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Inferring networks from multiple samples with Consensus LASSO
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International audience. Networks are very useful tools to decipher complex regulatory relationships between genes in an organism. Most work address this issue in the context of i.i.d., treated vs. control or time-series samples. However, many data sets include expression obtained for the same cell type of an organism, but in several conditions. We introduce a novel method for inferring networks from samples obtained in various but related experimental conditions. This approach is based on a double penalization: a first penalty aims at controlling the global sparsity of the solution whilst a second penalty is used to make condition-specific networks consistent with a consensual network. This ''consensual network'' is introduced to represent the dependency structure between genes, which is shared by all conditions. We show that different ''consensus'' penalty can be used, some integrating prior (e.g., bibliographic) knowledge and others that are adapted along the optimization scheme. In all situations, the proposed double penalty can be expressed in terms of a LASSO problem and hence, solved using standard approaches which address quadratic problems with $L_1$-regularization. This approach is combined with a bootstrap approach and is made available in the R package therese. Our proposal is illustrated on simulated datasets and compared with independent estimations and alternative methods. It is also applied to a real dataset to emphasize the differences in regulatory networks before and after a low-calorie diet.
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