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This work studies the maximum possible sign rank ofN×N sign matrices with a given VC dimension d. For d = 1, this maximum is three. For d = 2, this maximum is Θ̃(N1/2). For d > 2, similar but slightly less accurate statements hold. The lower bounds improve over previous ones by Ben-David et al., and the upper bounds are novel. The lower bounds are obtained by probabilistic constructions, using a...
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ژورنال
عنوان ژورنال: The Lancet
سال: 1887
ISSN: 0140-6736
DOI: 10.1016/s0140-6736(02)39093-7