  When multitudes of features can plausibly be associated with a response, both
privacy considerations and model parsimony suggest grouping them to increase
the predictive power of a regression model. Specifically, the identification of
groups of predictors significantly associated with the response variable eases
further downstream analysis and decision-making. This paper proposes a new data
analysis methodology that utilizes the high-dimensional predictor space to
construct an implicit network with weighted edges %and weights on the edges to
identify significant associations between the response and the predictors.
Using a population model for groups of predictors defined via network-wide
metrics, a new supervised grouping algorithm is proposed to determine the
correct group, with probability tending to one as the sample size diverges to
infinity. For this reason, we establish several theoretical properties of the
estimates of network-wide metrics. A novel model-assisted bootstrap procedure
that substantially decreases computational complexity is developed,
facilitating the assessment of uncertainty in the estimates of network-wide
metrics. The proposed methods account for several challenges that arise in the
high-dimensional data setting, including (i) a large number of predictors, (ii)
uncertainty regarding the true statistical model, and (iii) model selection
variability. The performance of the proposed methods is demonstrated through
numerical experiments, data from sports analytics, and breast cancer data.
