Four Types of Learning Curves
Four Types of Learning Curves
复制标题
四种类型的学习曲线
作者：
S. Amari;Naotake Fujita;S. Shinomoto
如果机器正在学习在给定大量示例的情况下做出决策，则泛化误差(t)定义为机器在使用t个示例进行训练时对新示例做出错误决策的平均概率。泛化误差随着t的增加而减小，曲线(t)称为学习曲线。本文使用贝叶斯方法证明，给定退火近似，学习曲线可以分为四种渐近类型。如果机器具有无噪声的教师信号是确定性的，则当正确的机器参数是唯一的时(1)at-1，当正确的参数集具有有限测度时(2)at-2。如果教师信号是有噪声的，则(3)at-1/2对于确定性机器，(4)c + at-1对于随机机器。
If machines are learning to make decisions given a number of examples, the generalization error (t) is defined as the average probability that an incorrect decision is made for a new example by a machine when trained with t examples. The generalization error decreases as t increases, and the curve (t) is called a learning curve. The present paper uses the Bayesian approach to show that given the annealed approximation, learning curves can be classified into four asymptotic types. If the machine is deterministic with noiseless teacher signals, then (1) at-1 when the correct machine parameter is unique, and (2) at-2 when the set of the correct parameters has a finite measure. If the teacher signals are noisy, then (3) at-1/2 for a deterministic machine, and (4) c + at-1 for a stochastic machine.