Sparse identification in chemical master equations for monomolecular reaction networks

This paper considers the identification of kinetic parameters associated with the dynamics of closed biochemical reaction networks. These reaction networks are modeled by chemical master equations in which the reactions and the associated concentrations/populations of species are characterized by probability distributions. The vector of unknown kinetic parameters is usually highly sparse. Using this sparsity, a robust statistical estimation algorithm is developed to estimate the kinetic parameters from stochastic experimental data. The algorithm is based on regularized maximum likelihood estimation and it is shown to be decomposable into a two-stage optimization. The first-stage optimization has a closed-form solution and the second-stage optimization is to maximize sparsity in the kinetic parameter vector with a guaranteed data-fitting error. The second-stage optimization can be solved using off-the-shelf algorithms for constrained ℓ1 minimization.