  Accurate gene regulatory networks can be used to explain the emergence of
different phenotypes, disease mechanisms, and other biological functions. Many
methods have been proposed to infer networks from gene expression data but have
been hampered by problems such as low sample size, inaccurate constraints, and
incomplete characterizations of regulatory dynamics. Since expression
regulation is dynamic, time-course data can be used to infer causality, but
these datasets tend to be short or sparsely sampled. In addition, temporal
methods typically assume that the expression of a gene at a time point depends
on the expression of other genes at only the immediately preceding time point,
while other methods include additional time points without any constraints to
account for their temporal distance. These limitations can contribute to
inaccurate networks with many missing and anomalous links.
  We adapted the time-lagged Ordered Lasso, a regularized regression method
with temporal monotonicity constraints, for \textit{de novo} reconstruction. We
also developed a semi-supervised method that embeds prior network information
into the Ordered Lasso to discover novel regulatory dependencies in existing
pathways. We evaluated these approaches on simulated data for a repressilator,
time-course data from past DREAM challenges, and a HeLa cell cycle dataset to
show that they can produce accurate networks subject to the dynamics and
assumptions of the time-lagged Ordered Lasso regression.
