Statistical mechanics calculation of Vapnik-Chervonenkis bounds for perceptrons
Statistical mechanics calculation of Vapnik-Chervonenkis bounds for perceptrons
复制标题
感知器 Vapnik-Chervonenkis 界限的统计力学计算
DOI：
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复制
发表时间：
1993
期刊：
影响因子：
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通讯作者：
Wolfgang Fink
中科院分区：
文献类型：
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作者：
A. Engel;Wolfgang Fink
使用复制技术，我们计算感知器从示例中学习线性可分离布尔分类的学习误差和泛化误差之间的最大可能差异。我们考虑感知器耦合的球形和伊辛约束，研究可学习和不可学习的问题，并研究所考虑的感知器类别仅限于版本空间的特殊情况。将结果与 Vapnik-Chervonenkis 结合及其变体进行比较。我们发现这些界限在对数校正内是渐近紧密的。
Using the replica technique we calculate the maximal possible difference between the learning and the generalization error of a perceptron learning a linearly separable Boolean classification from examples. We consider both spherical and Ising constraints on the couplings of the perceptron, investigate learnable as well as unlearnable problems and study the special situation where the class of perceptrons considered is restricted to the version space. The results are compared with the Vapnik-Chervonenkis bound and variants thereof. We find that these bounds are asymptotically tight within logarithmic corrections.