  Variable selection is a procedure to attain the truly important predictors
from inputs. Complex nonlinear dependencies and strong coupling pose great
challenges for variable selection in high-dimensional data. In addition,
real-world applications have increased demands for interpretability of the
selection process. A pragmatic approach should not only attain the most
predictive covariates, but also provide ample and easy-to-understand grounds
for removing certain covariates. In view of these requirements, this paper puts
forward an approach for transparent and nonlinear variable selection. In order
to transparently decouple information within the input predictors, a three-step
heuristic search is designed, via which the input predictors are grouped into
four subsets: the relevant to be selected, and the uninformative, redundant,
and conditionally independent to be removed. A nonlinear partial correlation
coefficient is introduced to better identify the predictors which have
nonlinear functional dependence with the response. The proposed method is
model-free and the selected subset can be competent input for commonly used
predictive models. Experiments demonstrate the superior performance of the
proposed method against the state-of-the-art baselines in terms of prediction
accuracy and model interpretability.
