Regularized Least Square Regression with Unbounded and Dependent Sampling
نویسندگان
چکیده
and Applied Analysis 3 Theorem 4. Suppose that the unbounded hypothesis with p > 2 holds, L−r K f ρ ∈ L 2 ρX (X) for some r > 0, and theα-mixing coefficients satisfy a polynomial decay, that is, α l ≤ bl −t for some b > 0 and t > 0. Then, for any 0 < η < 1, one has with confidence 1 − η, fz,γ − ρ ρX = O(m −θmin{(p−2)t/p,1} (logm)1/2) , (13) where θ is given by θ = { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { {
منابع مشابه
Regularized Least Square Regression with Spherical Polynomial Kernels
This article considers regularized least square regression on the sphere. It develops a theoretical analysis of the generalization performances of regularized least square regression algorithm with spherical polynomial kernels. The explicit bounds are derived for the excess risk error. The learning rates depend on the eigenvalues of spherical polynomial integral operators and on the dimension o...
متن کاملConcentration estimates for learning with unbounded sampling
We consider the least-square regularization schemes for regression problems in reproducing kernel Hilbert spaces. The learning algorithm is implemented with samples drawn from unbounded sampling processes. The purpose of this talk is to present concentration estimates for the error based on 2-empirical covering numbers, which improves learning rates in the literature.
متن کاملPerformance Analysis Of Regularized Linear Regression Models For Oxazolines And Oxazoles Derivitive Descriptor Dataset
Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized regression in model choice are introduced, and we distinguish the conditions in which regularized regression develops our ability to discriminate models. We a...
متن کاملReproducing Kernel Banach Spaces with the ℓ1 Norm II: Error Analysis for Regularized Least Square Regression
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we ...
متن کاملConvergence Rate of Coefficient Regularized Kernel-based Learning Algorithms
We investigate machine learning for the least square regression with data dependent hypothesis and coefficient regularization algorithms based on general kernels. We provide some estimates for the learning raters of both regression and classification when the hypothesis spaces are sample dependent. Under a weak condition on the kernels we derive learning error by estimating the rate of some K-f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014