We propose a variable selection method for high dimensional regression models, which allows for complex, nonlinear, and high-order interactions among variables. The proposed method approximates this complex system using a penalized neural network and selects explanatory variables by measuring their utility in explaining the variance of the response variable. This measurement is based on a novel statistic called Drop-Out-One Loss. The proposed method also allows (overlapping) group variable selection. We prove that the proposed method can select relevant variables and exclude irrelevant variables with probability one as the sample size goes to infinity, which is referred to as the Oracle Property. Experimental results on simulated and real world datasets show the efficiency of our method in terms of variable selection and prediction accuracy.