Title :
Covering numbers for real-valued function classes
Author :
Bartlett, P.L. ; Kulkarni, S.R. ; Posner, S.E.
Author_Institution :
Dept. of Syst. Eng., Australian Nat. Univ., Canberra, ACT, Australia
fDate :
9/1/1997 12:00:00 AM
Abstract :
We find tight upper and lower bounds on the growth rate for the covering numbers of functions of bounded variation in the L1 metric in terms of all the relevant constants. We also find upper and lower bounds on covering numbers for general function classes over the family of L1(dP) metrics in terms of a scale-sensitive combinatorial dimension of the function class
Keywords :
combinatorial mathematics; entropy; functions; information theory; ℒ1 metric; ℒ1(dP) metrics; covering numbers; general function classes; growth rate; lower bounds; real-valued function classes; scale-sensitive combinatorial dimension; upper bounds; Atmosphere; Cyclic redundancy check; Entropy; Fourier transforms; Mathematics; Polynomials; Sampling methods; Virtual colonoscopy;
Journal_Title :
Information Theory, IEEE Transactions on
