Granger causality, based on a vector autoregressive model, is one of the most popular methods for uncovering the temporal dependencies between time series. The application of Granger causality to detect inference among a large number of variables (such as genes) requires a variable selection procedure. To address the lack of informative data, so-called regularization procedures are applied. In this chapter, we review current literature on Granger causality with Lasso regularization techniques for ill-posed problems (i.e. problems with multiple solutions). We discuss regularization procedures for inverse and ill-posed problems and present our recent approaches. These approaches are evaluated in a case study on gene regulatory networks reconstruction.

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