کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4608702 1338373 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Covering numbers of Gaussian reproducing kernel Hilbert spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Covering numbers of Gaussian reproducing kernel Hilbert spaces
چکیده انگلیسی

Metric entropy quantities, like covering numbers or entropy numbers, and positive definite kernels play an important role in mathematical learning theory. Using smoothness properties of the Fourier transform of the kernels, Zhou [D.-X. Zhou, The covering number in learning theory, J. Complexity 18 (3) (2002) 739–767] proved an upper estimate for the covering numbers of the unit ball of Gaussian reproducing kernel Hilbert spaces (RKHSs), considered as a subset of the space of continuous functions.In this note we determine the exact asymptotic order of these covering numbers, exploiting an explicit description of Gaussian RKHSs via orthonormal bases. We show that Zhou’s estimate is almost sharp (up to a double logarithmic factor), but his conjecture on the correct asymptotic rate is far too optimistic. Moreover we give an application of our entropy results to small deviations of certain smooth Gaussian processes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 27, Issue 5, October 2011, Pages 489–499
نویسندگان
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