# Fitting Low-rank Models on Egocentrically Sampled Partial Networks

arXiv: https://arxiv.org/abs/2303.11230 · HTML: https://mlsanity.com/paper/2303.11230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 59 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 19 of 19)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [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)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Network Cross-Validation for Determining the Number of Communities in Network Data](https://mlsanity.com/paper/1411.1715/) (2014)
- [Hierarchical community detection by recursive partitioning](https://mlsanity.com/paper/1810.01509/) (2018)
- [Bayesian hierarchical stacking: Some models are (somewhere) useful](https://mlsanity.com/paper/2101.08954/) (2021)
- [Reconstructing networks with unknown and heterogeneous errors](https://mlsanity.com/paper/1806.07956/) (2018)
- [On clustering network-valued data](https://mlsanity.com/paper/1606.02401/) (2016)
- [Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing](https://mlsanity.com/paper/1811.06055/) (2018)
- [Linear regression and its inference on noisy network-linked data](https://mlsanity.com/paper/2007.00803/) (2020)
- [Link prediction for partially observed networks](https://mlsanity.com/paper/1301.7047/) (2013)
- [Consistent Spectral Clustering of Network Block Models under Local Differential Privacy](https://mlsanity.com/paper/2105.12615/) (2021)
- [Link prediction for egocentrically sampled networks](https://mlsanity.com/paper/1803.04084/) (2018)
- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [On the Theoretical Properties of the Network Jackknife](https://mlsanity.com/paper/2004.08935/) (2020)

## Abstract (arXiv)

The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via egocentric sampling: a subset of nodes is sampled first, after which all links involving this subset are recorded; all other information is missing. Compared with the assumption of ``uniformly missing at random", egocentrically sampled partial networks require specially designed modeling strategies. Current statistical methods are either computationally infeasible or based on intuitive designs without theoretical justification. Here, we propose an approach to fit general low-rank models for egocentrically sampled networks, which include several popular network models. This method is based on graph spectral properties and is computationally efficient for large-scale networks. It results in consistent recovery of missing subnetworks due to egocentric sampling for sparse networks. To our knowledge, this method offers the first theoretical guarantee for egocentric partial network estimation in the scope of low-rank models. We evaluate the technique on several synthetic and real-world networks and show that it delivers competitive performance in link prediction tasks.