Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
A result of Vapnik with applications
Discrete Applied Mathematics
An introduction to computational learning theory
An introduction to computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Machine Learning
Uniform approximation by neural networks
Journal of Approximation Theory
A sharp concentration inequality with application
Random Structures & Algorithms
AI Game Programming Wisdom
Generalisation Error Bounds for Sparse Linear Classifiers
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
The Journal of Machine Learning Research
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Structural risk minimization over data-dependent hierarchies
IEEE Transactions on Information Theory
An introduction to boosting and leveraging
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The Journal of Machine Learning Research
On the Importance of Small Coordinate Projections
The Journal of Machine Learning Research
The cross entropy method for classification
ICML '05 Proceedings of the 22nd international conference on Machine learning
Simpler knowledge-based support vector machines
ICML '06 Proceedings of the 23rd international conference on Machine learning
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ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Exact combinatorial bounds on the probability of overfitting for empirical risk minimization
Pattern Recognition and Image Analysis
The Sample Complexity of Dictionary Learning
The Journal of Machine Learning Research
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ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Reverse-Convex programming for sparse image codes
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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Classical statistical learning theory studies the generalisation performance of machine learning algorithms rather indirectly. One of the main detours is that algorithms are studied in terms of the hypothesis class that they draw their hypotheses from. In this paper, motivated by the luckiness framework of Shawe-Taylor et al. (1998), we study learning algorithms more directly and in a way that allows us to exploit the serendipity of the training sample. The main difference to previous approaches lies in the complexity measure; rather than covering all hypotheses in a given hypothesis space it is only necessary to cover the functions which could have been learned using the fixed learning algorithm. We show how the resulting framework relates to the VC, luckiness and compression frameworks. Finally, we present an application of this framework to the maximum margin algorithm for linear classifiers which results in a bound that exploits the margin, the sparsity of the resultant weight vector, and the degree of clustering of the training data in feature space.