Machine Learning Bias, Statistical Bias, and Statistical Variance of Decision Tree Algorithms

The term \bias" is widely used|and with diierent meanings|in the elds of machine learning and statistics. This paper clariies the uses of this term and shows how to measure and visualize the statistical bias and variance of learning algorithms. Statistical bias and variance can be applied to diagnose problems with machine learning bias, and the paper shows four examples of this. Finally, the paper discusses methods of reducing bias and variance. Methods based on voting can reduce variance, and the paper compares Breiman's bagging method and our own tree randomization method for voting decision trees. Both methods uniformly improve performance on data sets from the Irvine repository. Tree randomization yields perfect performance on the Letter Recognition task. A weighted nearest neighbor algorithm based on the innnite bootstrap is also introduced. In general, decision tree algorithms have moderate-to-high variance, so an important implication of this work is that variance|rather than appropriate or inappropriate machine learning bias|is an important cause of poor performance for decision tree algorithms.