# Nonparametric learning of heterogeneous graphical model on network-linked data

arXiv: https://arxiv.org/abs/2507.01473 · HTML: https://mlsanity.com/paper/2507.01473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Density Estimation in Infinite Dimensional Exponential Families](https://mlsanity.com/paper/1312.3516/) (2013)
- [Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding](https://mlsanity.com/paper/1310.0532/) (2013)
- [Nonparametric Score Estimators](https://mlsanity.com/paper/2005.10099/) (2020)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Learning non-Gaussian graphical models via Hessian scores and triangular transport](https://mlsanity.com/paper/2101.03093/) (2021)
- [Prediction models for network-linked data](https://mlsanity.com/paper/1602.01192/) (2016)
- [Estimating Time-Varying Graphical Models](https://mlsanity.com/paper/1804.03811/) (2018)
- [Linear regression and its inference on noisy network-linked data](https://mlsanity.com/paper/2007.00803/) (2020)
- [High-dimensional Gaussian graphical model for network-linked data](https://mlsanity.com/paper/1907.02443/) (2019)
- [Statistical Inference on Latent Space Models for Network Data](https://mlsanity.com/paper/2312.06605/) (2023)

## Abstract (arXiv)

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex datasets such as network-linked data. This paper proposes a nonparametric graphical model that addresses these limitations by accommodating heterogeneous graph structures without imposing any specific distributional assumptions. The proposed estimation method effectively integrates network embedding with nonparametric graphical model estimation. It further transforms the graph learning task into solving a finite-dimensional linear equation system by leveraging the properties of vector-valued reproducing kernel Hilbert space. Moreover, theoretical guarantees are established for the proposed method in terms of the estimation consistency and exact recovery of the heterogeneous graph structures. Its effectiveness is also demonstrated through a variety of simulated examples and a real application to the statistician coauthorship dataset.