| 泛空间上学习理论的关键定理 |
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| 引用本文： | 高林庆,李鑫,白云超,哈明虎.泛空间上学习理论的关键定理[J].计算机工程与应用,2010,46(31):32-35. |
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| 作者姓名： | 高林庆 李鑫 白云超 哈明虎 |
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| 作者单位： | 河北大学 数学与计算机学院，河北 保定 071002 |
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| 基金项目： | 国家自然科学基金，河北省自然科学基金 |
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| 摘 要： | 给出泛空间上泛随机变量及其分布函数、泛期望和泛方差的定义和性质，证明泛空间上的Chebyshev不等式和Khinchine大数定律；给出泛空间上期望风险泛函、经验风险泛函以及经验风险最小化原则严格一致收敛的定义，证明了泛空间上学习理论的关键定理，把概率空间和可能性测度空间上的学习理论的关键定理统一推广到了泛空间上。
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| 关 键 词： | 泛空间 泛可加测度 经验风险最小化原则 关键定理 |
| 收稿时间： | 2010-1-20 |
| 修稿时间： | 2010-5-26
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Key theorem of learning theory on pan-space |
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| GAO Lin-qing,LI Xin,BAI Yun-chao,HA Ming-hu.Key theorem of learning theory on pan-space[J].Computer Engineering and Applications,2010,46(31):32-35. |
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| Authors: | GAO Lin-qing LI Xin BAI Yun-chao HA Ming-hu |
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| Affiliation: | College of Mathematics & Computer，Hebei University，Baoding，Hebei 071002，China |
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| Abstract: | Some definitions and properties of pan-random variable and its distribution,pan-expectation and pan-variance on pan-space are introduced, and Chebyshev＇ inequality and the Khinchine＇ s strong law of large numbers on pan-space are proved.The definitions of expected risk functional,empirical risk functional and the empirical risk minimization inductive principle on pan-space are proposed,and then the key theorem of learning theory on pan-space is proved.As a result,the key theorems of learning theory on probability measure space and possibility space are unified and extended to pan-space. |
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| Keywords: | pan-space pan additive measure the empirical risk minimization inductive principle the key theorems |
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