Machine Learning Embedded Nonparametric Mixture Regression Models

A new class of nonparametric mixture regression models with covariate-varyingmixing proportions is introduced by embedding machine learning methods into mixtures of regressions. Two new methods proposed in this article for the above topic. One method uses the neural network to estimate mixing proportions nonparametrically while using the maximum likelihood estimate to estimate all other component parameters. The new machine learning embedded nonparametric mixture regression models offer more flexible estimation compared to the traditional ones. More importantly, the new hybrid method could better estimate the effects of multivariate covariates nonparametrically than the traditional kernel regression methods that suffer from the well-known “curse of dimensionality". Additionally, we extend the first approach by incorporating the neural network to estimate both mixing proportions and regression component nonparametrically. Two modified EM algorithms are proposed to carry out the estimation procedure for the two new approaches