A linear reformulation of Boolean optimization problems and its application to the problem of estimating the structure of gene regulation networks

International audienceWe consider the problem of estimating Boolean models of gene regulation networks from few and noisy mea- surements. To this end, we use a representation of Boolean functions as multilinear 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