Knowledge of the activation patterns of transcription factors (TFs) is fundamental to elucidate the dynamics of gene regulation in response to environmental conditions. Direct experimental measurement of TFs activities is, however, challenging, resulting in a need to develop statistical tools to infer TF activities from mRNA expression levels of target genes. Current models, however, neglect important features of transcriptional regulation, in particular, the combinatorial nature of regulation, which is fundamental for signal integration, is not accounted for.