Approximate location of relevant variables under the crossover distribution Original Research Article

Searching for genes involved in traits (e.g. diseases), based on genetic data, is considered from a computational learning perspective. This leads to the problem of learning relevant variables of probabilistic Boolean functions by function value queries for many assignments. These assignments are sampled from a certain class of distributions that generalizes the uniform distribution, and is motivated by the mechanism of inheritance of genetic material. The Fourier transform of Boolean functions is applied to translate the problem into a conceptually simpler one: searching for local extrema of certain functions of observables. We work out the combinatorial structure of this approach and illustrate its potential use.