# A local direct method for module identification in dynamic networks with correlated noise

arXiv: https://arxiv.org/abs/1908.00976 · HTML: https://mlsanity.com/paper/1908.00976/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [A scalable multi-step least squares method for network identification with unknown disturbance topology](https://mlsanity.com/paper/2106.07548/) (2021)
- [Dealing with collinearity in large-scale linear system identification using Bayesian regularization](https://mlsanity.com/paper/2203.13633/) (2022)
- [Learning linear modules in a dynamic network with missing node observations](https://mlsanity.com/paper/2208.10995/) (2022)
- [Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression](https://mlsanity.com/paper/2302.10959/) (2023)

## Abstract (arXiv)

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes.