Generalization of the PAC-model for learning with partial information

Maiorov, Vitaly

doi:10.1007/3-540-62685-9_6

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…The proof is the same as that of Lemma 6 in [25] which treats only the case of W r, l . For any y # R n , we define…”

Section: Pac-learning a Sobolev Target Classmentioning

confidence: 85%

On the Learnability of Rich Function Classes

Maiorov

1999

Journal of Computer and System Sciences

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The probably approximately correct (PAC) model of learning and its extension to real-valued function classes sets a rigorous framework based upon which the complexity of learning a target from a function class using a finite sample can be computed. There is one main restriction, however, that the function class have a finite VC-dimension or scale-sensitive pseudo-dimension. In this paper we present an extension of the PAC framework with which rich function classes with possibly infinite pseudo-dimension may be learned with a finite number of examples and a finite amount of partial information. As an example we consider learning a family of infinite dimensional Sobolev classes.] 1999 Academic Press

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“…The proof is the same as that of Lemma 6 in [25] which treats only the case of W r, l . For any y # R n , we define…”

Section: Pac-learning a Sobolev Target Classmentioning

confidence: 85%

On the Learnability of Rich Function Classes

Maiorov

1999

Journal of Computer and System Sciences

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“…where the left-hand infimum is taken over all affine subsets M n ⊆ X of dimension at most n, and the middle infimum is taken over all continuous affine maps A from affine subsets of X containing W into M n . Finally, we will also have estimates for yet another width, the pseudo-dimensional width which was introduced by Maiorov and Ratsaby [11,12,15] using the concept of pseudo-dimension due to Pollard [13]. Namely, let M = M(T) be a set of real-valued functions x( • ) defined on the set T, and denote Sgn(a) := 1 if a > 0, 0 if a ≤ 0.…”

Section: Introduction Preliminaries and The Main Resultsmentioning

confidence: 99%

Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of s-Monotone Functions in 𝕃_p, 0 < p < 1

Konovalov¹,

Kopotun²

2008

Can. math. bull.

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Abstract. Let B p be the unit ball in L p , 0 < p < 1, and let ∆ s + , s ∈ N, be the set of all s-monotone functions on a finite interval I, i.e., ∆ s + consists of all functions x : I → R such that the divided differences [x; t 0 , . . . , t s ] of order s are nonnegative for all choices of (s + 1) distinct points t 0 , . . . , t s ∈ I. For the classes ∆ s + B p := ∆ s + ∩ B p , we obtain exact orders of Kolmogorov, linear and pseudodimensional widths in the spaces L q , 0 < q < p < 1:

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