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

Lu Liu, Wei Huang and Li Shen

Applied Mathematics and Computation, 2021, vol. 409, issue C

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.

Keywords: Learning performance; Uniformly ergodic Markov chain (u.e.M.c.); Markov observations; Multiscale kernels (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004756

DOI: 10.1016/j.amc.2021.126386

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