An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness
This addresses a key limitation in network reconstruction for practical scenarios where strictly causal models are inadequate, though it is incremental as it focuses on a specific triangle-free class.
The paper tackles the problem of reconstructing dynamic networks with direct feedthrough terms, proving that consistent reconstruction is generally impossible but presenting a method that either exactly recovers the topology of triangle-free networks or outputs a sparser graph with no false positives.
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by strictly causal transfer functions. However, in many practical scenarios, strictly causal models are not adequate to describe the system and it is necessary to consider models with dynamics that include direct feedthrough terms. In presence of direct feedthroughs, guaranteeing a consistent reconstruction is a more challenging task. Indeed, under no additional assumptions on the network, we prove that, even in the limit of infinite data, any reconstruction method is susceptible to inferring edges that do not exist in the true network (false positives) or not detecting edges that are present in the network (false negative). However, for a class of triangle-free networks introduced in this article, some consistency guarantees can be provided. We present a method that either exactly recovers the topology of a triangle-free network certifying its correctness or outputs a graph that is sparser than the topology of the actual network, specifying that such a graph has no false positives, but there are false negatives.