Often, variables are linked to each other via a network. When such a network structure is known, this knowledge can be incorporated into regularized regression settings via a network penalty term. However, when the type of interaction via the network is unknown (that is, whether connections are of an activating or a repressing type), the connection signs have to be estimated simultaneously with the covariate coefficients. This can be done with an algorithm iterating a connection sign estimation step and a covariate coefficient estimation step. We develop such an algorithm and show detailed simulation results and an application forecasting event times. The algorithm performs well in a variety of settings. We also briefly describe the R-package that we developed for this purpose, which is publicly available.