Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables most active. Variable activity in BART usually measured by counting the number times a tree splits for each variable. Such one-way counts have advantage fast computations. Despite their convenience, s...

Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped stochastic variable selection, are known to also adapt the unknown intrinsic dimension sparse true function. But it remains unclear if such offer selection consistency, that is, subset i...