The Rademacher Complexity of Linear Transformation Classes

  • Andreas Maurer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4005)


Bounds are given for the empirical and expected Rademacher complexity of classes of linear transformations from a Hilbert space H to a finite dimensional space. The results imply generalization guarantees for graph regularization and multi-task subspace learning.


Function Class Compact Operator Covariance Operator Single Task Machine Learn Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ando, R.K., Zhang, T.: A framework for learning predictive structures from multiple tasks and unlabeled data. Journal of Machine Learning Research 6, 1817–1853 (2005)MathSciNetGoogle Scholar
  2. 2.
    Bartlett, P.L., Mendelson, S.: Rademacher and Gaussian Complexities: Risk Bounds and Structural Results. Journal of Machine Learning Research 3, 463–482 (2002)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bartlett, P., Bousquet, O., Mendelson, S.: Local Rademacher complexities. Available online:
  4. 4.
    Baxter, J.: Theoretical Models of Learning to Learn. In: Thrun, S., Pratt, L. (eds.) Learning to Learn, Springer, Heidelberg (1998)Google Scholar
  5. 5.
    Baxter, J.: A Model of Inductive Bias Learning. Journal of Artificial Intelligence Research 12, 149–198 (2000)MathSciNetMATHGoogle Scholar
  6. 6.
    Ben-David, S., Schuller, R.: Exploiting task relatedness for multiple task learning. In: COLT 2003 (2003)Google Scholar
  7. 7.
    Caruana, R.: Multitask Learning. In: Thrun, S., Pratt, L. (eds.) Learning to Learn, Springer, Heidelberg (1998)Google Scholar
  8. 8.
    Evgeniou, T., Pontil, M.: Regularized multi-task learning. In: Proc. Conference on Knowledge Discovery and Data Mining (2004)Google Scholar
  9. 9.
    Evgeniou, T., Micchelli, C., Pontil, M.: Learning multiple tasks with kernel methods. JMLR 6, 615–637 (2005)MathSciNetGoogle Scholar
  10. 10.
    Koltchinskii, V., Panchenko, D.: Empirical margin distributions and bounding the generalization error of combined classifiers. The Annals of Statistics 30(1), 1–50Google Scholar
  11. 11.
    Ledoux, M., Talagrand, M.: Probability in Banach Spaces: isoperimetry and processes. Springer, Heidelberg (1991)MATHGoogle Scholar
  12. 12.
    Maurer, A.: Bounds for linear multi-task learning. Journal of Machine Learning Research 7, 117–139 (2006)MathSciNetGoogle Scholar
  13. 13.
    Reed, M., Simon, B.: Fourier Analysis, Self-Adjointness, Methods of Mathematical Physics, part II. Academic Press, London (1980)Google Scholar
  14. 14.
    Reed, M., Simon, B.: Functional Analysis. Methods of Mathematical Physics, vol. I. Academic Press, London (1980)MATHGoogle Scholar
  15. 15.
    Thrun, S.: Lifelong Learning Algorithms. In: Thrun, S., Pratt, L. (eds.) Learning to Learn, Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andreas Maurer
    • 1
  1. 1.Adalbertstr. 55München

Personalised recommendations