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	1. The Generalization Performance of ERM Algorithm with Strongly Mixing Observations
	Zou Bin,Li Luoqing
	Mathematics 27 November 2007
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	Abstract:The generalization performance is the main purpose of machine learning theoretical research. The previous main bounds describing the generalization ability of ERM algorithm are based on independent and identically distributed (i.i.d.) samples. When the complexity of the given function set is high, the problem of solving the ERM algorithm is usually ill-posed and overfitting may happen. In order to study the generalization performance of ERM algorithm with dependent observations, in this paper we decompose firstly the given function set into different compact subsets, and then we establish the exponential bound on the rate of relative uniform convergence on these compact subsets for ERM algorithm with strongly mixing observations. In the end, we obtain the bounds on the generalization ability of ERM algorithm with strongly mixing observations over the given function set, which extend the previous results of i.i.d. observations to the case of strongly mixing observations.
	TO cite this article:Zou Bin,Li Luoqing. The Generalization Performance of ERM Algorithm with Strongly Mixing Observations[OL].[27 November 2007] http://en.paper.edu.cn/en_releasepaper/content/16592


	2. The Complexity of Function Approximation by the Linear Monte Carlo Methods
	Fang Gensun ,Duan Liqin
	Mathematics 30 April 2007
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	Abstract:We study the information-based complexity of the approximation problem on the multivariate Sobolev space with bounded mixed derivative by the linear Monte Carlo methods. Applying the Maiorov\\\
	TO cite this article:Fang Gensun ,Duan Liqin . The Complexity of Function Approximation by the Linear Monte Carlo Methods[OL].[30 April 2007] http://en.paper.edu.cn/en_releasepaper/content/12609


	3. Optimal Recovery on the Class of Functions with Bounded Mixed Derivative
	Fang Gensun ,Duan Liqin
	Mathematics 27 April 2007
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	Abstract:In this paper, we determine the asymptotic orders of the optimal recovery on the class of functions with bounded mixed derivative by standard information in Sobolev space, and give a nearly optimal algorithm.
	TO cite this article:Fang Gensun ,Duan Liqin . Optimal Recovery on the Class of Functions with Bounded Mixed Derivative[OL].[27 April 2007] http://en.paper.edu.cn/en_releasepaper/content/12537

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