Structural Risk Minimization Over Data-Dependent Hierarchies

By John Shawe-Taylor, Peter L. Bartlett, Robert C. Williamson, Martin H. Anthony. 1998

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Citations in the corpus

Rademacher and Gaussian Complexities: Risk Bounds and Structural Results (2003, background): “…a number of results bounding error in terms of a sample average of a margin error plus a penalty term involving the complexity of the real-valued class (such as covering numbers and fat-shattering dimensions; see Bartlett, 1998, Mason et al., 2000, Schapire et al., 1998, Shawe-Taylor et al., 1998).”
Spectrally-normalized margin bounds for neural networks (2017, background): “The first rigorous generalization bounds for large margin linear classifiers [Shawe-Taylor et al., 1998] required a scale-sensitive complexity analysis of real-valued function classes.”
Generalization in Deep Learning (2017, methodology): “For example, data-dependent bounds with the luckiness framework (Shawe-Taylor et al., 1998; Herbrich and Williamson, 2002) and empirical Rademacher complexity (Koltchinskii and Panchenko, 2000; Bartlett et al.”
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (2003, methodology): “I would recommend the book by Cristianini and Shawe-Taylor (2000) for a reader looking to understand the basics of support vector machines, Learning With Kernels for someone looking for a comprehensive and in-depth treatment of the wide diversity of kernel algorithms, and Learning Kernel Classi ers”
Kernel Matching Pursuit (2002, background): “A related direction to pursue might be to take advantage of the data-dependent structural risk minimization results of Shawe-Taylor et al. (1998).”
The Sample Complexity of Pattern Classification with Neural Networks: The Size of the Weights is More Important than the Size of the Network (1998, background): “The result is essentially the main result in [38], where it was observed that a similar but slightly weaker result follows trivially from the main result in [2].”
Rademacher penalties and structural risk minimization (2001, result): “This resembles the recent work of some other authors on developing more flexible data-driven versions of risk minimization (such as “simple empirical covering” of Buescher and Kumar [28]; “structural risk minimization over data-dependent hierarchies” of Shawe-Taylor, Bartlett, Williamson, and Anthon”
Analysis of a greedy active learning strategy (2004, unknown): “This technique is not specific to active learning, and has been analyzed elsewhere (for instance, [12]).”
PAC-Bayes-Bernstein Inequality for Martingales and its Application to Multiarmed Bandits (2011, methodology): “The PAC-Bayesian analysis was introduced over a decade ago (Shawe-Taylor and Williamson, 1997; Shawe-Taylor et al., 1998; McAllester, 1998; Seeger, 2002) and has since made a significant contribution to the analysis and development of supervised learning methods.”
A Tutorial on Support Vector Machines for Pattern Recognition (1998, background): “On the other hand, it is known how to do structural risk minimization for systems where the structure does depend on the data (Shawe-Taylor et al., 1996a; Shawe-Taylor et al., 1996b).”
PAC-Bayesian Analysis of Co-clustering and Beyond (2010, methodology): “and build upon preceding works on PAC analysis of Bayesian learning models (Shawe-Taylor et al., 1998; Shawe-Taylor and Williamson, 1997).”