  Additive nonparametric regression models provide an attractive tool for
variable selection in high dimensions when the relationship between the
response and predictors is complex. They offer greater flexibility compared to
parametric non-linear regression models and better interpretability and
scalability than the non-parametric regression models. However, achieving
sparsity simultaneously in the number of nonparametric components as well as in
the variables within each nonparametric component poses a stiff computational
challenge. In this article, we develop a novel Bayesian additive regression
model using a combination of hard and soft shrinkages to separately control the
number of additive components and the variables within each component. An
efficient algorithm is developed to select the importance variables and
estimate the interaction network. Excellent performance is obtained in
simulated and real data examples.
