# Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise

arXiv: https://arxiv.org/abs/2312.11324 · HTML: https://mlsanity.com/paper/2312.11324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 8 of 8)

- [Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models](https://mlsanity.com/paper/1708.03395/) (2017)
- [Network dismantling](https://mlsanity.com/paper/1603.08883/) (2016)
- [SILVar: Single Index Latent Variable Models](https://mlsanity.com/paper/1705.03536/) (2017)
- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Local Tomography of Large Networks under the Low-Observability Regime](https://mlsanity.com/paper/1805.09081/) (2018)
- [Topology Identification under Spatially Correlated Noise](https://mlsanity.com/paper/2012.04175/) (2020)
- [An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability](https://mlsanity.com/paper/2203.15500/) (2022)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)

## Built on by (most cited first, 1 of 1)

- [Inferring the Graph Structure of Images for Graph Neural Networks](https://mlsanity.com/paper/2509.04677/) (2025)

## Abstract (arXiv)

In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) Partial observability -- time series data is only available over a subset of the nodes; ii) Input noise -- it is correlated across distinct nodes while temporally independent, i.e., it is spatially colored. We present a feasibility condition on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation.