An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness

TL;DR

This paper introduces an algorithm for reconstructing triangle-free linear dynamic networks from observational data, providing correctness guarantees or sparser approximations, especially when direct feedthrough terms are present.

Contribution

The paper proposes a novel reconstruction method with correctness guarantees for triangle-free networks, addressing challenges posed by direct feedthroughs in dynamic systems.

Findings

Exact topology recovery with correctness certification

Sparser network outputs with no false positives

Limitations in reconstructing networks with feedthroughs

Abstract

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.