# Estimating network edge probabilities by neighborhood smoothing

arXiv: https://arxiv.org/abs/1509.08588 · HTML: https://mlsanity.com/paper/1509.08588/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2015.

## Built on by (most cited first, 28 of 28)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Convergence of Invariant Graph Networks](https://mlsanity.com/paper/2201.10129/) (2022)
- [Graphon based Clustering and Testing of Networks: Algorithms and Theory](https://mlsanity.com/paper/2110.02722/) (2021)
- [Federated Optimization of Smooth Loss Functions](https://mlsanity.com/paper/2201.01954/) (2022)
- [Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials](https://mlsanity.com/paper/2308.15728/) (2023)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Nonparametric Modeling of Higher-Order Interactions via Hypergraphons](https://mlsanity.com/paper/2105.08678/) (2021)
- [Network Estimation by Mixing: Adaptivity and More](https://mlsanity.com/paper/2106.02803/) (2021)
- [Training Graph Neural Networks by Graphon Estimation](https://mlsanity.com/paper/2109.01918/) (2021)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [Transfer Learning for Latent Variable Network Models](https://mlsanity.com/paper/2406.03437/) (2024)
- [Local-to-global Perspectives on Graph Neural Networks](https://mlsanity.com/paper/2306.06547/) (2023)
- [Identification of Average Treatment Effects in Nonparametric Panel Models](https://mlsanity.com/paper/2503.19873/) (2025)
- [Causal Inference in Possibly Nonlinear Factor Models](https://mlsanity.com/paper/2008.13651/) (2020)
- [Modularity maximisation for graphons](https://mlsanity.com/paper/2101.00503/) (2021)
- [High-order joint embedding for multi-level link prediction](https://mlsanity.com/paper/2111.05265/) (2021)
- [Higher-order accurate two-sample network inference and network hashing](https://mlsanity.com/paper/2208.07573/) (2022)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Transfer Learning on Edge Connecting Probability Estimation under Graphon Model](https://mlsanity.com/paper/2510.05527/) (2025)
- [Fitting Low-rank Models on Egocentrically Sampled Partial Networks](https://mlsanity.com/paper/2303.11230/) (2023)
- [Estimating Dyadic Treatment Effects with Unknown Confounders](https://mlsanity.com/paper/2405.16547/) (2024)
- [Network-based Neighborhood regression](https://mlsanity.com/paper/2407.04104/) (2024)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (2025)
- [Simultaneous estimation of connectivity and dimensionality in samples of networks](https://mlsanity.com/paper/2508.12483/) (2025)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)
- [Network Learning with Semi-relaxed Gromov-Wasserstein](https://mlsanity.com/paper/2606.02223/) (2026)

## Abstract (arXiv)

The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighborhood smoothing to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighborhood smoothing method requires little tuning, has a competitive mean-squared error rate, and outperforms many benchmark methods on link prediction in simulated and real networks.