The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Monotonicity and connectedness in learning systems
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An introduction to support Vector Machines: and other kernel-based learning methods
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AI Game Programming Wisdom
Learning in Neural Networks: Theoretical Foundations
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Quantitatively tight sample complexity bounds
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SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Exact combinatorial bounds on the probability of overfitting for empirical risk minimization
Pattern Recognition and Image Analysis
Combinatorial shell bounds for generalization ability
Pattern Recognition and Image Analysis
Tight combinatorial generalization bounds for threshold conjunction rules
PReMI'11 Proceedings of the 4th international conference on Pattern recognition and machine intelligence
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The paper is concerned with the problem of function approximation on a finite training sample. Generalization ability of an approximation method is characterized by a probability of large deviation of a test sample error from the training sample error. We obtain upper bounds on this probability based on combinatorial inclusion-exclusion techniques and metric properties of a set A of binary error vectors induced by a given approximating family of functions on a finite population. We introduce a notion of connectivity-splitting profile of A; accounting for a connectivity degree q in generalization bounds allows to reduce the bound by the factor exponential in q.