  A new method called the aggregated sure independence screening is proposed
for the computational challenges in variable selection of interactions when the
number of explanatory variables is much higher than the number of observations
(i.e., $p\gg n$). In this problem, the two main challenges are the strong
hierarchical restriction and the number of candidates for the main effects and
interactions. If $n$ is a few hundred and $p$ is ten thousand, then the memory
needed for the augmented matrix of the full model is more than $100{\rm GB}$ in
size, beyond the memory capacity of a personal computer. This issue can be
solved by our proposed method but not by our competitors. Two advantages are
that the proposed method can include important interactions even if the related
main effects are weak or absent, and it can be combined with an arbitrary
variable selection method for interactions. The research addresses the main
concern for variable selection of interactions because it makes previous
methods applicable to the case when $p$ is extremely large.
