  Networks pervade many disciplines of science for analyzing complex systems
with interacting components. In particular, this concept is commonly used to
model interactions between genes and identify closely associated genes forming
functional modules. In this paper, we focus on gene group interactions and
infer these interactions using appropriate partial correlations between genes,
that is, the conditional dependencies between genes after removing the
influences of a set of other functionally related genes. We introduce a new
method for estimating group interactions using sparse canonical correlation
analysis (SCCA) coupled with repeated random partition and subsampling of the
gene expression data set. By considering different subsets of genes and ways of
grouping them, our interaction measure can be viewed as an aggregated estimate
of partial correlations of different orders. Our approach is unique in
evaluating conditional dependencies when the correct dependent sets are unknown
or only partially known. As a result, a gene network can be constructed using
the interaction measures as edge weights and gene functional groups can be
inferred as tightly connected communities from the network. Comparisons with
several popular approaches using simulated and real data show our procedure
improves both the statistical significance and biological interpretability of
the results. In addition to achieving considerably lower false positive rates,
our procedure shows better performance in detecting important biological
pathways.
