Matches in SemOpenAlex for { <https://semopenalex.org/work/W4249207878> ?p ?o ?g. }
Showing items 1 to 96 of
96
with 100 items per page.
- W4249207878 endingPage "148" @default.
- W4249207878 startingPage "131" @default.
- W4249207878 abstract "The Vapnik-Chervonenkis (V-C) dimension is an important combinatorial tool in the analysis of learning problems in the PAC framework. For polynomial learnability, we seek upper bounds on the V-C dimension that are polynomial in the syntactic complexity of concepts. Such upper bounds are automatic for discrete concept classes, but hitherto little has been known about what general conditions guarantee polynomial bounds on V-C dimension for classes in which concepts and examples are represented by tuples of real numbers. In this paper, we show that for two general kinds of concept class the V-C dimension is polynomially bounded in the number of real numbers used to define a problem instance. One is classes where the criterion for membership of an instance in a concept can be expressed as a formula (in the first-order theory of the reals) with fixed quantification depth and exponentially-bounded length, whose atomic predicates are polynomial inequalities of exponentially-bounded degree. The other is classes where containment of an instance in a concept is testable in polynomial time, assuming we may compute standard arithmetic operations on reals exactly in constant time. Our results show that in the continuous case, as in the discrete, the real barrier to efficient learning in the Occam sense is complexity-theoretic and not information-theoretic. We present examples to show how these results apply to concept classes defined by geometrical figures and neural nets, and derive polynomial bounds on the V-C dimension for these classes." @default.
- W4249207878 created "2022-05-12" @default.
- W4249207878 creator A5067662147 @default.
- W4249207878 creator A5090122841 @default.
- W4249207878 date "1995-01-01" @default.
- W4249207878 modified "2023-09-26" @default.
- W4249207878 title "Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers" @default.
- W4249207878 cites W1977957682 @default.
- W4249207878 cites W1991581432 @default.
- W4249207878 cites W1991813962 @default.
- W4249207878 cites W1995002436 @default.
- W4249207878 cites W2031585281 @default.
- W4249207878 cites W2042132284 @default.
- W4249207878 cites W2044850435 @default.
- W4249207878 cites W2045313701 @default.
- W4249207878 cites W2046907549 @default.
- W4249207878 cites W2058309331 @default.
- W4249207878 cites W2059985428 @default.
- W4249207878 cites W2062567923 @default.
- W4249207878 cites W2068589781 @default.
- W4249207878 cites W2070902649 @default.
- W4249207878 cites W2122735222 @default.
- W4249207878 cites W2154952480 @default.
- W4249207878 cites W2165758113 @default.
- W4249207878 cites W4238284510 @default.
- W4249207878 cites W4238893454 @default.
- W4249207878 doi "https://doi.org/10.1007/bf00993408" @default.
- W4249207878 hasPublicationYear "1995" @default.
- W4249207878 type Work @default.
- W4249207878 citedByCount "42" @default.
- W4249207878 countsByYear W42492078782012 @default.
- W4249207878 countsByYear W42492078782014 @default.
- W4249207878 countsByYear W42492078782016 @default.
- W4249207878 countsByYear W42492078782017 @default.
- W4249207878 countsByYear W42492078782018 @default.
- W4249207878 countsByYear W42492078782019 @default.
- W4249207878 countsByYear W42492078782020 @default.
- W4249207878 countsByYear W42492078782021 @default.
- W4249207878 countsByYear W42492078782022 @default.
- W4249207878 countsByYear W42492078782023 @default.
- W4249207878 crossrefType "journal-article" @default.
- W4249207878 hasAuthorship W4249207878A5067662147 @default.
- W4249207878 hasAuthorship W4249207878A5090122841 @default.
- W4249207878 hasBestOaLocation W42492078781 @default.
- W4249207878 hasConcept C114614502 @default.
- W4249207878 hasConcept C118615104 @default.
- W4249207878 hasConcept C118930307 @default.
- W4249207878 hasConcept C119322782 @default.
- W4249207878 hasConcept C134306372 @default.
- W4249207878 hasConcept C154945302 @default.
- W4249207878 hasConcept C165464430 @default.
- W4249207878 hasConcept C2776013622 @default.
- W4249207878 hasConcept C2777723229 @default.
- W4249207878 hasConcept C311688 @default.
- W4249207878 hasConcept C33676613 @default.
- W4249207878 hasConcept C33923547 @default.
- W4249207878 hasConcept C34388435 @default.
- W4249207878 hasConcept C39637292 @default.
- W4249207878 hasConcept C41008148 @default.
- W4249207878 hasConcept C90119067 @default.
- W4249207878 hasConceptScore W4249207878C114614502 @default.
- W4249207878 hasConceptScore W4249207878C118615104 @default.
- W4249207878 hasConceptScore W4249207878C118930307 @default.
- W4249207878 hasConceptScore W4249207878C119322782 @default.
- W4249207878 hasConceptScore W4249207878C134306372 @default.
- W4249207878 hasConceptScore W4249207878C154945302 @default.
- W4249207878 hasConceptScore W4249207878C165464430 @default.
- W4249207878 hasConceptScore W4249207878C2776013622 @default.
- W4249207878 hasConceptScore W4249207878C2777723229 @default.
- W4249207878 hasConceptScore W4249207878C311688 @default.
- W4249207878 hasConceptScore W4249207878C33676613 @default.
- W4249207878 hasConceptScore W4249207878C33923547 @default.
- W4249207878 hasConceptScore W4249207878C34388435 @default.
- W4249207878 hasConceptScore W4249207878C39637292 @default.
- W4249207878 hasConceptScore W4249207878C41008148 @default.
- W4249207878 hasConceptScore W4249207878C90119067 @default.
- W4249207878 hasIssue "2-3" @default.
- W4249207878 hasLocation W42492078781 @default.
- W4249207878 hasOpenAccess W4249207878 @default.
- W4249207878 hasPrimaryLocation W42492078781 @default.
- W4249207878 hasRelatedWork W1504200807 @default.
- W4249207878 hasRelatedWork W1606810574 @default.
- W4249207878 hasRelatedWork W1978343600 @default.
- W4249207878 hasRelatedWork W2019671617 @default.
- W4249207878 hasRelatedWork W2158154629 @default.
- W4249207878 hasRelatedWork W2170520833 @default.
- W4249207878 hasRelatedWork W2394942112 @default.
- W4249207878 hasRelatedWork W2798907744 @default.
- W4249207878 hasRelatedWork W3098927428 @default.
- W4249207878 hasRelatedWork W4249207878 @default.
- W4249207878 hasVolume "18" @default.
- W4249207878 isParatext "false" @default.
- W4249207878 isRetracted "false" @default.
- W4249207878 workType "article" @default.