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Learning performance of regularized regression with multiscale kernels based on Markov observations

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  • Liu, Lu
  • Huang, Wei
  • Shen, Li

Abstract

We analyze a least square regularized regression (LSRR) problem with multiscale kernels on the assumption that observations are subject to be non-independent and identically distributed, such as uniformly ergodic Markov chain (u.e.M.c.) observations. Unlike some existing known analysis for non-i.i.d. observations, we establish error bound on the learning performance according to the complexity of hypothesis spaces with the u.e.M.c. observations, and also derive the learning rate of the multiscale LSRR (i.e., MLSRR) problem with the u.e.M.c. observations, which is with the order of O(m−1). The Markov observing algorithm with MLSRR has also been proposed to generate the u.e.M.c. observations for handling nonflat objective function approximation problem, and then we provide empirical evaluations on simulation dataset and UCI repository to compare the learning performance of MLSRR algorithm with u.e.M.c. observations and i.i.d. observations.

Suggested Citation

  • Liu, Lu & Huang, Wei & Shen, Li, 2021. "Learning performance of regularized regression with multiscale kernels based on Markov observations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004756
    DOI: 10.1016/j.amc.2021.126386
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    References listed on IDEAS

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    1. Yong-Li Xu & Di-Rong Chen & Han-Xiong Li, 2013. "Least Square Regularized Regression for Multitask Learning," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    2. Steinwart, Ingo & Hush, Don & Scovel, Clint, 2009. "Learning from dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 175-194, January.
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