Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of \emph{feature selection} in which only a subset of the predictors $X_t$ are dependent on the multidimensional variate $Y$, and the remainder of the predictors constitute a "noise set" $X_u$ independent of $Y$. Using Monte Carlo simulations, we investigated the relative performance of two methods: thresholding and singular-value decomposition, in combination with stochastic optimization to determine "empirical bounds" on the small-sample accuracy of an asymptotic approximation. We demonstrate utility of the thresholding and SVD feature selection methods to with respect to a recent infant intestinal gene expression and metagenomics dataset. ; Comment: Submitted