learning classifier systems (introduction) muhammad iqbal evolutionary computation research group...
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Learning Classifier Systems(Introduction)
Muhammad Iqbal
Evolutionary Computation Research GroupSchool of Engineering and Computer Science
Victoria University of WellingtonNew Zealand
Outline
• Examples • Classification Problems• Rules Format
• Overview of LCS
• Detailed XCS Process
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3-bit Boolean Classification Problem
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A B C Y
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
0 0 # 0
1 # 1 1
If A = 0 and B = 0, then Y = 0
If A = 0 and B = 1, then Y = 1
If A = 1 and C = 0, then Y = 0
If A = 1 and C = 1, then Y = 1
0 1 # 1
1 # 0 0
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Condition Action0 # # 1
0 1 1 1
Over-general Rule
Over-fitted Rule
Optim
al Rules
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1 1 1 0 1 0 1 0 1 0 11 1 0 0 1 0 1 0 1 0 11 0 1 0 0 1 1 0 0 1 11 0 0 0 0 1 1 0 0 1 10 1 1 0 0 0 0 1 1 1 10 1 0 0 0 0 0 1 1 1 10 0 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0
00
100
010
110
001
101
011
111
11###1 : 1
11###0 : 0
10##1# : 1
10##0# : 0
01#1## : 1
01#0## : 0
001### : 1 000### : 0
A B C
F
E
D
6-bit Boolean Classification Problem
3-bit Real-Valued Classification Problem
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A B C Y
5 3.6 20 210 9.8 52 415 12.3 34 17 8.7 15 2
…..
[3 7] [1.0 20.6] [13 25] 2
If 3≤A ≤ 7 and 1.0 ≤ B ≤ 20.6 and 13 ≤ C ≤ 25, then Y = 2
All input attributes can be normalized, say, between 0.0 and 1.0. 5
Different Rich Encoding Schemes
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Condition Action
{0, 1, #}n Genetic Programming like Trees
Genetic Programming like Trees Constant Numeric Values
{0, 1, #}n Finite State Machines
Numeric Intervals Artificial Neural Networks
etc
LCS Overview
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Learning Classifier System (LCS)
Populationcondition : action
C1 A1
C2 A2
C3 A3
... ... CN AN
Evolutionary Computation Componentrule selection, reproduction, mutation,
recombination, and deletion
Machine Learning Componentrule evaluation, and action decision
ENVIRONMENT
problem instance
action feedback
1 0 0 0 1 : 00 1 0 1 # : 11 # # 0 # : 1# # 1 # 0 : 0
In LCS the ‘#’ sign, known as ‘don’t care’ symbol, can be either 0 or 1.
0 1 1 0 0
1 0 0 0 1 : 00 1 0 1 # : 11 # # 0 # : 1# # 1 # 0 : 0
The XCS classifier system evolves a set of maximally general
and accurate classifier rules that collectively solve the problem.
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0
0
XCS Details
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Rules in XCS
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if condition then action; with certain attributes
Attribute Description
pPrediction: an estimate of the payoff that the classifier will receive if its action is selected.
εPrediction Error: which estimates the error between the classifier’s prediction and the received payoff.
F Fitness: computed as an inverse function of the prediction error.
expExperience: which is a count of the number of times the classifier has been updated.
n Numerosity: which is a count of the number of copies of each unique classifier.
tsTime Stamp: keeps the time-step of the last occurrence of a GA in an action set to which this classifier belonged.
asAction Set Size: which estimates the average size of the action sets this classifier has belonged to.
Source: Wilson, XCS tutorial
((43*99)+(27*3))/102
Action: 00
Action: 01
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Applying GA in Action Set0 0 1 0 1 0
condition A F
0 0 1 # # 0
1 90
0 # # 0 # #
0 82
0 0 # 1 0 1
1 50
0 # 1 0 1 0
1 20
1 0 0 # 1 1
0 43
0 0 1 0 # #
1 70condition A F
0 0 1 # # 0 1 90
0 # 1 0 1 0 1 20
0 0 1 0 # # 1 70
condition A F
0 0 1 # # 0 1 90
0 0 1 0 # # 1 70
condition A F
0 0 1 # # 0 1 90
0 0 1 0 # # 1 70
condition A F
0 0 1 0 # 0 1 8
0 0 1 # # # 1 8condition A F
0 # 1 0 # 0 0 8
# 0 1 # 1 # 1 8
condition A F
0 # 1 0 # 0 0 8
# 0 1 # 1 # 1 8
( (90+70)/2 ) × 0.1
population
action set selected parents
reproduced children
crossed over children
mutated children (niche mutation)
final children
subsumption deletion12
if it is a well experienced and accurate classifier rule.
Thank You All!
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