Bayesian Distribution Regression Learning Based Random Multi-scale Kernels

This paper proposes an easily implemented Bayesian distribution regression learning framework based on random multi-scale kernels(RMK-BDR),which applies to distribution regression problems with complex data forms.We introduce a finite-dimensional empirical kernel mean embedding estimation(KME)with the same dimension in the first stage of the distribution regression learning.This method can adaptively select the optimal number of center points according to the sample set.Then,in the second stage multi-scale Gaussian kernels with different scale parameters randomly sampled from a predefined distribution are used as the regression model.Under the Bayesian inference theory,the automatic relevance determination(ARD)priors are added on the linear combination weights of the regression model and the second type of maximum likelihood method are used to obtain the prediction distribution with the sparse solutions.This paper performs the related algorithms experimental analysis based on the simulated data sets and a real data.The experimental results show that,the proposed algorithm RMK-BDR only needs a small number of center points to construct the empirical kernel mean embedding estimation and the satisfactory generalization performance of the regression model can be obtained.At the same time,a series of experimental results verify the effectiveness of the proposed algorithm.