Network inference: from theory to applications

Abstract: Knowing exactly how components are interconnected can help detect and correct faults in large-scale systems, such as power grids (lost of transmission lines), internet (loss of servers) and biological systems (diseases). The first part of this talk defines linear dynamical networks, called dynamical structure functions (DSF), in contrast with transfer functions (TF) that define input/output maps. It discusses challenges in identifying DSF, which include complex interconnections, feedbacks, noise, and a possible large number of unmeasured states. It also explains the different levels of complexity that state-space, DSF and TF encode. The talk then presents conditions for identifiability of DFS with either deterministic or noise inputs. In the second part, the talk outlines a practical algorithm to use low informative biological data to infer dynamical networks and to study the effect of perturbations. In particular, it focuses on wide-spread perturbations that target unknown components of the system. The talk describes a simple yet powerful network inference tool followed by a method for network differentiation, where it detects the effects of perturbations in large scale-systems. The method is based on the nu-gap, a control engineering tool that measures the distance between linear models. Through real data on gene expression of circadian rhythms in a plant (Arabidopsis), it shows how perturbations impact certain links in the network, which can then be captured by differences between LTIs with the ν-gap.