  We present a procedure for effective estimation of entropy and mutual
information from small-sample data, and apply it to the problem of inferring
high-dimensional gene association networks. Specifically, we develop a
James-Stein-type shrinkage estimator, resulting in a procedure that is highly
efficient statistically as well as computationally. Despite its simplicity, we
show that it outperforms eight other entropy estimation procedures across a
diverse range of sampling scenarios and data-generating models, even in cases
of severe undersampling. We illustrate the approach by analyzing E. coli gene
expression data and computing an entropy-based gene-association network from
gene expression data. A computer program is available that implements the
proposed shrinkage estimator.
