1. Presented by: Dr Beatriz de la Iglesia
Managing Population Diversity Through the Use of Weighted Objectives and Modified Dominance: An Example from Data Mining Alan P. Reynolds and Beatriz de la Iglesia School of Computing Sciences University of East Anglia Norwich, Norfolk, UK
Presented by:
Dr Beatriz de la Iglesia
MCDM 2007

2. Overview The context: Multi-objective predictive classification
The problem: Loss of diversity
Managing diversity using three objectives
Managing diversity using adaptive objectives
Managing diversity by modifying the dominance relation
Conclusions and further research
Acknowledgement: Work supported by EPSRC Grant GR/T04298
B de la Iglesia
MCDM 2007

3. Multi-Objective (MO) Predictive Classification
NSGA II applied to optimize rules in the form of expression trees.
Internal nodes are Boolean operators (‘AND’, ‘OR’), leaf nodes contain Attribute Tests (ATs) (e.g. sex=male, color  red, age 29).
Expression trees used to predict class in binary classification problems.
B de la Iglesia
MCDM 2007

4. Objectives for MO approach
Minimizing misclassification costs:
simple error rate;
balanced error rate;
any other measure of overall misclassification cost.
Minimizing rule complexity:
simple count of ATs or other measures of complexity;
to encourage the production of rules that are easily understood by the client;
to reduce the chance of overfitting the data.
B de la Iglesia
MCDM 2007

5. Applying NSGA II
Initialization: population initialized with random balanced trees of depth two.
Crossover: subtree crossover which selects two nodes at random and swaps associated subtrees.
Mutation applied whenever crossover is not applied
50% chance of AT mutated;
25% chance random AT and its parent node removed
25% chance random AT and parent node inserted
B de la Iglesia
MCDM 2007

6. Rule evaluation
Rule Simplification: effort is made before each rule is evaluated to simplify the rule.
Rule Reduction: If, after rule simplification, the rule is still larger than a preset maximum size (20 ATs in the experiments reported here), ATs and their parent nodes are removed at random until the rule meets the size constraint.
B de la Iglesia
MCDM 2007

7. Using two objectives
Validation performance for UCI ML repository Adult dataset
Population of 100 and crossover rate of 30%.
Algorithm run 30 times, error bars give Standard Deviation
14.45% error rate on test data (STD 0.12%)
15.98 % error rate on test data (STD 0.70%)
B de la Iglesia
MCDM 2007

8. Loss of population diversity
Analysis of performance reveals loss of population diversity (genetic material) early in the search.
Information entropy used as a measure of population diversity
Entropy is 0 if all solutions are the same in population
If all solutions are unique
B de la Iglesia
MCDM 2007

9. Population entropy
B de la Iglesia
MCDM 2007

10. Population Diversity in MO GAs
Early in the search few solutions are non-dominated.
Algorithms like NSGA II and SPEA 2 become too elitist.
May also be a problem, especially early on in the search, whenever objectives are correlated in other MO scenarios.
Solution: artificially increase the fraction of non- dominated solutions early in the search to counteract the loss of population diversity.
B de la Iglesia
MCDM 2007

11. Using three objectives
If the client is unsure how to calculate misclassification costs, it is tempting to optimise rule complexity, number of False Positives (FP) and False Negatives (FN).
In practice, the client usually a rough idea – this knowledge can be used to improve the search.
Rule complexity
 FP + (1- ) FN
(1- ) FP +  FN
False positives
False negatives
Dominated
area
3 basic objectives v. 3 objectives with =0.8
at constant rule complexity
B de la Iglesia
MCDM 2007

12. Optimizing 3 objectives- 200 generations
Results after 200 generations, scaled with respect to =0.5
=0 equivalent to optimizing 3 objectives (Complexity, FP,FN)
=0.5 equivalent to optimizing 2 objectives (Complexity, simple error rate)
B de la Iglesia
MCDM 2007

13. Optimizing 3 objectives- 2000 generations
Results after 2000 generations, scaled with respect to =0.5 including 95% confidence intervals
Two objective approach outperforms others, except for =0.4
B de la Iglesia
MCDM 2007

14. Population Diversity
Three objectives reduce loss of diversity early in the search
Three objectives’ search does not find best large rules under error rate and rule simplicity
Solution: Combination approach should be used
B de la Iglesia
MCDM 2007

15. Adaptive objectives (2000 gen)
Initialise =0.
Measuring entropy of population at each iteration, increase  by 0.01 up to 0.5, whenever entropy is greater than 5 and decrease by 0.01 up to 0 whenever entropy less than three.
Mean error rates (scaled) on training data using 2000 generations
B de la Iglesia
MCDM 2007

16. Adaptive objectives (200 gen)
15.98 % error rate on test data (STD 0.70%)
15.00 % error rate on test data (STD 0.25%)
B de la Iglesia
MCDM 2007

17. Modifying the dominance relation
Breaking one objective into two or more parts not always easy.
An alternative is to use linear combinations of objectives as before, but where one of the weights is negative.
For example, minimize
1.1 * complexity – 0.1 * cost
1.1 * cost – 0.1 * complexity
Problem: All 1 AT rules become non-dominated.
B de la Iglesia
MCDM 2007

18. Modifying dominance relation
Alternative is to modify dominance relation by allowing a certain amount of leeway; r1 dominates r2 iff
Opposite to -dominance which allows a solution to dominate more of the objective space to control spread of Pareto-front or external archive.
B de la Iglesia
MCDM 2007

19. Modifying dominance
Results are similar to those obtained when using three objectives in terms of
Solution quality
Effect on population diversity
Results also suggest an adaptive scheme whereby early in the search more leeway is given and this is reduced later.
Results of adaptive leeway also provide improvements for both 200 and 2000 generations, although less marked than when using three adaptive objectives.
B de la Iglesia
MCDM 2007

20. Conclusions
Expression trees optimisation – loss of population diversity early in the search process as small rule with low cost dominates population.
This can also be expected in MO problems with few positively correlated objectives.
Two methods for maintaining population diversity:
Split objective into component parts and use linear combinations of new objectives
Modify dominance relation to give leeway in one objective
Parameters result in feedback control mechanism depending on diversity in the population
B de la Iglesia
MCDM 2007

21. Further research Further experimentation required
crossover, population size
feedback mechanism
other measures of population diversity
Effects of diversity loss in other problem domains should be studied.
B de la Iglesia
MCDM 2007