J. Ratsaby and V. Maiorov, "On the value of partial information for learning from examples," Journal of Complexity, vol. 13, no. 4, pp. 509--544, December 1997. Home/Search Document Details and Download
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On the Degree of Approximation by Manifolds of Finite.. - Maiorov, Ratsaby (1999) (1 citation) Self-citation (Ratsaby Maiorov) (Correct)
....by Manifolds of Finite Pseudo Dimension V. Maiorov and J. Ratsaby Abstract. The pseudo dimension of a real valued function class is an extension of the VC dimension for set indicator function classes. A class of finite pseudo dimension possesses a useful statistical smoothness property. In [10] we introduced a nonlinear approximation width # n (F , L q ) n dist(F , L q ) which measures the worstcase approximation error over all functions f by the best manifold of pseudodimension n. In this paper we obtain tight upper and lower bounds on # n (W p , L q ) both being a ....
....it follows that VC(G) n. Using Proposition A2.1(ii) of Blumer et al. we obtain C 1 which is true for all m 0 and n 1. Since A C it follows that A 1, which proves Property 2. Consider some normed space consisting of functions f (x) x X . In Ratsaby and Maiorov [9] [10] we introduced a new nonlinear n width of a subset F of a space defined as # n (F, F) # h#F , 1) runs over all classes in with dim p (H n. Let us compare this width to the classical Alexandrov nonlinear width, see Tikhomirov [11] and DeVore [3] Let ##be a norm on . ....
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J. RATSABY,V.MAIOROV (1997): On the value of partial information for learning from examples. J. Complexity, 13:509--544.
Learning with Side Information: Part I - Kuusela, Ocone (2002) (Correct)
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J. Ratsaby and V. Maiorov, "On the value of partial information for learning from examples," Journal of Complexity, vol. 13, no. 4, pp. 509--544, December 1997.
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