Summary
In this chapter, the important concepts of bias and variance are introduced. After an intuitive introduction to the bias/variance tradeoff, we discuss the bias/variance decompositions of the mean square error (in the context of regression problems) and of the mean misclassification error (in the context of classification problems). Then, we carry out a small empirical study providing some insight about how the parameters of a learning algorithm influence bias and variance.
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References
Bauer, E., Kohavi, R. An Empirical Comparison of Voting Classification Algorithms: Bagging, Boosting, and Variants. Machine Learning 1999; 36:105-139.
Bishop, C.M. Neural Networks for Pattern Recognition. Oxford: Oxford University Press, 1995.
Breiman, L., Friedman, J.H., Olsen, R.A., Stone, C.J. Classification and Regression Trees. California: Wadsworth International, 1984.
Breiman, L. Bias, Variance, and Arcing Classifiers. Technical Report 460, Statistics Department, University of California Berkeley, 1996.
Breiman, L. Bagging Predictors. Machine Learning 1996; 24(2):123-140.
Breiman, L. Randomizing Outputs to Increase Prediction Accuracy. Machine Learning 2000; 40(3):229-242.
Dietterich, T.G. and Kong, E.B. Machine Learning Bias, Statistical Bias, and Statistical Variance of Decision Tree Algorithms. Technical Report. Department of Computer Science, Oregon State University, 1995.
Domingos, P. An unified Bias-Variance Decomposition for Zero-One and Squa-red Loss. Proceedings of the 17th International Conference on Machine Learning, Morgan Kaufman, San Francisco, CA, 2000.
Efron, B., Tibshirani, R.J. An Introduction to the Bootstrap. Chapman & Hall, 1993.
Freund, Y., Schapire, R.E. A Decision-Theoretic Generalization of Online Learning and an Application to Boosting. Proceedings of the second European Conference on Computational Learning Theory, 1995.
Friedman, J.H. On Bias, Variance, 0/1-Loss, and the Curse-of-Dimensionality. Data Mining and Knowledge Discovery 1997; 1:55-77.
Geman, S., Bienenstock, E. and Doursat, R. Neural Networks and the Bias/Vari-ance Dilemna. Neural computation 1992; 4:1-58.
Geurts, P. Contribution to Decision Tree Induction: Bias/Variance Tradeoff and Time Series Classification. Phd thesis. Department of Electrical Engineering and Computer Science, University of Liège, 2002.
Hansen, J.V. Combining Predictors: Meta Machine Learning Methods and Bias/Variance & Ambiguity Decompositions. PhD thesis. Department of Computer Science, University of Aarhus, 2000.
Heskes, T. Bias/Variance Decompositions for Likelihood-Based Estimators. Neural Computation 1998; 10(6):1425-1433.
James, G.M. Variance and Bias for General Loss Functions. Machine Learning 2003; 51:115- 135.
Kohavi, R. and Wolpert, D. H. Bias Plus Variance Decomposition for Zero-One Loss Functions. Proceedings of the 13th International Conference on Machine Learning, Morgan Kaufman, 1996.
Tibshirani, R. Bias, Variance and Prediction Error for Classification Rules. Technical Report, Department of Statistics, University of Toronto, 1996.
Wolpert, D.H. On Bias plus Variance. Neural Computation 1997; 1211-1243.
Webb, G. MultiBoosting: A Technique for Combining Boosting and Wagging. Machine Learning 2000; 40(2):159-196.
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Geurts, P. (2009). Bias vs Variance Decomposition for Regression and Classification. In: Maimon, O., Rokach, L. (eds) Data Mining and Knowledge Discovery Handbook. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09823-4_37
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DOI: https://doi.org/10.1007/978-0-387-09823-4_37
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