Near-optimal selection of parallel inputs in Bayesian experimental design for systems biology

This study concerns the efficient design of experiments in the context Bayesian model selection, and is primarily motivated by applications to systems biology. We introduce a design method to select an informative subset of inputs, each with unit cost, under a given budget constraint. The inputs are applied as interventions to the biological system, either in parallel or in sequence, each time starting from the same initial conditions. The method aims at maximizing a Bayesian information-theoretic objective: the mutual information between models and data. By taking advantage of submodularity, we prove by reduction that our design method is computationally efficient and near-optimal, as it requires only a polynomial number of evaluations of the objective to yield near-optimal value. It follows from the reduction that the constant factor of the introduced approximation dominates all efficient design techniques, unless P=NP. We discuss the main theoretical properties of the method, as well as practical design choices and current limitations of the approach.