LAUSR

ABSTRACT Recent advances in high-throughput biotechnologies have provided an unprecedented opportunity for biomarker discovery, which, from a statistical point of view, can be cast as a variable selection problem. This problem is challenging due to the high-dimensional and nonlinear nature of omics data and, in general, it suffers three difficulties: (i) an unknown functional form of the nonlinear system, (ii) variable selection consistency, and (iii) high-demanding computation. To circumvent the first difficulty, we employ a feed-forward neural network to approximate the unknown nonlinear function motivated by its universal approximation ability. To circumvent the second difficulty, we conduct structure selection for the neural network, which induces variable selection, by choosing appropriate prior distributions that lead to the consistency of variable selection. To circumvent the third difficulty, we implement the population stochastic approximation Monte Carlo algorithm, a parallel adaptive Markov Chain Monte Carlo algorithm, on the OpenMP platform that provides a linear speedup for the simulation with the number of cores of the computer. The numerical results indicate that the proposed method can work very well for identification of relevant variables for high-dimensional nonlinear systems. The proposed method is successfully applied to identification of the genes that are associated with anticancer drug sensitivities based on the data collected in the cancer cell line encyclopedia study. Supplementary materials for this article are available online.