Flexible multivariate regression density estimation. Issue 20 (8th September 2021) - Dao, Tung; Tran, Minh-Ngoc
Abstract: We consider the problem of flexibly modeling the conditional density of a multivariate response given covariates. We model the regression density function as a mixture of multivariate normals density with the mean vectors and mixing probabilities varying smoothly as functions of the covariates. A fast Variational Bayes fitting algorithm is developed with variable selection and the number of components selection conveniently and efficiently embedded within the variational Bayes update. The proposed method is applicable to high-dimensional settings where the number of potential covariates can be larger than the sample size. The methodology is demonstrated through simulated and real data examples. The R code is available upon request.