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Evaluating Classifier Accuracy: Bootstrap

  • Bootstrap
    • Works well with small data sets
    • Samples the given training tuples uniformly with replacement
      • i.e., each time a tuple is selected, it is equally likely to be selected again and re-added to the training set
  • Several bootstrap methods, and a common one is .632 boostrap
    • A data set with d tuples is sampled d times, with replacement, resulting in a training set of d samples. The data tuples that did not make it into the training set end up forming the test set. About 63.2% of the original data end up in the bootstrap, and the remaining 36.8% form the test set (since (1 – 1/d)d ≈ e-1 = 0.368)
    • Repeat the sampling procedure k times, overall accuracy of the model:

\[Acc(M)=\frac{1}{k}\sum_{i=1}^{k}(0.632 \times Acc(M_{i})_{test-set}+0.368 \times Acc(M_{i})_{train-set})\]

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