M. Anthony and J. Shawe-Taylor. A sufficient condition for polynomial distribution-dependent learnability. Discrete Applied Mathematics, 77:1--12, 1997. Home/Search Document Details and Download
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Generalization Ability of Folding Networks - Hammer (Correct)
....bounds on the generalization error cannot exist in these situations. In order to take the specific distribution into account we modify two approaches from the literature which guarantee learnability even for infinite VC dimension but an adequate stratification of the function class instead [2, 27]. These approaches are only formulated for binary valued function classes and consider the generalization error of an algorithm with zero empirical error. We generalize the situation to function classes and arbitrary error such that it applies to folding networks and standard learning algorithms ....
M. Anthony and J. Shawe-Taylor. A sufficient condition for polynomial distribution-dependent learnability. Discrete Applied Mathematics, 77, 1997.
Probabilistic Analysis of Learning in Artificial Neural Networks: .. - Anthony (1997) (10 citations) Self-citation (Anthony) (Correct)
....complexity. Note that this is a stronger conclusion than described above, since it says that all consistent learning algorithms learn and have sample complexity polynomial in the relevant parameters, rather than simply that there is some efficient learning algorithm. Anthony and Shawe Taylor [5, 17] found a further sufficient condition for polynomial sample complexity. Let us say that a sequence fS k g 1 k=1 of subsets of X is non decreasing if for each k, S k S k 1 . For S X, let HjS denote the set of functions in H restricted to domain S. Suppose that X = 1 k=1 S k , where fS k ....
....Let us say that a sequence fS k g 1 k=1 of subsets of X is non decreasing if for each k, S k S k 1 . For S X, let HjS denote the set of functions in H restricted to domain S. Suppose that X = 1 k=1 S k , where fS k g is non decreasing and VCdim(HjS k ) k. Anthony and Shawe Taylor [5, 17] proved that if the probability distribution satisfies 1 Gamma (S k ) O(k Gammafi ) for some fi 0, then any consistent learning algorithm for H learns with respect to and has polynomial sample complexity. For further discussion of distribution dependent learning, we refer the reader ....
M. Anthony and J. Shawe-Taylor. A sufficient condition for polynomial distribution-dependent learnability. To appear, Discrete Applied Mathematics..
Structural Risk Minimization over Data-Dependent Hierarchies - Shawe-Taylor, Bartlett, al. (1998) (12 citations) Self-citation (Shawe-taylor) (Correct)
....in the sense that it can detect, whether the situation which Sontag predicts will sometimes occur, has in fact occurred. Further, it can then exploit this to give better bounds on generalization error. A further motivation can be seen from the distribution dependent learning described in [5], where it is shown that classes which have infinite VC dimension may still be learnable provided that the distribution is sufficiently concentrated on regions of the input space where the set of hypotheses has low VC dimension. The problem with that analysis is that there is no apparent way of ....
Martin Anthony and John Shawe-Taylor, "A sufficient condition for polynomial distribution-dependent learnability," Discrete Applied Mathematics, 77, 1--12, (1997).
A PAC-style Model for Learning from Labeled and Unlabeled Data - Balcan, Blum (2004) (1 citation) (Correct)
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M. Anthony and J. Shawe-Taylor. A sufficient condition for polynomial distribution-dependent learnability. Discrete Applied Mathematics, 77:1--12, 1997.
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