Splitting Criteria with the Bias Term

  • Leszek RutkowskiEmail author
  • Maciej Jaworski
  • Piotr Duda
Part of the Studies in Big Data book series (SBD, volume 56)


The Mean Squared Error (MSE) of any estimator \(\widehat{\Theta }\) of some quantity \(\Theta \) is a sum of two terms
$$\begin{aligned} E\left[ \left( \widehat{\Theta }-\Theta \right) ^{2}\right] =E\left[ \left( \widehat{\Theta }-E\left[ \widehat{\Theta }\right] \right) ^{2}\right] + \left( E\left[ \widehat{\Theta }\right] -\Theta \right) ^{2}. \end{aligned}$$


  1. 1.
    Domingos, P.: A unified bias-variance decomposition and its applications. In: Proceedings of the 17th International Conference on Machine Learning, pp. 231–238. Morgan Kaufmann (2000)Google Scholar
  2. 2.
    James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning with Applications in R. Springer Texts in Statistics. Springer, Berlin (2013)Google Scholar
  3. 3.
    Briscoe, E., Feldman, J.: Conceptual complexity and the bias/variance tradeoff. Cognition 118(1), 2–16 (2011)CrossRefGoogle Scholar
  4. 4.
    Zhang, T., Zhang, Q., Wang, Q.: Model detection for functional polynomial regression. Comput. Stat. Data Anal. 70, 183–197 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Geman, S., Bienenstock, E., Doursat, R.: Neural networks and the bias/variance dilemma. Neural Comput. 4(1), 1–58 (1992)CrossRefGoogle Scholar
  6. 6.
    Domingos, P., Hulten, G.: Mining high-speed data streams. In: Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 71–80 (2000)Google Scholar
  7. 7.
    Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the McDiarmid’s bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)CrossRefGoogle Scholar
  8. 8.
    Matuszyk, P., Krempl, G., Spiliopoulou, M.: Correcting the usage of the Hoeffding inequality in stream mining. In: Tucker, A., Höppner, F., Siebes, A., Swift, S. (eds.) Advances in Intelligent Data Analysis XII. Lecture Notes in Computer Science, vol. 8207, pp. 298–309. Springer, Berlin (2013)Google Scholar
  9. 9.
    Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the Gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)CrossRefGoogle Scholar
  10. 10.
    Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Netw. Learn. Syst. 26(5), 1048–1059 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    De Rosa, R., Cesa-Bianchi, N.: Splitting with confidence in decision trees with application to stream mining. In: 2015 International Joint Conference on Neural Networks (IJCNN), July 2015, pp. 1–8 (2015)Google Scholar
  12. 12.
    De Rosa, R., Cesa-Bianchi, N.: Confidence decision trees via online and active learning for streaming data. J. Artif. Intell. Res. 60(60), 1031–1055 (2017)CrossRefGoogle Scholar
  13. 13.
    Jaworski, M., Duda, P., Rutkowski, L.: New splitting criteria for decision trees in stationary data streams. IEEE Trans. Neural Netw. Learn. Syst. 29, 2516–2529 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Leszek Rutkowski
    • 1
    • 2
    Email author
  • Maciej Jaworski
    • 1
  • Piotr Duda
    • 1
  1. 1.Institute of Computational IntelligenceCzestochowa University of TechnologyCzęstochowaPoland
  2. 2.Information Technology InstituteUniversity of Social SciencesLodzPoland

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