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Sample compression, learnability, and the Vapnik-Chervonenkis dimension (1993)  (Make Corrections)  (6 citations)
Sally Floyd, Manfred Warmuth



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Abstract: Within the framework of pac-learning, we explore the learnability of concepts from samples using the paradigm of sample compression schemes. A sample compression scheme of size d for a concept class C ` 2 X consists of a compression function and a reconstruction function. The compression function, given a finite sample set consistent with some concept in C, chooses a subset of k examples as the compression set. The reconstruction function, given a compression set of k examples,... (Update)

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...at most k = O(1) examples and O(log log n) additional bits. The notion of space bounded learning appears, for example, in [AFHM93, Ame94, Ame95, Flo89, FW95]. In addition the set of hypotheses used by A must have a VC dimension of O(1) this implies in particular that VC...

...scheme for a class. We shall discuss several types of compression schemes, in the spirit of the schemes discussed by Floyd and Warmuth [FW95], each of these schemes gives rise to its own parameter) ffl The optimal mistake bound for learning the class online (sometimes called...

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BibTeX entry:   (Update)

Sally Floyd and Manfred Warmuth, "Sample Compression, learnability, and the Vapnik-Chervonenkis Dimension," Machine Learning, 21, 269--304 (1995). http://citeseer.ist.psu.edu/floyd93sample.html   More

@techreport{ floyd93sample,
    author = "Sally Floyd and Manfred Warmuth",
    title = "{SAMPLE} {COMPRESSION}, {LEARNABILITY}, {AND} {THE} {VAPNIK}-{CHERVONENKIS} {DIMENSION}",
    number = "UCSC-CRL-93-13",
    year = "1993",
    url = "citeseer.ist.psu.edu/floyd93sample.html" }
Citations (may not include all citations):
537   A theory of the learnable (context) - Valiant - 1984
465   Learnability and the VapnikChervonenkis Dimension (context) - Blumer, Ehrenfeucht et al. - 1989
454   the Uniform Convergence of Relative Frequencies of Events to.. (context) - Vapnik, Chervonenkis - 1971
273   The strength of weak learnability - Schapire - 1990
180   Boosting a weak learning algorithm by majority - Freund - 1990
151   A General Lower Bound on the Number of Examples Needed for L.. (context) - Ehrenfeucht, Haussler et al. - 1988
117   Estimation of Dependencies based on Empirical Data (context) - Vapnik - 1982
115   the Density of Families of Sets (context) - Sauer
96   Occam's Razor (context) - Blumer, Ehrenfeucht et al. - 1987
29   Learning Nested Differences of Intersection Closed Concept C.. (context) - Haussler, Sloan et al. - 1989
24   Bounding Sample Size with the VapnikChervonenkis Dimension (context) - Shawe-Taylor, Anthony et al. - 1989
21   Relating Data Compression and Learnability - Littlestone, Warmuth - 1986
12   On Space-bounded Learning and the Vapnik-Chervonenkis Dimens.. (context) - Floyd - 1989
5   Complete Range Spaces (context) - Welzl
3   Learning Faster than Promised by the VapnikChervonenkis Dime.. (context) - Blumer, Littlestone - 1989
1   Lower Bounds on PAC learning and the Size of Epsilon-Nets (context) - Haussler, Littlestone et al.
1   Hypothesis Schemas (context) - Littlestone, Schapire
1   Soem New Bounds for Epsilon-Nets (context) - Pach, Woeginger - 1990
1   A Appendix Proof of Theorem 6 (context) - Welzl, Woeginger - 1987



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