  Graphical lasso is one of the most used estimators for inferring genetic
networks. Despite its diffusion, there are several fields in applied research
where the limits of detection of modern measurement technologies make the use
of this estimator theoretically unfounded, even when the assumption of a
multivariate Gaussian distribution is satisfied. Typical examples are data
generated by polymerase chain reactions and flow cytometer. The combination of
censoring and high-dimensionality make inference of the underlying genetic
networks from these data very challenging. In this paper we propose an
$\ell_1$-penalized Gaussian graphical model for censored data and derive two
EM-like algorithms for inference. By an extensive simulation study, we evaluate
the computational efficiency of the proposed algorithms and show that our
proposal overcomes existing competitors when censored data are available. We
apply the proposed method to gene expression data coming from microfluidic
RT-qPCR technology in order to make inference on the regulatory mechanisms of
blood development.
