Neural Comput - Learning rates of lq coefficient regularization learning with gaussian kernel.

Tópicos

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Resumo

Regularization is a well-recognized powerful strategy to improve the performance of a learning machine and l(q) regularization schemes with 0 < q < 8 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 < 8. That is, the upper and lower bounds of learning rates for l(q) regularization learning are asymptotically identical for all 0 < q < 8. 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.

Resumo Limpo

regular wellrecogn power strategi improv perform learn machin lq regular scheme q central use known differ q lead differ properti deduc estim say l regular lead smooth estim l regular lead spars estim general capabl lq regular learn vari q worthi investig letter studi problem framework statist learn theori main result show implement lq coeffici regular scheme sampledepend hypothesi space associ gaussian kernel can attain almost optim learn rate q upper lower bound learn rate lq regular learn asymptot ident q find tentat reveal model context choic q might strong impact general capabl perspect q can arbitrarili specifi specifi mere nongener criteria like smooth comput complex sparsiti

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