数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 905-916.

• 论文 • 上一篇    下一篇

压缩回归学习算法的泛化界

曹飞龙|戴腾辉|张永全   

  1. 中国计量学院 数学与信息科学系 杭州 |310018
  • 收稿日期:2012-07-21 修回日期:2013-11-27 出版日期:2014-08-25 发布日期:2014-08-25
  • 基金资助:

    国家自然科学基金(61272023, 91330118, 11301494)资助.

Generalization Bounds of Compressed Regression Learning Algorithm

 CAO Fei-Long, DAI Teng-Hui, ZHANG Yong-Quan   

  1. Department of Information and Mathematics Sciences, China Jiliang University, |Hangzhou 310018
  • Received:2012-07-21 Revised:2013-11-27 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    国家自然科学基金(61272023, 91330118, 11301494)资助.

摘要:

研究了压缩最小平方回归学习算法的泛化性问题. 利用随机投影、覆盖数等理论以及概率不等式得到了该学习算法的泛化误差上界. 所获结果表明:压缩学习虽以增大逼近误差的方式降低样本误差, 但其增量是可控的. 此外, 通过压缩学习, 在一定程度上克服了学习过程中所出现的过拟合现象.

关键词: 机器学习, 压缩感知, 回归学习算法, 误差界, 逼近

Abstract:

This paper addresses the generalization performance of compressed least-square regression learning algorithm. A generalization error bound of this algorithm is established by using the random projection and the theory of the covering number. The obtained results show that the compressed learning can reduce the sample error at the price of increasing the approximation error, but the increment can be controlled. In addition,  by using compressed projection, the overfitting problem for the learning algorithm can be overcome to a certain extent.

Key words: Machine learning, Compressed sensing, Regression learning algorithm, Error bound, Approximation

中图分类号: 

  • 41A25