# Semisupervised regression in latent structure networks on unknown manifolds

arXiv: https://arxiv.org/abs/2305.02473 · HTML: https://mlsanity.com/paper/2305.02473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 4 May 2023.

## Builds on (most cited first, 11 of 11)

- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Manifold structure in graph embeddings](https://mlsanity.com/paper/2006.05168/) (2020)
- [On estimation and inference in latent structure random graphs](https://mlsanity.com/paper/1806.01401/) (2018)
- [Optimal Change Point Detection and Localization in Sparse Dynamic Networks](https://mlsanity.com/paper/1809.09602/) (2018)
- [Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphs](https://mlsanity.com/paper/2004.07348/) (2020)
- [Semiparametric spectral modeling of the Drosophila connectome](https://mlsanity.com/paper/1705.03297/) (2017)
- [Rehabilitating Isomap: Euclidean Representation of Geodesic Structure](https://mlsanity.com/paper/2006.10858/) (2020)
- [Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators](https://mlsanity.com/paper/2002.06143/) (2020)
- [Correcting a Nonparametric Two-sample Graph Hypothesis Test for Graphs with Different Numbers of Vertices with Applications to Connectomics](https://mlsanity.com/paper/2008.09434/) (2020)
- [Approximate Information Tests on Statistical Submanifolds](https://mlsanity.com/paper/1903.08656/) (2019)

## Abstract (arXiv)

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.