# Enhanced graph-learning schemes driven by similar distributions of motifs

arXiv: https://arxiv.org/abs/2207.04747 · HTML: https://mlsanity.com/paper/2207.04747/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2022.

## Built on by (most cited first, 11 of 11)

- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [Joint graph learning from Gaussian observations in the presence of hidden nodes](https://mlsanity.com/paper/2212.01816/) (2022)
- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [Windowed Fourier Analysis for Signal Processing on Graph Bundles](https://mlsanity.com/paper/2302.05592/) (2023)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Non-negative DAG Learning from Time-Series Data](https://mlsanity.com/paper/2512.07267/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of motifs of the unknown graph to enhance the inference of classical Gaussian graphical models. Dealing with the density of motifs directly constitutes a challenging combinatorial task. However, we note that if two graphs have similar motif densities, one can show that the expected value of a polynomial applied to their empirical spectral distributions will be similar. Guided by this, we first assume that we have a reference graph that is related to the sought graph (in the sense of having similar motif densities) and then, we exploit this relation by incorporating a similarity constraint and a regularization term in the network topology inference optimization problem. The (non-)convexity of the optimization problem is discussed and a computational efficient alternating majorization-minimization algorithm is designed. We assess the performance of the proposed method through exhaustive numerical experiments where different constraints are considered and compared against popular baselines algorithms on both synthetic and real-world datasets.