大数据分析日益成为制约信息技术发展的瓶颈。大数据分析中，并行计算与分布式学习的思想得到广泛的关注。本项目针对面向大数据的正则化分布式回归学习算法，开展如下几个方面的研究。(1)基于正则化核网络的分布式回归学习。包括取系数的q（q=1,2）范数作为正则项的分布式算法、基于一般凸损失函数的正则化分布式学习算法的一致性；采取偏差校正方法来改进正则化核网络在分布式回归中的应用。(2) MEE回归学习的一致性。包括基于非二阶Renyi熵与Shannon熵的最小误差熵算法的收敛性分析；研究将最小误差熵算法用作分布式学习的基础算法的可行性与算法一致性；建立对应于最小误差熵算法的在线学习算法并研究其收敛性。(3) 研究强混合条件下，大数据分成多个子数据集的合理方法，并将其用于核网络分布式算法；提出独立但非同边缘分布的样本假设，在此基础上分析核网络算法的收敛性；进而研究基于非同分布数据的分布式算法的收敛性。

Big data analysis is the key point of the development of information technology. Parallel computing and distributed learning have been wildly applied in big data analysis. This project studies the consistency of distributed regularized regression learning, mainly focuses on the following problems.(1) For coefficient based distributed regularized regression learning. We intend to study the performance of distributed q（q=1,2）norm regularization; to give the mathematical analysis of distributed regularized regression learning with general convex loss functions；we also want to improve the application of regularization kernel network in distributed regression by searching suitable deviation correction methods. (2) The consistence of empirical minimum error entropy(MEE) algorithms for regression learning is considered, including the convergence analysis of MEE algorithms based on the Renyi’s entropy of order or Shannon entropy; the performance of distributed learning using MEE algorithms in an individual machine ; also we intend to construct the online learning associated with MEE algorithms and discuss its convergence. (3) Under the strong mixing condition, we consider how to divide a big data set into some disjoint subsets, to ensure the convergence of distributed kernel network regression algorithms . In other way, we propose a more weak and practical condition for the marginal distribution sequence, and prove the consistence of regularized regression learning based on this kind non-iid sampling, after that we discuss the consistence analysis of distributed regression learning with more general non-iid sampling.