Experimental design for system identification of Boolean Control Networks in biology

This study is primarily motivated by biological applications and focuses on the identification of Boolean networks from scarce and noisy data. We consider two Bayesian experimental design scenarios: selection of the observations under a budget, and input design. The goal is to maximize the mutual information between models and data, that is the ultimate statistical upper bound on the identifiability of a system from empirical data. First, we introduce a method to select which components of the state variable to measure under a budget constraint, and at which time points. Our greedy approach takes advantage of the submodularity of the mutual information, and hence requires only a polynomial number of evaluations of the objective to achieve near-optimal designs. Second, we consider the computationally harder task of designing sequences of input interventions, and propose a likelihood-free approximation method. Exact and approximate design solutions are verified with predictive models of genetic regulatory interaction networks in embryonic development.