Predicting {0, 1}-Functions on Randomly Drawn Points

Haussler, David; Littlestone, Nick; Warmuth, Manfred K.

doi:10.1006/inco.1994.1097

Cited by 138 publications

(146 citation statements)

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“…The following expression matches theory a little more closely (Vapnik, 1982;Haussler, Littlestone, & Warmuth, 1994;Talagrand, 1994;Li, Long, & Srinivasan, 2001) emp…”

Section: Adaboost-vcsupporting

confidence: 68%

Untitled

Long

Vega

2003

Machine Learning

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Abstract.We have found one reason why AdaBoost tends not to perform well on gene expression data, and identified simple modifications that improve its ability to find accurate class prediction rules. These modifications appear especially to be needed when there is a strong association between expression profiles and class designations. Cross-validation analysis of six microarray datasets with different characteristics suggests that, suitably modified, boosting provides competitive classification accuracy in general.Sometimes the goal in a microarray analysis is to find a class prediction rule that is not only accurate, but that depends on the level of expression of few genes. Because boosting makes an effort to find genes that are complementary sources of evidence of the correct classification of a tissue sample, it appears especially useful for such gene-efficient class prediction. This appears particularly to be true when there is a strong association between expression profiles and class designations, which is often the case for example when comparing tumor and normal samples.

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“…The following expression matches theory a little more closely (Vapnik, 1982;Haussler, Littlestone, & Warmuth, 1994;Talagrand, 1994;Li, Long, & Srinivasan, 2001) emp…”

Section: Adaboost-vcsupporting

confidence: 68%

Untitled

Long

Vega

2003

Machine Learning

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“…In Section 3 we provide strong minimax lower bounds for the expected probability of error EL(g n ) if the concept class C k is the class of unions of k initial segments. (This class was introduced in (Haussler et al, 1994).) In particular, we show that for every sequence of learning rules {g n }, there exist a distribution-target pair (µ, C) such that if C is the "true" concept, then…”

Section: El(g N )mentioning

confidence: 97%

“…If s(k) = 2 k for all k, then, by definition, V = ∞. Haussler et al (1994) showed that there exists a learning rule such that for all distributiontarget pairs,…”

Section: El(g N )mentioning

confidence: 99%

“…where the last equality follows from direct calculation, which is detailed in the proof of Theorem 3.2 in (Haussler et al, 1994).…”

Section: Bounds For the Expected Probability Of Errormentioning

confidence: 99%

“…(see (Haussler et al, 1994)). Haussler et al (1994) considered minimax lower bounds for the expected cumulative error.…”

Section: Cumulative Error Boundsmentioning

confidence: 99%

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AntosAndrás

LugosiGábor

1998

Machine Learning

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Abstract. Minimax lower bounds for concept learning state, for example, that for each sample size n and learning rule g n , there exists a distribution of the observation X and a concept C to be learnt such that the expected error of g n is at least a constant times V /n, where V is the VC dimension of the concept class. However, these bounds do not tell anything about the rate of decrease of the error for a fixed distribution-concept pair.In this paper we investigate minimax lower bounds in such a (stronger) sense. We show that for several natural k-parameter concept classes, including the class of linear halfspaces, the class of balls, the class of polyhedra with a certain number of faces, and a class of neural networks, for any sequence of learning rules {g n }, there exists a fixed distribution of X and a fixed concept C such that the expected error is larger than a constant times k/n for infinitely many n. We also obtain such strong minimax lower bounds for the tail distribution of the probability of error, which extend the corresponding minimax lower bounds.

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