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Bagging (Bootstrap aggregating) was proposed by Leo Breiman in 1994 to improve classification by combining classifications of randomly generated training sets.
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Bootstrap aggregating, also called bagging (from bootstrap aggregating), is a machine learning ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification and regression. It also reduces variance and helps to avoid overfitting. Although it is usually applied to decision tree methods, it can be used with any type of method. Bagging is a special case of the model averaging approach.
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Bootstrap aggregating, often abbreviated as bagging, involves having each model in the ensemble vote with equal weight. In order to promote model variance, bagging trains each model in the ensemble using a randomly drawn subset of the training set. As an example, the random forest algorithm combines random decision trees with bagging to achieve very high classification accuracy.Breiman, L., Bagging Predictors, Machine Learning, 24(2), pp.
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More generally, when drawing with replacement n′ values out of a set of n (different and equally likely), the expected number of unique draws is n(1 - e^{-n'/n}). This kind of sample is known as a bootstrap sample. Then, m models are fitted using the above m bootstrap samples and combined by averaging the output (for regression) or voting (for classification). An illustration for the concept of bootstrap aggregating Bagging leads to "improvements for unstable procedures", which include, for example, artificial neural networks, classification and regression trees, and subset selection in linear regression.
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In ensemble learning one tries to combine the models produced by several learners into an ensemble that performs better than the original learners. One way of combining learners is bootstrap aggregating or bagging, which shows each learner a randomly sampled subset of the training points so that the learners will produce different models that can be sensibly averaged. In bagging, one samples training points with replacement from the full training set. The random subspace method is similar to bagging except that the features ("attributes", "predictors", "independent variables") are randomly sampled, with replacement, for each learner.
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Out-of-bag (OOB) error, also called out-of-bag estimate, is a method of measuring the prediction error of random forests, boosted decision trees, and other machine learning models utilizing bootstrap aggregating (bagging) to sub-sample data samples used for training. OOB is the mean prediction error on each training sample , using only the trees that did not have in their bootstrap sample. Subsampling allows one to define an out-of-bag estimate of the prediction performance improvement by evaluating predictions on those observations which were not used in the building of the next base learner.
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