The degree of approximation of sets in euclidean space using sets with bounded Vapnik-Chervonenkis dimension

Vitaly Maiorov, Joel Ratsaby

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

12 اقتباسات (Scopus)

ملخص

The degree of approximation of infinite-dimensional function classes using finite n-dimensional manifolds has been the subject of a classical field of study in the area of mathematical approximation theory. In Ratsaby and Maiorov (1997), a new quantity ρn(F, Lq) which measures the degree of approximation of a function class F by the best manifold Hn of pseudo-dimension less than or equal to n in the Lq-metric has been introduced. For sets F ⊂ ℝm it is defined as ρn(F, lmq) = infHn. dist(F, Hn), where dist(F, Hn)- supx∈F infy∈Hn ∥x-y∥lmq and Hn ⊂ ℝm is any set of VC-dimension less than or equal to n where n < m. It measures the degree of approximation of the set F by the optimal set Hn ⊂ ℝm of VC-dimension less than or equal to n in the lmq-metric. In this paper we compute ρn(F, lmq) for F being the unit ball Bmp = {x ∈ ℝm : ∥x∥lmp ≤ 1} for any 1 ≤ p, q ≤ ∞, and for F being any subset of the boolean m-cube of size larger than 2, for any 1/2 < γ < 1.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)81-93
عدد الصفحات13
دوريةDiscrete Applied Mathematics
مستوى الصوت86
رقم الإصدار1
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 18 أغسطس 1998
منشور خارجيًانعم

بصمة

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