The inference of genetic regulatory networks in the Boolean network model is considered. Given a set of measurements, a reasonably good approximation of the Boolean functions attached to each of the n nodes has to be found. Besides the fact that measurements are inherently noisy, another problem to deal with, is the huge amount of irrelevant data, as it is reasonable to assume that each node is only controlled by an unknown subset of all possible nodes. An algorithm is proposed based on previous work of Mossel et al. It proceeds by estimating the Fourier spectra of the unknown Boolean functions. Although it requires slightly more samples than exhaustive search, it provides a significant speed up. It is shown that the running time can be further decreased for functions with low average sensitivity and the so-called nested canalyzing functions which were claimed to be an important class of functions for genetic regulatory networks.
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