Consideration on Singularities in Learning Theory and the Learning Coefficient
Consideration on Singularities in Learning Theory and the Learning Coefficient
复制标题
DOI：
10.3390/e15093714
复制
发表时间：
2013-09-01
期刊：
影响因子：
2.7
通讯作者：
Aoyagi, Miki
中科院分区：
文献类型：
--
作者：
Aoyagi, Miki
我们考虑学习理论中的学习系数，并给出了两种新的方法来获得这些系数在齐次的情况下：一种方法用于寻找一个最深的奇点和一种方法添加变量。在Vandermonde矩阵型奇点的应用中，我们证明了这些方法是有效的。贝叶斯估计中泛化误差的学习系数用来衡量奇异学习模型的学习效率。在数学上，学习系数对应于学习理论中Kullback函数（相对熵）的奇异性的真实的对数正则阈值。
We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy) in learning theory.