Consistency Analysis of Regularization of Coefficient Based on Weak Correlation Sampling

Aiming at the weakly correlated sampling satisfying the strong mixing condition, and the coefficient satisfies the polynomial decay, with the use of the sample operator and the integral operator. The proof of the least squares coefficient regularization algorithm is obtained, and it is concluded that the regularization conditionfor the learning speed of. At the same time, the saturation index of the regularization algorithm based on weak correlation sampling is 2, which shows that the coefficient regularization algorithm has some advantages in learning the smooth function compared with the usual least squares Tikhonov regularization algorithm.