统计可学习理论的几个问题(英文)

On Several Problems of Statistical Learning Theory

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 P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。

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.