A linear reformulation of Boolean optimization problems and structure identification of gene regulation networks

We consider the problem of estimating Boolean models of gene regulation networks from few and noisy measurements. To this end, we use a representation of Boolean functions as multi-affine polynomials, leading to a reformulation of the estimation problem as mixed integer linear program. We then show that the integer constraints can be omitted which improves existing results and reduces the required computing time drastically. Also certain properties of Boolean functions such as unateness or the canalizing property can be included in the linear formulation. The benefits of this reformulation are demonstrated with the help of a large Boolean model of the network of the segment polarity genes in Drosophila melanogaster.