Linear system identifiability from single-cell data

In this brief article, we prove a result on identifiability of a discrete-time linear system from measurements of the mean and the covariance of the state distribution, obtained from population snapshot observations over time. We show that three time points of such measurements are sufficient for unique identifiability. This is in stark contrast to identifiability from time series data, in which case n + 1 measurements are required for identifiability of an n-dimensional system. Robustness of the identifiability is investigated by numerical experiments. The work is motivated by the problem of gene regulatory network inference from single-cell data and will serve as a foundation for the development of modelling algorithms.