Detection of Cooperative Interactions in Logistic Regression Models
  An important problem in the field of bioinformatics is to identify
interactive effects among profiled variables for outcome prediction. In this
paper, a logistic regression model with pairwise interactions among a set of
binary covariates is considered. Modeling the structure of the interactions by
a graph, our goal is to recover the interaction graph from independently
identically distributed (i.i.d.) samples of the covariates and the outcome.
  When viewed as a feature selection problem, a simple quantity called
influence is proposed as a measure of the marginal effects of the interaction
terms on the outcome. For the case when the underlying interaction graph is
known to be acyclic, it is shown that a simple algorithm that is based on a
maximum-weight spanning tree with respect to the plug-in estimates of the
influences not only has strong theoretical performance guarantees, but can also
outperform generic feature selection algorithms for recovering the interaction
graph from i.i.d. samples of the covariates and the outcome. Our results can
also be extended to the model that includes both individual effects and
pairwise interactions via the help of an auxiliary covariate.
