title: Learning rates of lq coefficient regularization learning with gaussian kernel.
abstract: Regularization is a well-recognized powerful strategy to improve the performance of a learning machine and l(q) regularization schemes with 0 < q < ∞ are central in use. It is known that different q leads to different properties of the deduced estimators, say, l(2) regularization leads to a smooth estimator, while l(1) regularization leads to a sparse estimator. Then how the generalization capability of l(q) regularization learning varies with q is worthy of investigation. In this letter, we study this problem in the framework of statistical learning theory. Our main results show that implementing l(q) coefficient regularization schemes in the sample-dependent hypothesis space associated with a gaussian kernel can attain the same almost optimal learning rates for all 0 < q < ∞. That is, the upper and lower bounds of learning rates for l(q) regularization learning are asymptotically identical for all 0 < q < ∞. Our finding tentatively reveals that in some modeling contexts, the choice of q might not have a strong impact on the generalization capability. From this perspective, q can be arbitrarily specified, or specified merely by other nongeneralization criteria like smoothness, computational complexity or sparsity.
authors: Institute for Information and System Sciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, P.R.C. sblin1983@gmail.com.
authors: Shaobo
authors: S
authors: Lin
authors: Jinshan
authors: J
authors: Zeng
authors: Jian
authors: J
authors: Fang
authors: Zongben
authors: Z
authors: Xu
mesh_terms: D001185:Artificial Intelligence; D006801:Humans; D007858:Learning / Q000502:physiology*; D016011:Normal Distribution; D012815:Signal Processing, Computer-Assisted