  In many applied fields, such as genomics, different types of data are
collected on the same system, and it is not uncommon that some of these
datasets are subject to censoring as a result of the measurement technologies
used, such as data generated by polymerase chain reactions and flow cytometer.
When the overall objective is that of network inference, at possibly different
levels of a system, information coming from different sources and/or different
steps of the analysis can be integrated into one model with the use of
conditional graphical models. In this paper, we develop a doubly penalized
inferential procedure for a conditional Gaussian graphical model when data can
be subject to censoring. The computational challenges of handling censored data
in high dimensionality are met with the development of an efficient
Expectation-Maximization algorithm, based on approximate calculations of the
moments of truncated Gaussian distributions and on a suitably derived two-step
procedure alternating graphical lasso with a novel block-coordinate
multivariate lasso approach. We evaluate the performance of this approach on an
extensive simulation study and on gene expression data generated by RT-qPCR
technologies, where we are able to integrate network inference, differential
expression detection and data normalization into one model.
