  There is a renewed interest in polynomial regression in the form of
identifying influential interactions between features. In many settings, this
takes place in a high-dimensional model, making the number of interactions
unwieldy or computationally infeasible. Furthermore, it is difficult to analyze
such spaces directly as they are often highly correlated. Standard feature
selection issues remain such as how to determine a final model which
generalizes well. This paper solves these problems with a sequential algorithm
called Revisiting Alpha-Investing (RAI). RAI is motivated by the principle of
marginality and searches the feature-space of higher-order interactions by
greedily building upon lower-order terms. RAI controls a notion of false
rejections and comes with a performance guarantee relative to the best-subset
model. This ensures that signal is identified while providing a valid stopping
criterion to prevent over-selection. We apply RAI in a novel setting over a
family of regressions in order to select gene-specific interaction models for
differential expression profiling.
