Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome association (WGA) mapping, remains an open problem in statistical learning. We propose a block-regularized regression model for sparse variable selection in a high-dimensional space where the covariates are linearly ordered, and are possibly subject to local statistical linkages (e.g., block structures) due to spacial or temporal proximity of the features.

Our goal is to identify a small subset of relevant covariates that are not merely from random positions in the ordering, but grouped as contiguous blocks from large number of ordered covariates. Following a typical linear regression framework between the features and the response, our proposed model employs a sparsity-enforcing Laplacian prior for the regression coefficients, augmented by a 1st-order Markovian process along the feature sequence that "activates" the regression coefficients in a coupled fashion. We describe a sampling-based learning algorithm and demonstrate the performance of our method on simulated and biological data for marker identification under WGA.