Boosting Main idea: train classifiers (e.g. decision trees) in a sequence. a new classifier should focus on those cases which were incorrectly classified.

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Presentation transcript:

Boosting Main idea: train classifiers (e.g. decision trees) in a sequence. a new classifier should focus on those cases which were incorrectly classified in the last round. combine the classifiers by letting them vote on the final prediction (like bagging). each classifier could be (should be) very “weak”, e.g. a decision stump.

Example this line is one simple classifier saying that everything to the left + and everything to the right is -

Boosting Intuition We adaptively weigh each data case. Data cases which are wrongly classified get high weight (the algorithm will focus on them) Each boosting round learns a new (simple) classifier on the weighed dataset. These classifiers are weighed to combine them into a single powerful classifier. Classifiers that that obtain low training error rate have high weight. We stop by using monitoring a hold out set (cross-validation).

Boosting in a Picture boosting rounds training cases correctly classified training case has large weight in this round this DT has a strong vote.

And in animation Original Training set : Equal Weights to all training samples Taken from “A Tutorial on Boosting” by Yoav Freund and Rob Schapire

AdaBoost(Example) ROUND 1

AdaBoost(Example) ROUND 2

AdaBoost(Example) ROUND 3

AdaBoost(Example)

AdaBoost Given: where Initialise . For : . For : Find the classifier that minimizes the error with respect to the distribution Dt: Prerequisite: εt < 0.5, otherwise stop. Choose , typically where εt is the weighted error rate of classifier ht. Update: where Zt is a normalisation factor (chosen so that Dt + 1 will be a distribution). Output the final classifier: The equation to update the distribution Dt is constructed so that: Thus, after selecting an optimal classifier for the distribution , the examples that the classifier identified correctly are weighted less and those that it identified incorrectly are weighted more. Therefore, when the algorithm is testing the classifiers on the distribution , it will select a classifier that better identifies those examples that the previous classifer missed.