# Identification of Low Rank Vector Processes

arXiv: https://arxiv.org/abs/2111.10899 · HTML: https://mlsanity.com/paper/2111.10899/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2021.

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

- [Dealing with collinearity in large-scale linear system identification using Bayesian regularization](https://mlsanity.com/paper/2203.13633/) (2022)
- [Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression](https://mlsanity.com/paper/2302.10959/) (2023)
- [Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections](https://mlsanity.com/paper/2401.07206/) (2024)
- [Modeling and Topology Estimation of Low Rank Dynamical Networks](https://mlsanity.com/paper/2511.06674/) (2025)

## Abstract (arXiv)

We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable. We show that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identification in two steps, one of which can be based on standard algorithms while the other is based on a deterministic least squares fit. Identifiability of the feedback system is analyzed and a unique identifiable structure is characterized. Simulations show that the proposed procedure works well in some simple examples.