# Reconstructing networks with unknown and heterogeneous errors

arXiv: https://arxiv.org/abs/1806.07956 · HTML: https://mlsanity.com/paper/1806.07956/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2018.

## Built on by (most cited first, 11 of 11)

- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
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- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Uncertainty quantification and posterior sampling for network reconstruction](https://mlsanity.com/paper/2503.07736/) (2025)
- [Geodesic Length Distribution in Sparse Network Ensembles](https://mlsanity.com/paper/2111.02330/) (2021)
- [Cognitive modelling with multilayer networks: Insights, advancements and future challenges](https://mlsanity.com/paper/2210.00500/) (2022)
- [Bayesian Inference of Transition Matrices from Incomplete Graph Data with a Topological Prior](https://mlsanity.com/paper/2210.15410/) (2022)
- [Fitting Low-rank Models on Egocentrically Sampled Partial Networks](https://mlsanity.com/paper/2303.11230/) (2023)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network reconstruction approaches based on Bayesian inference. These approaches, however, rely on assumptions of uniform error rates and on direct estimations of the existence of each edge via repeated measurements, something that is currently unavailable for the majority of network data. Here we develop a Bayesian reconstruction approach that lifts these limitations by not only allowing for heterogeneous errors, but also for single edge measurements without direct error estimates. Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable uncertainty estimates. Although our approach is general, we focus on the stochastic block model as the basic generative process, from which efficient nonparametric inference can be performed, and yields a principled method to infer hierarchical community structure from noisy data. We demonstrate the efficacy of our approach with a variety of empirical and artificial networks.