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arXiv 1406.11112014-06-04math.LOcs.LGcs.LO

PAC学习、VC维度和算术层次

PAC Learning, VC Dimension, and the Arithmetic Hierarchy

Southern Illinois University, Carbondale（南伊利诺伊大学卡本代尔分校）

Wesley Calvert

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摘要：

我们计算出PAC可学习的概念类的索引集是$m$ -完备的$Σ^0_3$，在所有合理形式的概念类的索引集内。考虑的所有概念类都是可计算$Π^0_1$类的可计算枚举，在某种意义上在这里是精确的。这个概念类族足以覆盖所有标准示例，并且还具有PAC可学习性等价于有限VC维的性质。

英文摘要：

We compute that the index set of PAC-learnable concept classes is $m$-complete $Σ^0_3$ within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable $Π^0_1$ classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that PAC learnability is equivalent to finite VC dimension.

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