English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper considers a <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-coefficient regularized regression algorithm with multiscale kernels based on non-independent and identically distributed (non-i.i.d.) samples. The data-dependent hypothesis space with multiscale kernels contains more functions than single-kernel-based data-dependent hypothesis space and therefore has stronger approximation capability. Some concentration inequalities are applied to estimate the sample error and hypothesis error. We establish the bound on the generalization performance of <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-coefficient regularized regression algorithm with multiscale kernels based on uniformly ergodic Markov chain (u.e.M.c.) samples (i.e., <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-CRRMM) under some assumptions on the the input space, the marginal distribution, kernels, and the regression function. We also prove that that the learning rate of our proposed <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-CRRMM algorithm is with the order of <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(m^{-1/3})$ </tex-math></inline-formula> by choosing suitable values of the regularization parameter.

Generalization Performance of $\ell_1$ -Coefficient Regularized Regression With Multiscale Kernels Based on Markov Chain Samples