WebWhen a learning algorithm maximizes the proportion of distinctly correct training examples, the misclassification prob- ability depends not on the VC dimension of the function class, but on a scale-sensitive version of this dimension known as the fat-shattering dimension. WebAug 6, 2024 · Since fat-shattering characterizes uniform convergence (see, e.g., http://homes.dsi.unimi.it/~cesabian/Pubblicazioni/jacm-97b.pdf ), you can get a precise relationship between the Lipschitz constant and the generalization error. Share Cite Improve this answer Follow answered Dec 6, 2024 at 14:29 Aryeh Kontorovich 5,303 28 41 Add a …
MATH 281C: Mathematical Statistics - University of …
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WebThe notion of fat shattering dimension is particularly useful to upper bound the packing number of the class of (i) uniformly bounded monotone functions and (ii) uniformly bound … WebThe fat shattering dimensions measures the complexity of the class Fat some scale . Definition 3.2. Let F [0;1]X. We say that FP -shatters a set X= fx 1;:::;x ng Xif there exist … Webfat-shattering dimension before we proceed to use these quantities. De nition 3. Given FˆRXand a X-valued tree x, we say that Fshatters x at scale , if there exists a R-valued witness tree s such that, 8 2f 1gn;9f 2Fs.t. (f(x t( ) s t( )) t =2 Further we de ne the sequential fat-shattering dimension of a class Fas : fatsq (F) = supfd: 9X ... natural hair care affirmations