Application Of Least Square Regularized Regression With Markov Chain Samples

With the advance in science and technology,massive data are rapidly generated every day in various areas such as social network data,e-commerce data and medical data.However,the large amount of data makes it very challenging to learn useful infor-mation from the data with current computing resources.Sampling from the original data has been deemed as an effective strategy to handle the problem with big data.Through learning Markov sampling extraction part of data-Markov chain sample,instead of training all of the data,can significantly improve the efficiency of the algorithm.Regularization algorithm is ill-posed problems in learning theory of a powerful tool.Nevertheless,previous known results in this topic are almost based on the assump-tion of i.i.d.inputs.However,independence is a very restrictive concept and this i.i.d.assumption cannot be strictly justified in real-world problems.This paper goes beyond the classical framework by establishing the bound on the learning rates of regulariza-tion regression based on uniformly ergodic Markov chain(u.e.M.c.)samples.Moreover,we give an error analysis for the LSRR algorithm based on u.e.M.c.samples and obtain the optimal learning rate 0(m-1)by adjusting the regularization parameter.In this paper,the experimental results show that the least squares regularized re-gression algorithm on uniformly ergodic Markov chain sample has a better performance than on i.i.d.samples.