Log In Sign Up

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

by   Mihaela Dimovska, et al.

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.


page 1

page 2

page 3

page 4


A Uniformly Consistent Estimator of non-Gaussian Causal Effects Under the k-Triangle-Faithfulness Assumption

Kalisch and Bühlmann (2007) showed that for linear Gaussian models, unde...

(Theta, triangle)-free and (even hole, K_4)-free graphs. Part 2 : bounds on treewidth

A theta is a graph made of three internally vertex-disjoint chordless p...

Proper Orientation Number of Triangle-free Bridgeless Outerplanar Graphs

An orientation of G is a digraph obtained from G by replacing each edge ...

A simple combinatorial algorithm for restricted 2-matchings in subcubic graphs – via half-edges

We consider three variants of the problem of finding a maximum weight re...

Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering

Triangle counting is a fundamental technique in network analysis, that h...

Robustness to fundamental uncertainty in AGI alignment

The AGI alignment problem has a bimodal distribution of outcomes with mo...

Learning sparse linear dynamic networks in a hyper-parameter free setting

We address the issue of estimating the topology and dynamics of sparse l...