# Robust Estimation from Multiple Graphs under Gross Error Contamination

arXiv: https://arxiv.org/abs/1707.03487 · HTML: https://mlsanity.com/paper/1707.03487/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2017.

## Built on by (most cited first, 5 of 5)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Online Change Point Detection for Weighted and Directed Random Dot Product Graphs](https://mlsanity.com/paper/2201.11222/) (2022)
- [Consensus Knowledge Graph Learning via Multi-view Sparse Low Rank Block Model](https://mlsanity.com/paper/2209.13762/) (2022)
- [Gradient-Based Spectral Embeddings of Random Dot Product Graphs](https://mlsanity.com/paper/2307.13818/) (2023)
- [Weighted Random Dot Product Graphs](https://mlsanity.com/paper/2505.03649/) (2025)

## Abstract (arXiv)

Estimation of graph parameters based on a collection of graphs is essential for a wide range of graph inference tasks. In practice, weighted graphs are generally observed with edge contamination. We consider a weighted latent position graph model contaminated via an edge weight gross error model and propose an estimation methodology based on robust Lq estimation followed by low-rank adjacency spectral decomposition. We demonstrate that, under appropriate conditions, our estimator both maintains Lq robustness and wins the bias-variance tradeoff by exploiting low-rank graph structure. We illustrate the improvement offered by our estimator via both simulations and a human connectome data experiment.