Study Of Distribution Regression Based On Stochastic Configuration Networks

With the popularity and application of the Internet and the increasing speed and storage capacity of computers,the data obtained in various industries and fields is becoming more and more complex.Obtaining useful information from these data brings great challenges to current data analysis and machine learning.Classical machine learning algorithms usually perform regression or classification learning on a large number of vector training samples.When the input variable becomes a distribution function,that is,regression or classification learning between the distribution functions space and the target variable needs to be established,the conventional algorithm cannot be directly applied.Instead,we need to map the distribution functions to a regenerative kernel Hilbert space by means of the kernel mean embedding method,then apply the ridge regression learning algorithm in this space.This algorithm is defined as kernel mean embedding based ridge regression(MERR).However,due to the selection of the kernel function in the kernel mean embedded ridge regression algorithm,especially the determination of the parameters in the kernel function,it has a significant impact on the final model's effect.Therefore,this paper explores how to choose reasonable kernel function and kernel function parameters,and improves the fitting performance of the model.Our contribution in this paper is to establish the learning theory of a simple,kernel mean embedding ridge regression based on Stochastic Configuration Multi-scale RBF Networks(SCMRBFN-MERR).Firstly,being an important innovation in the field of neural networks,the Stochastic Configuration Networks can optimize the number of nodes of the random neural network while preserving sufficient network performance and generalization ability of the neural network.And it can prevent the emergence of Over-fitting phenomenon,effectively.Secondly,the radial basis function(RBF)has strong nonlinear fitting ability and can map arbitrarily complex nonlinear relations,which is very suitable for nonlinear mapping of distributed regression.Finally,the Stochastic Configuration RBF Networks can be used to randomly optimize the parameters in the kernel function,so that the kernel function can be more adapted to the sample,which provides a method for parameter selection.The comparison experiments of eight sets of experimental data show that the kernel mean embedding ridge regression based on Stochastic Configuration Multi-scale RBF Networks(SCMRBFN-MERR)has better fitting performance than the existing distributed regression algorithm.