Learning from noisy data: An exactly solvable model.
Learning from noisy data: An exactly solvable model.
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从噪声数据中学习：一个完全可解的模型。
DOI：
10.1103/physreve.52.r4624
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Martin Stechert
中科院分区：
文献类型：
--
作者：
Michael Biehl;Peter Riegler;Martin Stechert
给出了用单层感知器学习线性可分规则的精确结果。我们考虑了训练数据中的两种噪声源：样本输出的随机反转和教师网络中的权重噪声。在这两种情况下，我们研究了在线学习方案，该方案仅利用一系列不相关随机示例中的最新示例来更新学生权重。我们研究了Hebbian学习和在线算法，以达到最优的减少泛化误差。后者实现了泛化误差的渐近衰减，除了前因子外，它与离线方案的误差一致。
Exact results are derived for the learning of a linearly separable rule with a single-layer perceptron. We consider two sources of noise in the training data: the random inversion of the example outputs and weight noise in the teacher network. In both scenarios, we investigate on-line learning schemes that utilize only the latest in a sequence of uncorrelated random examples for an update of the student weights. We study Hebbian learning as well as on-line algorithms that achieve an optimal decrease of the generalization error. The latter realize an asymptotic decay of the generalization error that coincides, apart from prefactors, with the one found for off-line schemes.