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Corrigendum to “Shifting: One-inclusion mistake bounds and sample compression”. (English) Zbl 1201.68103

Summary: H. U. Simon and B. Szörényi have found an error in the proof of Theorem 52 of [B. I. P. Rubinstein, P. L. Barlett and J. H. Rubinstein, “Shifting: One-inclusion mistake bounds and sample compression”, ibid. 75, No. 1, 37–59 (2009; Zbl 1158.68452)]. In this note we provide a corrected proof of a slightly weakened version of this theorem. Our new bound on the density of one-inclusion hypergraphs is again in terms of the capacity of the multilabel concept class. H. U. Simon and B. Szörényi have recently proved an alternate result in [“One-inclusion hypergraph density revisited”, Inf. Process. Lett. 110, No. 8–9, 341–344 (2010; Zbl 1197.68063)].

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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References:

[1] Ben-David, Shai; Cesa-Bianchi, Nicolò; Haussler, David; Long, Philip M., Characterizations of learnability for classes of \(\{0, \ldots, n \}\)-valued functions, J. comput. system sci., 50, 1, 74-86, (1995) · Zbl 0827.68095
[2] Haussler, David, Sphere packing numbers for subsets of the Boolean n-cube with bounded vapnik – chervonenkis dimension, J. combin. theory ser. A, 69, 2, 217-232, (1995) · Zbl 0818.60005
[3] Rubinstein, Benjamin I.P.; Bartlett, Peter L.; Rubinstein, J. Hyam, Shifting: one-inclusion mistake bounds and sample compression, J. comput. system sci., 75, 1, 37-59, (2009) · Zbl 1158.68452
[4] Hans Ulrich Simon, Balázs Szörényi, One-inclusion hypergraph density revisited, 2009, submitted for publication
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