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作者单位:Adityanand Guntuboyina (1)
1. Department of Statistics, University of California, 423 Evans Hall, Berkeley, CA, 94720, USA
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Numerical Analysis Analysis
出版者:Springer New York
ISSN:1432-0940
文摘
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it with weaker integral constraints. The existing results can be recovered as special cases of our results. Keywords Covering numbers Packing numbers Convex functions Integral constraints Metric entropy Komogorov \(\epsilon \)-entropy