# On estimation and inference in latent structure random graphs

arXiv: https://arxiv.org/abs/1806.01401 · HTML: https://mlsanity.com/paper/1806.01401/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2018.

## Built on by (most cited first, 9 of 9)

- [Learning on Large Graphs using Intersecting Communities](https://mlsanity.com/paper/2405.20724/) (2024)
- [Localization in 1D non-parametric latent space models from pairwise affinities](https://mlsanity.com/paper/2108.03098/) (2021)
- [Matrix factorisation and the interpretation of geodesic distance](https://mlsanity.com/paper/2106.01260/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Implications of sparsity and high triangle density for graph representation learning](https://mlsanity.com/paper/2210.15277/) (2022)
- [Latent structure blockmodels for Bayesian spectral graph clustering](https://mlsanity.com/paper/2107.01734/) (2021)
- [Spectral embedding and the latent geometry of multipartite networks](https://mlsanity.com/paper/2202.03945/) (2022)
- [Semisupervised regression in latent structure networks on unknown manifolds](https://mlsanity.com/paper/2305.02473/) (2023)
- [Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory](https://mlsanity.com/paper/2609.19357/) (2026)

## Abstract (arXiv)

We define a latent structure model (LSM) random graph as a random dot product graph (RDPG) in which the latent position distribution incorporates both probabilistic and geometric constraints, delineated by a family of underlying distributions on some fixed Euclidean space, and a structural support submanifold from which the latent positions for the graph are drawn. For a one-dimensional latent structure model with known structural support, we show how spectral estimates of the latent positions of an RDPG can be used for efficient estimation of the paramaters of the LSM. We describe how to estimate or learn the structural support in cases where it is unknown, with an illustrative focus on graphs with latent positions along the Hardy-Weinberg curve. Finally, we use the latent structure model formulation to test bilateral homology in the Drosophila connectome.