Statistical Science


Peter L. Bartlett, Michael I. Jordan, and Jon D. McAuliffe

Full-text: Open access

Article information

Statist. Sci. Volume 21, Number 3 (2006), 341-346.

First available: 20 December 2006

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Bartlett, Peter L.; Jordan, Michael I.; McAuliffe, Jon D. Comment. Statistical Science 21 (2006), no. 3, 341--346. doi:10.1214/088342306000000475.

Export citation


  • Arora, S., Babai, L., Stern, J. and Sweedyk, Z. (1997). The hardness of approximate optima in lattices, codes, and systems of linear equations. J. Comput. System Sci. 54 317--331.
  • Bach, F. R. and Jordan, M. I. (2002). Kernel independent component analysis. J. Mach. Learn. Res. 3 1--48.
  • Bartlett, P. L. (1998). The sample complexity of pattern classification with neural networks: The size of the weights is more important than the size of the network. IEEE Trans. Inform. Theory 44 525--536.
  • Bartlett, P. L., Bousquet, O. and Mendelson, S. (2005). Local Rademacher complexities. Ann. Statist. 33 1497--1537.
  • Bartlett, P. L., Jordan, M. I. and McAuliffe, J. D. (2006). Convexity, classification and risk bounds. J. Amer. Statist. Assoc. 101 138--156.
  • Bartlett, P. L. and Shawe-Taylor, J. (1999). Generalization performance of support vector machines and other pattern classifiers. In Advances in Kernel Methods---Support Vector Learning (B. Schölkopf, C. J. C. Burges and A. J. Smola, eds.) 43--54. MIT Press, Cambridge, MA.
  • Bartlett, P. L. and Tewari, A. (2004). Sparseness versus estimating conditional probabilities: Some asymptotic results. Learning Theory. Lecture Notes in Comput. Sci. 3120 564--578. Springer, Berlin.
  • Blanchard, G., Bousquet, O. and Massart, P. (2006). Statistical performance of support vector machines. Preprint. Available at publi/BlaBouMas06_rev01.pdf.
  • Borwein, J. M. and Lewis, A. S. (2000). Convex Analysis and Nonlinear Optimization. Springer, New York.
  • Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge Univ. Press.
  • Cook, R. D. (1998). Regression Graphics. Wiley, New York.
  • Fukumizu, K., Bach, F. R. and Jordan, M. I. (2006). Kernel dimension reduction for regression. Technical report, Dept. Statistics, Univ. California, Berkeley.
  • Gretton, A., Herbrich, R., Smola, A., Bousquet, O. and Schölkopf, B. (2005). Kernel methods for measuring independence. J. Mach. Learn. Res. 6 2075--2129.
  • Hiriart-Urruty, J.-B. and Lemaréchal, C. (1993). Convex Analysis and Minimization Algorithms 1, 2. Springer, Berlin.,
  • Leurgans, S. E., Moyeed, R. A. and Silverman, B. (1993). Canonical correlation analysis when the data are curves. J. Roy. Statist. Soc. Ser. B 55 725--740.
  • Mendelson, S. (2002). Geometric parameters of kernel machines. Computational Learning Theory. Lecture Notes in Comput. Sci. 2375 29--43. Springer, Berlin.
  • Schapire, R. E., Freund, Y., Bartlett, P. L. and Lee, W. S. (1998). Boosting the margin: A new explanation for the effectiveness of voting methods. Ann. Statist. 26 1651--1686.
  • Schapire, R. E. and Singer, Y. (1999). Improved boosting algorithms using confidence-rated predictions. Machine Learning 37 297--336.
  • Shawe-Taylor, J., Bartlett, P. L., Williamson, R. C. and Anthony, M. (1998). Structural risk minimization over data-dependent hierarchies. IEEE Trans. Inform. Theory 44 1926--1940.
  • Steinwart, I. (2002). Support vector machines are universally consistent. J. Complexity 18 768--791.
  • Steinwart, I. (2003). Sparseness of support vector machines. J. Mach. Learn. Res. 4 1071--1105.
  • Steinwart, I. (2004). Sparseness of support vector machines---Some asymptotically sharp bounds. In Advances in Neural Information Processing Systems (B. Schölkopf, L. K. Saul and S. Thrun, eds.) 16 1069--1076. MIT Press, Cambridge, MA.
  • Steinwart, I. (2005). Consistency of support vector machines and other regularized kernel machines. IEEE Trans. Inform. Theory 51 128--142.
  • Williamson, R. C., Smola, A. J. and Schölkopf, B. (1999). Entropy numbers, operators and support vector kernels. In Advances in Kernel Methods---Support Vector Learning (B. Schölkopf, C. J. C. Burges and A. J. Smola, eds.) 127--144. MIT Press, Cambridge, MA.
  • Zhang, T. (2004). Statistical behavior and consistency of classification methods based on convex risk minimization. Ann. Statist. 32 56--85.
  • Zhu, J. and Hastie, T. (2005). Kernel logistic regression and the import vector machine. J. Comput. Graph. Statist. 14 185--205.