  Modern bio-technologies have produced a vast amount of high-throughput data
with the number of predictors far greater than the sample size. In order to
identify more novel biomarkers and understand biological mechanisms, it is
vital to detect signals weakly associated with outcomes among
ultrahigh-dimensional predictors. However, existing screening methods, which
typically ignore correlation information, are likely to miss these weak
signals. By incorporating the inter-feature dependence, we propose a
covariance-insured screening methodology to identify predictors that are
jointly informative but only marginally weakly associated with outcomes. The
validity of the method is examined via extensive simulations and real data
studies for selecting potential genetic factors related to the onset of cancer.
