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Examples of Ensemble Methods

Examples of Ensemble Methods. How to generate an ensemble of classifiers? Bagging Boosting. Bagging. Sampling with replacement Build a classifier on each bootstrap sample Each example has probability 1/N being selected

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Examples of Ensemble Methods

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  1. Examples of Ensemble Methods • How to generate an ensemble of classifiers? • Bagging • Boosting

  2. Bagging • Sampling with replacement • Build a classifier on each bootstrap sample • Each example has probability 1/N being selected • For an example not being selected after N times, the probability is (1 – 1/N)N (when N is large, it is close to 1/e) • For an example being selected after N times, the probability is 1 – 1/e = 0.632 • A bootstrap sample contains 63% of the original data

  3. Boosting • An iterative procedure to adaptively change distribution of training data by focusing more on previously misclassified records • Initially, all N records are assigned equal weights • Unlike bagging, weights may change at the end of boosting round

  4. Boosting • Records that are wrongly classified will have their weights increased • Records that are classified correctly will have their weights decreased • Example 4 is hard to classify • Its weight is increased, therefore it is more likely to be chosen again in subsequent rounds

  5. Example: AdaBoost • Base classifiers: C1, C2, …, CT • Error rate: • Importance of a classifier:

  6. Example: AdaBoost • Weight update: • If any intermediate rounds produce error rate higher than 50%, the weights are reverted back to 1/n and the resampling procedure is repeated • Classification:

  7. Initial weights for each data point Data points for training Illustrating AdaBoost

  8. Illustrating AdaBoost

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