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The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space 被引量:16
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作者 HA Minghu LI Yan +1 位作者 LI Jia TIAN Dazeng 《Science in China(Series F)》 2006年第3期372-385,共14页
Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and varianc... Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev's inequality and the Khinchine's Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given. 展开更多
关键词 Sugeno measure the empirical risk minimization principle the key theorem the bounds on the rate of uniform convergence.
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