| Regression learning with non-identically and non-independently sampling is one of the most important research fields in statistical learning theory,the non-iid samples are drawn from different probability distributions with the same conditional distribution.Internationally renowned scholars S.Smale and D.X.Zhou put forward the Marginal Distribution Converging Assumption,the marginal distributionXρhas no direct relation with the consistency of regression learning,which only may affect the convergence rate.So we guess that the consistence of regression learning algorithms could be proved without the strongly assumption that the marginal distribution sequence converging exponentially in (CS(X))*.Under this assumption,the consistency of the regularization kernel network(RKN)and the coefficient regularization kernel network(CRKN)are proved.Satisfactory capacity independently error bounds and learning rates are derived by the techniques of integral operator.The main contents of this paper are as follows:In Chapter 1,the basic framework and basic knowledges of learning theory are introduced.In Chapter 2,the regularized kernel regression learning is introduced.Mainly includes the research status of reproducing kernel Hilbert space,regularized least-square regression learning algorithms and coefficient regularized learning algorithms.The main contents of this paper are as well as basic theorems and lemmas.In Chapter 3,regression learning with non-identically and non-independently sampling is introduced.The set of random sequence satisfies a strongly mixing condition and theα-mixing coefficients satisfy a polynomial decay,satisfactory capacity independently error bounds and learning rates are derived by the techniques of integral operator.In Chapter 4,the quantile regression learning is introduced.We present the research progress of the learning algorithm.Mainly includes that analysis of ε-insensitive quantile learning,the objective function of the algorithm is given,and the algorithm is preliminary analysis.However,there are some difficulties in the estimation of the difference between the objective function and the quantile function.At present,there is no error analysis and learning rate.In Chapter 5,we summarize the whole thesis and look forward to the future work. |
