Se p 20 02 Entropy and the Combinatorial Dimension
نویسنده
چکیده
We solve Talagrand’s entropy problem: the L2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley’s theorem on classes of {0, 1}valued functions, for which the shattering dimension is the VapnikChervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a number of consequences, including the optimal Elton’s Theorem and estimates on the uniform central limit theorem in the real valued case.
منابع مشابه
Geometric parameters in Learning Theory
3 Uniform measures of complexity 12 3.1 Metric entropy and the combinatorial dimension . . . . . . . . . 12 3.1.1 Binary valued classes . . . . . . . . . . . . . . . . . . . . . 13 3.1.2 Real valued classes . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Random averages and the combinatorial dimension . . . . . . . . 17 3.3 Phase transitions in GC classes . . . . . . . . . . . . . . . . . . ...
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