0.0
I(x3: 0, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x11: 2, ) = 0.0
I(x3: 0, x11: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x11: 3, ) = 0.0
I(x3: 0, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x11: 4, ) = 0.0
I(x3: 0, x11: 5, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 0, x11: 5, ) = 0.04685212298682284
I(x3: 0, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 0, x11: 6, ) = 0.0
I(x3: 1, x11: 1, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 1, x11: 1, ) = 0.010248901903367497
I(x3: 1, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x11: 2, ) = 0.0
I(x3: 1, x11: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x11: 3, ) = 0.0
I(x3: 1, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x11: 4, ) = 0.0
I(x3: 1, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x11: 5, ) = 0.0
I(x3: 1, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 1, x11: 6, ) = 0.0
I(x3: 2, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x11: 1, ) = 0.0
I(x3: 2, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x11: 2, ) = 0.0
I(x3: 2, x11: 3, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 2, x11: 3, ) = 0.22108345534407028
I(x3: 2, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x11: 4, ) = 0.0
I(x3: 2, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x11: 5, ) = 0.0
I(x3: 2, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 2, x11: 6, ) = 0.0
I(x3: 3, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x11: 1, ) = 0.0
I(x3: 3, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x11: 2, ) = 0.0
I(x3: 3, x11: 3, -> ER) = -1 * (
0 +
0.0 +
0 +
)
= -0.0
P(x3: 3, x11: 3, ) = 0.29428989751098095
I(x3: 3, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x11: 4, ) = 0.0
I(x3: 3, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x11: 5, ) = 0.0
I(x3: 3, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 3, x11: 6, ) = 0.0
I(x3: 4, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x11: 1, ) = 0.0
I(x3: 4, x11: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 4, x11: 2, ) = 0.0629575402635432
I(x3: 4, x11: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x11: 3, ) = 0.0
I(x3: 4, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x11: 4, ) = 0.0
I(x3: 4, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x11: 5, ) = 0.0
I(x3: 4, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 4, x11: 6, ) = 0.0
I(x3: 5, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x11: 1, ) = 0.0
I(x3: 5, x11: 2, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 5, x11: 2, ) = 0.0029282576866764276
I(x3: 5, x11: 3, -> ER) = -1 * (
-0.4381806747685098 +
-0.22694406324942082 +
0 +
)
= 0.6651247380179306
P(x3: 5, x11: 3, ) = 0.2957540263543192
I(x3: 5, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x11: 4, ) = 0.0
I(x3: 5, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x11: 5, ) = 0.0
I(x3: 5, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 5, x11: 6, ) = 0.0
I(x3: 6, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x11: 1, ) = 0.0
I(x3: 6, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x11: 2, ) = 0.0
I(x3: 6, x11: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x11: 3, ) = 0.0
I(x3: 6, x11: 4, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x11: 4, ) = 0.0
I(x3: 6, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 6, x11: 5, ) = 0.0
I(x3: 6, x11: 6, -> ER) = -1 * (
0 +
0 +
0.0 +
)
= -0.0
P(x3: 6, x11: 6, ) = 0.048316251830161056
I(x3: 7, x11: 1, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x11: 1, ) = 0.0
I(x3: 7, x11: 2, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x11: 2, ) = 0.0
I(x3: 7, x11: 3, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x11: 3, ) = 0.0
I(x3: 7, x11: 4, -> ER) = -1 * (
0.0 +
0 +
0 +
)
= -0.0
P(x3: 7, x11: 4, ) = 0.017569546120058566
I(x3: 7, x11: 5, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x11: 5, ) = 0.0
I(x3: 7, x11: 6, -> ER) = -1 * (
0 +
0 +
0 +
)
= 0
P(x3: 7, x11: 6, ) = 0.0
E[I(Q: x3, x11 -> ER] = 0.1967133192966647
_______________________________________________________________
The next characteristic/level in the tree is: x2
_______________________________________________________________
The tree should be: x3-> x2