Presentation given at the International Workshop of Learning Classifier Systems 2010.

1. BioHEL GBML System
right-logo
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Analysing BioHEL Using Challenging
Boolean Functions
María A. Franco, Natalio Krasnogor and Jaume Bacardit
University of Nottingham, UK,
ASAP Research Group,
School of Computer Science
{mxf,nxk,jqb}@cs.nott.ac.uk
July 8, 2010
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 1 / 27

2. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
1 BioHEL GBML System
Characteristics of the system
BioHEL fitness function
Open questions for BioHEL
2 k-Disjuntive Normal functions
3 Experiments
Experiment Setup
Iterations and execution time
Learning and overgeneralisation
4 Conclusions and Further Work
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 2 / 27

3. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
The BioHEL GBML System
BIOinformatics-oriented Hierarchical Evolutionary Learning
- BioHEL[Bacardit et al., 2009]
BioHEL was designed to handle large scale bioinformatics
datasets[Stout et al., 2008]
BioHEL is a GBML system that employs the Iterative Rule
Learning (IRL) paradigm
First used in EC in Venturini’s SIA system[Venturini, 1993]
Widely used for both Fuzzy and non-fuzzy evolutionary
learning
BioHEL inherits most of its components from
GAssist[Bacardit, 2004], a Pittsburgh GBML system
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 3 / 27

4. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
The BioHEL GBML System
BIOinformatics-oriented Hierarchical Evolutionary Learning
- BioHEL[Bacardit et al., 2009]
BioHEL was designed to handle large scale bioinformatics
datasets[Stout et al., 2008]
BioHEL is a GBML system that employs the Iterative Rule
Learning (IRL) paradigm
First used in EC in Venturini’s SIA system[Venturini, 1993]
Widely used for both Fuzzy and non-fuzzy evolutionary
learning
BioHEL inherits most of its components from
GAssist[Bacardit, 2004], a Pittsburgh GBML system
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 3 / 27

5. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
The BioHEL GBML System
BIOinformatics-oriented Hierarchical Evolutionary Learning
- BioHEL[Bacardit et al., 2009]
BioHEL was designed to handle large scale bioinformatics
datasets[Stout et al., 2008]
BioHEL is a GBML system that employs the Iterative Rule
Learning (IRL) paradigm
First used in EC in Venturini’s SIA system[Venturini, 1993]
Widely used for both Fuzzy and non-fuzzy evolutionary
learning
BioHEL inherits most of its components from
GAssist[Bacardit, 2004], a Pittsburgh GBML system
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 3 / 27

6. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
The BioHEL GBML System
BIOinformatics-oriented Hierarchical Evolutionary Learning
- BioHEL[Bacardit et al., 2009]
BioHEL was designed to handle large scale bioinformatics
datasets[Stout et al., 2008]
BioHEL is a GBML system that employs the Iterative Rule
Learning (IRL) paradigm
First used in EC in Venturini’s SIA system[Venturini, 1993]
Widely used for both Fuzzy and non-fuzzy evolutionary
learning
BioHEL inherits most of its components from
GAssist[Bacardit, 2004], a Pittsburgh GBML system
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 3 / 27

7. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Iterative Rule Learning
IRL has been used for many years in the ML community, with the
name of separate-and-conquer
Algorithm 1.1: I TERATIVE RULE L EARNING(Examples)
Theory ← ∅
whileExample = ∅
Rule ← FindBestRule(Examples)

Covered ← Cover (Rule, Examples)



if RuleStoppingCriterion(Rule, Theory , Examples)

do
 then exit

Examples ← Examples − Covered



Theory ← Theory ∪ Rule

return (Theory )
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 4 / 27

8. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Characteristics of BioHEL
A fitness function based on the
Minimum-Description-Length (MDL) (Rissanen,1978)
principle that tries to
Evolve accurate rules
Evolve high coverage rules
Evolve rules with low complexity, as general as possible
The ILAS windowing scheme
Efficiency enhancement method, not all training points are
used for each fitness computation
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 5 / 27

9. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Characteristics of BioHEL
A fitness function based on the
Minimum-Description-Length (MDL) (Rissanen,1978)
principle that tries to
Evolve accurate rules
Evolve high coverage rules
Evolve rules with low complexity, as general as possible
The ILAS windowing scheme
Efficiency enhancement method, not all training points are
used for each fitness computation
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 5 / 27

10. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Characteristics of BioHEL
The Attribute List Knowledge representation
Representation designed to handle high-dimensionality
domains
An explicit default rule mechanism
Generating more compact rule sets
Ensembles for consensus prediction
Easy system to boost robustness
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 6 / 27

11. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Characteristics of BioHEL
The Attribute List Knowledge representation
Representation designed to handle high-dimensionality
domains
An explicit default rule mechanism
Generating more compact rule sets
Ensembles for consensus prediction
Easy system to boost robustness
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 6 / 27

12. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Characteristics of BioHEL
The Attribute List Knowledge representation
Representation designed to handle high-dimensionality
domains
An explicit default rule mechanism
Generating more compact rule sets
Ensembles for consensus prediction
Easy system to boost robustness
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 6 / 27

13. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
BioHEL fitness function
Coverage term penalises rules that do not cover a minimum
percentage of examples
Choosing the coverage break changes the behaviour and
performance of the entire system
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 7 / 27

14. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Open questions for BioHEL
Does a single coverage break work for the same family of
problems?
How difficult is to hand-tune the coverage break?
What is the performance impact of the coverage break
when it is not properly adjusted?
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 8 / 27

15. BioHEL GBML System
Characteristics of the system
k-Disjuntive Normal functions
BioHEL fitness function
Experiments
Open questions for BioHEL
Conclusions and Further Work
Open questions for BioHEL
Does a single coverage break work for the same family of
problems?
How difficult is to hand-tune the coverage break?
What is the performance impact of the coverage break
when it is not properly adjusted?
Motivation of the paper
The motivation of the paper is to answer this questions. We
used k-DNF problems to test exhaustively the system with
problems that vary their difficulty.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 8 / 27

16. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
k-Disjuntive Normal functions
r disjuntive terms
d possible attributes
k represented attributes in each term
Example
d = 10, k = 3, r = 3
(¬x1 ∧ x5 ∧ x7 ) ∨ (x1 ∧ ¬x2 ∧ x8 ) ∨ (x4 ∧ ¬x5 ∧ ¬x9 )
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 9 / 27

17. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
k-Disjuntive Normal functions
r disjuntive terms
d possible attributes
k represented attributes in each term
Example
d = 10, k = 3, r = 3
(¬x1 ∧ x5 ∧ x7 ) ∨ (x1 ∧ ¬x2 ∧ x8 ) ∨ (x4 ∧ ¬x5 ∧ ¬x9 )
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 9 / 27

18. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
k-DNF class imbalance
Probability of having a negative example
(1 - 2(-k))r
1
0.9
1 0.8
0.9 0.7
0.8 0.6
0.7
0.5
0.6
0.4
0.5
0.4 0.3
0.3 0.2
0.2 0.1
0.1 0
0
5
10
15
20
10 25
9 8 30 r - Number of terms
7 6 35
5 40
k - Attributes expressed 4 3 45
2 50
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 10 / 27

19. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Experimental setup
90 different k-DNF scenarios
d = 20
k ranging between 2 and 10
r ranging between 5 and 50
5 different coverage breaks
We show results in terms of:
Iterations to learn a optimal k-DNF term
Number of cases where the system overgeneralised and
learned.
Using a fixed default class and the majority policy
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 11 / 27

20. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Iterations to learn a optimal k-DNF term
Number of iterations to find a good rule
Model z=a*k + b*r + c*r2 + d
0.0001
0.001
0.01
0.1
14
12
10
8
6
4
2
0
-2
50
45
40
35
2 30
3 25
4 20 r - Number of rules
5
6 15
7
k - Number of terms in the rule 8 10
9
10 5
a>b>c >d
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 12 / 27

21. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Number of iterations to learn a good rule
Coverage break 0.0001
5 10 15 20 25 30 35 40 45 50
2 0,62
3 1,64 1,83 1,64
4 3,25 3,55 3,65 3,71 3,89 3,94 3,92
5 4,33 4,92 5,48 5,63 5,93 5,96 6,04 6,13 6,07 6,26
6 5,60 6,39 7,06 7,38 7,41 7,67 7,71 7,95 7,96 8,07
7 6,55 7,68 8,19 8,40 8,84 9,05 9,22 9,47 9,57 9,63
8 7,58 8,76 9,37 9,80 9,94 10,21 10,45 10,67 10,82 10,95
9 9,02 10,22 10,72 11,09 11,45 11,64 11,77 12,03 12,10 12,24
10 10,65 11,57 12,15 12,64 12,76 12,87 13,11 13,12 13,30 13,42
Coverage break 0.001
5 10 15 20 25 30 35 40 45 50
2 0,65
3 1,64 1,83 1,53
4 3,16 3,51 3,60 3,65 3,83 3,91 3,91
5 4,31 4,79 5,31 5,53 5,87 5,91 5,92 6,01 5,95 6,18
6 5,27 6,07 6,73 7,12 7,11 7,35 7,49 7,70 7,73 7,81
7 5,96 7,10 7,58 7,80 8,30 8,45 8,69 8,95 9,09 9,19
8 7,04 8,07 8,65 8,97 9,12 9,41 9,67 9,90 10,02 10,21
9 9,18 10,10 10,39 10,70 11,00 11,11 11,19 11,43 11,51 11,64
10 10,11 11,22 11,71
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 13 / 27

22. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Number of iterations to learn a good rule
Coverage break 0.0001
5 10 15 20 25 30 35 40 45 50
2 0,62
3 1,64 1,83 1,64
4 3,25 3,55 3,65 3,71 3,89 3,94 3,92
5 4,33 4,92 5,48 5,63 5,93 5,96 6,04 6,13 6,07 6,26
6 5,60 6,39 7,06 7,38 7,41 7,67 7,71 7,95 7,96 8,07
7 6,55 7,68 8,19 8,40 8,84 9,05 9,22 9,47 9,57 9,63
8 7,58 8,76 9,37 9,80 9,94 10,21 10,45 10,67 10,82 10,95
9 9,02 10,22 10,72 11,09 11,45 11,64 11,77 12,03 12,10 12,24
10 10,65 11,57 12,15 12,64 12,76 12,87 13,11 13,12 13,30 13,42
Coverage break 0.001
5 10 15 20 25 30 35 40 45 50
2 0,65
3 1,64 1,83 1,53
4 3,16 3,51 3,60 3,65 3,83 3,91 3,91
5 4,31 4,79 5,31 5,53 5,87 5,91 5,92 6,01 5,95 6,18
6 5,27 6,07 6,73 7,12 7,11 7,35 7,49 7,70 7,73 7,81
7 5,96 7,10 7,58 7,80 8,30 8,45 8,69 8,95 9,09 9,19
8 7,04 8,07 8,65 8,97 9,12 9,41 9,67 9,90 10,02 10,21
9 9,18 10,10 10,39 10,70 11,00 11,11 11,19 11,43 11,51 11,64
10 10,11 11,22 11,71
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 14 / 27

23. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Number of iterations to learn a good rule
Coverage break 0.01
5 10 15 20 25 30 35 40 45 50
2 0,61
3 1,48 1,68 1,54
4 2,73 3,09 3,19 3,23 3,48 3,59 3,53
5 3,64 4,11 4,55 4,75 5,20 5,29 5,34 5,52 5,52 5,75
6 4,95 5,40 5,96 6,25 6,30 6,68 6,76 6,96 7,04 7,30
7 7,53 7,88 7,88 8,02 8,35 8,46 8,56 8,78 8,88 9,07
8
9
10
Coverage break 0.1
5 10 15 20 25 30 35 40 45 50
2 0,50
3 1,29 1,45 1,39
4 3,21
5
6
7
8
9
10
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 15 / 27

24. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Which one is the best configuration?
Minimum values
5 10 15 20 25 30 35 40 45 50
2 0,50
3 1,29 1,45 1,39
4 2,73 3,09 3,19 3,23 3,48 3,59 3,53
5 3,64 4,11 4,55 4,75 5,20 5,29 5,34 5,52 5,52 5,75
6 4,95 5,40 5,96 6,25 6,30 6,68 6,76 6,96 7,04 7,30
7 5,96 7,10 7,58 7,80 8,30 8,45 8,56 8,78 8,88 9,07
8 7,04 8,07 8,65 8,97 9,12 9,41 9,67 9,90 10,02 10,21
9 9,02 10,10 10,39 10,70 11,00 11,11 11,19 11,43 11,51 11,64
10 10,11 11,22 12,15 11,71 12,76 12,87 13,11 13,12 13,30 13,42
The adequate coverage break depends on the
characteristics of the problem
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 16 / 27

25. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Execution time to learn the problem
Average execution time to learn the problem
0.0001
Execution time (s) 0.001
0.01
0.1
14000
12000
10000
8000
6000
4000
2000
0
50 45 40 9 10
35 30 7 8
25 6
r - Number of rules 20 15 4 k5- Number of terms in the rule
10 5 2 3
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 17 / 27

26. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Execution time to learn the problem - Majority policy
Average execution time to learn the problem
0.0001
Execution time (s) 0.001
0.01
0.1
60000
50000
40000
30000
20000
10000
0
50 45 40 9 10
35 30 7 8
25 6
r - Number of rules 20 15 4 k5- Number of terms in the rule
10 5 2 3
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 18 / 27

27. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Execution time to learn the problem - Majority policy
Average execution time to learn the problem
0.0001
0.001
0.01
0.1
60000
50000
40000
30000
20000
10000
0
2
3
4
5 45 50
6
k - Number of terms in the rule 40
7 30 35
8 20 25
9 10 15 r - Number of rules
10 5
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 19 / 27

28. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Summary
The execution time and the iterations are proportional to:
Number of rules r
Number of specified attributes k
Learning with the minority policy is more similar to a real
life scenario.
Choosing the wrong default class might lead to learn a
more difficult problem.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 20 / 27

29. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Learning and overgeneralisation
Learning maps
Show different colours depending on the percentage of
examples that learned correctly, overgeneralised and did not
learn the correct set of rules.
Blue: total learning ⇒ All the runs learned the right set of
rules
Cyan: between learning and overgeneralisation
Purple: overgeneralisation ⇒ All the runs learned a set of
rules with less that 100% accuracy.
Orange: between overgeneralisation and no learning
Red: no learning ⇒ All the runs used the default rule to
cover all the examples. No rules were generated
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 21 / 27

30. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Learning and overgeneralisation
Learning maps
Show different colours depending on the percentage of
examples that learned correctly, overgeneralised and did not
learn the correct set of rules.
Blue: total learning ⇒ All the runs learned the right set of
rules
Cyan: between learning and overgeneralisation
Purple: overgeneralisation ⇒ All the runs learned a set of
rules with less that 100% accuracy.
Orange: between overgeneralisation and no learning
Red: no learning ⇒ All the runs used the default rule to
cover all the examples. No rules were generated
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 21 / 27

31. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Learning and overgeneralisation - Default class 0
Map of cases - Cov. break 0,0001 - Default Class 0 Map of cases - Cov. break 0,001 - Default Class 0 Map of cases - Cov. break 0,01 - Default Class 0
55 55 55
50 50 50
45 45 45
r - Number of terms or rules
r - Number of terms or rules
r - Number of terms or rules
40 40 40
35 35 35
30 30 30
25 25 25
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11
k - Attributes expressed k - Attributes expressed k - Attributes expressed
(a) Cov. Break 0,0001 (b) Cov. Break 0,001 (c) Cov. Break 0,01
Map of cases - Cov. break 0,1 - Default Class 0 Map of cases - Cov. break 0,5 - Default Class 0
55 55
50 50
45 45
r - Number of terms or rules
r - Number of terms or rules
40 40
35 35
30 30
25 25
20 20
15 15
10 10
5 5
0 0
1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11
k - Attributes expressed k - Attributes expressed
(d) Cov. Break 0,1 (e) Cov. Break 0,5
Blue: total learning, Cyan: between learning and overgeneralisation, Purple: overgeneralisation,
Orange: between overgeneralisation and no learning , Red: no learning
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 22 / 27

32. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Learning and overgeneralisation - Majority policy
Map of cases - Cov. break 0,0001 - Default Class major Map of cases - Cov. break 0,001 - Default Class major Map of cases - Cov. break 0,01 - Default Class major
55 55 55
50 50 50
45 45 45
r - Number of terms or rules
r - Number of terms or rules
r - Number of terms or rules
40 40 40
35 35 35
30 30 30
25 25 25
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11
k - Attributes expressed k - Attributes expressed k - Attributes expressed
(f) Cov. Break 0,0001 (g) Cov. Break 0,001 (h) Cov. Break 0,01
Map of cases - Cov. break 0,1 - Default Class major Map of cases - Cov. break 0,5 - Default Class major
55 55
50 50
45 45
r - Number of terms or rules
r - Number of terms or rules
40 40
35 35
30 30
25 25
20 20
15 15
10 10
5 5
0 0
1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11
k - Attributes expressed k - Attributes expressed
(i) Cov. Break 0,1 (j) Cov. Break 0,5
Blue: total learning, Cyan: between learning and overgeneralisation, Purple: overgeneralisation,
Orange: between overgeneralisation and no learning , Red: no learning
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 23 / 27

33. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Summary
The coverage break should be large enough to introduce
generalisation pressure over the system but low enough to
avoid overgeneral rules.
The adequate coverage break depends on k and also
depends on r .
The problems where the rules that cover wider areas are
more difficult to learn even with the right coverage break.
The difficulty of a k-DNF problem depends on the class
imbalance and the rule overlapping.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 24 / 27

34. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Summary
The coverage break should be large enough to introduce
generalisation pressure over the system but low enough to
avoid overgeneral rules.
The adequate coverage break depends on k and also
depends on r .
The problems where the rules that cover wider areas are
more difficult to learn even with the right coverage break.
The difficulty of a k-DNF problem depends on the class
imbalance and the rule overlapping.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 24 / 27

35. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Summary
The coverage break should be large enough to introduce
generalisation pressure over the system but low enough to
avoid overgeneral rules.
The adequate coverage break depends on k and also
depends on r .
The problems where the rules that cover wider areas are
more difficult to learn even with the right coverage break.
The difficulty of a k-DNF problem depends on the class
imbalance and the rule overlapping.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 24 / 27

36. BioHEL GBML System
Experiment Setup
k-Disjuntive Normal functions
Iterations and execution time
Experiments
Learning and overgeneralisation
Conclusions and Further Work
Summary
The coverage break should be large enough to introduce
generalisation pressure over the system but low enough to
avoid overgeneral rules.
The adequate coverage break depends on k and also
depends on r .
The problems where the rules that cover wider areas are
more difficult to learn even with the right coverage break.
The difficulty of a k-DNF problem depends on the class
imbalance and the rule overlapping.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 24 / 27

37. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Conclusions
There is no coverage break that works with all type of
problems ⇒ No Free Lunch
The adequate coverage break facilitates the learning
while the wrong coverage break makes it harder or even
impossible.
Open questions
Would it be possible to adapt the coverage break automatically
and reduce the cost of hand tuning the parameters?
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 25 / 27

38. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Conclusions
There is no coverage break that works with all type of
problems ⇒ No Free Lunch
The adequate coverage break facilitates the learning
while the wrong coverage break makes it harder or even
impossible.
Open questions
Would it be possible to adapt the coverage break automatically
and reduce the cost of hand tuning the parameters?
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 25 / 27

39. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Conclusions
There is no coverage break that works with all type of
problems ⇒ No Free Lunch
The adequate coverage break facilitates the learning
while the wrong coverage break makes it harder or even
impossible.
Open questions
Would it be possible to adapt the coverage break automatically
and reduce the cost of hand tuning the parameters?
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 25 / 27

40. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Further Work
Incorporate a heuristic inside BioHEL to determine a good
coverage break for the problem and readapt this coverage
break during the learning process
Analyse the learning map of other evolutionary learning
systems to determine strengths and weaknesses of the
systems.
Encourage the usage of the kDNF family of problems as a
common benchmark in the LCS community
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 26 / 27

41. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Further Work
Incorporate a heuristic inside BioHEL to determine a good
coverage break for the problem and readapt this coverage
break during the learning process
Analyse the learning map of other evolutionary learning
systems to determine strengths and weaknesses of the
systems.
Encourage the usage of the kDNF family of problems as a
common benchmark in the LCS community
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 26 / 27

42. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Further Work
Incorporate a heuristic inside BioHEL to determine a good
coverage break for the problem and readapt this coverage
break during the learning process
Analyse the learning map of other evolutionary learning
systems to determine strengths and weaknesses of the
systems.
Encourage the usage of the kDNF family of problems as a
common benchmark in the LCS community
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 26 / 27

43. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Bacardit, J. (2004).
Pittsburgh Genetics-Based Machine Learning in the Data Mining era: Representations, generalization, and
run-time.
PhD thesis, Ramon Llull University, Barcelona, Spain.
Bacardit, J., Burke, E., and Krasnogor, N. (2009).
Improving the scalability of rule-based evolutionary learning.
Memetic Computing, 1(1):55–67.
Stout, M., Bacardit, J., Hirst, J. D., and Krasnogor, N. (2008).
Prediction of recursive convex hull class assignments for protein residues.
Bioinformatics, 24(7):916–923.
Venturini, G. (1993).
SIA: a supervised inductive algorithm with genetic search for learning attributes based concepts.
In Brazdil, P. B., editor, Machine Learning: ECML-93 - Proceedings of the European Conference on Machine
Learning, pages 280–296. Springer-Verlag.
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 27 / 27

44. BioHEL GBML System
k-Disjuntive Normal functions
Experiments
Conclusions and Further Work
Questions or comments?
M. Franco, N. Krasnogor, J. Bacardit. Uni. Nottingham Analysing BioHEL Using Boolean Functions 27 / 27