introduction - computer sciencerlaz/prec2010/slides/majorityvote.pdf · voting. majority voting...
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Introduction
Voting: decision-making strategyMajority voteWeighted majority votingNaive Bayes combination
JustinTalbot,ErinWirchVoting
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Majority Voting
Three Main Types of Majority Voting
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Ensemble of Classifiers Increases Accuracy
The accuracy of the ensemble is
Pmaj =L�
m=�L/2�+1
�Lm
�pm(1 − p)L−m assuming that the
probability of success p is the same for all classifiers
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Majority Voting Perormance
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Patterns of Success and Failure
Upper bounds and lower bounds can be established on theperformance of the classifiersThe upper bound is pmaj =
� Ll+1
�α assumingα the probability
of each combination of classifiersThe lower bound is pmaj =
pL−1l+1 where p is the overall
accuracy of an individual classifier
JustinTalbot,ErinWirchVoting
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Weighted Voting
Classifiers are not all equalWeigh more accurate classifiers
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Examples
Where weighted voting worksWhere weighted voting does not work
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Maximizing Accuracy
bi ∝ log pi1−pi
Note: Minimum error not guaranteed
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Key Points
Weights give more accurate classifiers more powerWorks well in some cases, poorly in othersMinimum error not guaranteed
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Conclusion
Voting: decision-making strategyMajority voteWeighted majority votingNaive Bayes combination
JustinTalbot,ErinWirchVoting
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The End
Questions?
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References
Ludmila I. Kuncheva.Combining Pattern Classifiers: Methods and Algorithms.Wiley-Interscience, July 2004.
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