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DROP Learning

DROP Learning extracts the Agnostic Learning Bounds under Empirical Loss Minimization Schemes.

Component Packages

  • Bound DROP Learning Bound Package implements Covering Numbers, Concentration, Lipschitz Bounds.

  • Kernel DROP Learning Kernel Package implements the Statistical Learning Banach Mercer Kernels.

  • Regularization DROP Learning Kernel Regularization implements the Statistical Learning Empirical Loss Regularizer.

  • Rx -> R1 DROP Learning Kernel Regularization Rx -> R1 the Suite of Statistical Learning Empirical Loss Penalizers.

  • SVM DROP Learning SVM implements the Kernel SVM Decision Function Operator.

References

  • Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform Convergence, and Learnability Journal of Association of Computational Machinery 44 (4) 615-631

  • Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations Cambridge University Press Cambridge, UK

  • Ash, R. (1965): Information Theory Inter-science New York

  • Bartlett, P. L., P. Long, and R. C. Williamson (1996): Fat-shattering and the Learnability of Real Valued Functions Journal of Computational System Science 52 (3) 434-452

  • Boucheron, S., G. Lugosi, and P. Massart (2003): Concentration Inequalities Using the Entropy Method Annals of Probability 31 1583-1614

  • Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operator in Banach Spaces Annals of the Fourier Institute 35 (3) 79-118

  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators Cambridge University Press Cambridge UK

  • Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and Approximation Numbers of Operators Journal of Approximation Theory 49 219-237

  • Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): Towards Efficient Agnostic Learning Machine Learning 17 (2) 115-141

  • Konig, H. (1986): Eigenvalue Distribution of Compact Operators Birkhauser Basel, Switzerland

  • Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with Squared Loss IEEE Transactions on Information Theory 44 1974-1980

  • Lugosi, G. (2002): Pattern Classifi�cation and Learning Theory, in: L. Gyor�, editor, Principles of Non-parametric Learning Springer Wien 5-62

  • Shawe-Taylor, J., P. L. Bartlett, R. C. Williamson, and M. Anthony (1996): A Framework for Structural Risk Minimization, in: Proceedings of the 9th Annual Conference on Computational Learning Theory ACM New York 68-76

  • Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex Combinations and mlps, in: Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans - editors MIT Press Cambridge, MA

  • Vapnik, V., and A. Chervonenkis (1974): Theory of Pattern Recognition (in Russian) Nauka Moscow USSR

  • Vapnik, V. (1995): The Nature of Statistical Learning Springer-Verlag New York

  • Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory ACM New York

DROP Specifications