The theoretical guarantees on the identifiability and consistency of the inferred networks primarily hinge on the assumptions made regarding the underlying dynamical system and the nature of the perturbations applied. In the context of the proposed reference fitting approach, identifiability can be achieved under certain conditions, such as the availability of sufficient temporal data and perturbation information.
Specifically, the use of perturbations, such as gene knockouts, helps to resolve ambiguities that arise from snapshot data alone, which often leads to non-identifiability of the interaction matrix ( A ). The regularization term ( R(A) ) plays a crucial role in ensuring that the optimization problem remains well-posed, thus facilitating the recovery of a unique solution for ( A ) under the assumption that the perturbations provide informative constraints on the system dynamics.
Moreover, consistency of the inferred networks can be established through convergence results, which show that as the amount of data increases (both in terms of time points and perturbations), the estimated parameters converge to the true underlying parameters of the system. This is particularly relevant in the context of stochastic dynamics, where the presence of noise can affect the inference process. Theoretical results in the literature suggest that, under appropriate conditions, the reference fitting approach can yield consistent estimates of the interaction network, even in the presence of perturbations.