| 统计可学习理论的几个问题 |
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| 引用本文： | 段志生,黄琳.统计可学习理论的几个问题[J].北京大学学报(自然科学版),2000,36(3):347-357. |
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| 作者姓名： | 段志生 黄琳 |
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| 作者单位： | 北京大学系统与控制中心，力学与工程科学系，北京，100871 |
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| 摘 要： | 证明了如果函数族F具有UCEM性质，那么F是完全有界的。此外如果F关于概率族P是PAC可学习的或具有UCEM性质，则F关于P的闭包也具有同样的性质。构造了一个非多项式可学习的例子，说明了PAC可学习的概念族可以有任意的复杂性。最后讨论了概念族C关于概率族P及其凸包C(P)的可学习性，并纠正了文1]的一点错误。
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| 关 键 词： | UCEM性质 PAC可学习 PUAC可学习 完全有界 |
| 收稿时间： | 1999-04-07 |
On Several Problems of Statistical Learning Theory |
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| DUAN Zhisheng,HUANG Lin.On Several Problems of Statistical Learning Theory[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2000,36(3):347-357. |
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| Authors: | DUAN Zhisheng HUANG Lin |
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| Institution: | Center for Systems and Control Department of Mechanics and Engineering Science, Peking University, Beijing, 100871 |
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| Abstract: | It is proved that the UCEM property of a family of measurable functions F implies that F is totally bounded;the UCEMUP property and PAC learnability still preserve when the family of probabilities is replaced by its closure.And a concept class C is constructed to show that every PAC algorithm of C would require a super\|polynomial number of samples.Finally,the learnability of a concept class C with respect to the probability measures P and its convex hull C(P) is discussed and a mistake of \ is corrected. |
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| Keywords: | UCEM property PAC learnability PUAC learnability totally bounded |
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