Distributed learning and distribution regression of coefficient regularization

In this paper, we study the distributed learning algorithm and the distribution regression problem of coefficient regularization for Mercer kernels. By utilizing divided-and-conquer approach, we partition a data set into disjoint data subsets for different learning machines, and get the global estimator from local estimators. By using second order decomposition on the difference of operator inverse and properties of trace operator, we show that under some priori conditions of regression function, the result of distributed learning algorithm is as good as that in single batch data algorithm. On the other hand, we give a learning rate of distribution regression problem under the coefficient regularization scheme by using similar operator methods. We find that our learning scheme performs well when the regression function has stronger regularity. And we can see the deep relation of these two different problems.