The performance bounds of learning machines based on exponentially strongly mixing sequences
The performance bounds of learning machines based on exponentially strongly mixing sequences
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DOI：
10.1016/j.camwa.2006.07.015
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
Bin Zou;Luoqing Li
中科院分区：
文献类型：
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作者：
Bin Zou;Luoqing Li
泛化性能是机器学习理论研究的主要目的。 Vapnik、Cucker 和 Smale 之前已经表明，基于独立同分布的经验风险。 当样本数量接近无穷大时，序列必须统一收敛于学习机的预期风险。为了研究学习机在依赖输入序列条件下的泛化性能，本文将这些结果扩展到独立同分布的情况。 序列被指数强混合序列取代。我们利用指数强混合序列的伯恩斯坦不等式得到了学习机一致收敛率的上界，并建立了基于指数强混合序列的学习机相对一致收敛率的上界。最后，我们将这些界限与之前的结果进行比较。
Generalization performance is the main purpose of machine learning theoretical research. It has been shown previously by Vapnik, Cucker and Smale that the empirical risks based on an i.i.d. sequence must uniformly converge on their expected risks for learning machines as the number of samples approaches infinity. In order to study the generalization performance of learning machines under the condition of dependent input sequences, this paper extends these results to the case where the i.i.d. sequence is replaced by exponentially strongly mixing sequence. We obtain the bound on the rate of uniform convergence for learning machines by using Bernstein’s inequality for exponentially strongly mixing sequences, and establishing the bound on the rate of relative uniform convergence for learning machines based on exponentially strongly mixing sequence. In the end, we compare these bounds with previous results.