# Accurate Node Feature Estimation with Structured Variational Graph Autoencoder

arXiv: https://arxiv.org/abs/2206.04516 · HTML: https://mlsanity.com/paper/2206.04516/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)
- [Learning on Attribute-Missing Graphs](https://mlsanity.com/paper/2011.01623/) (2020)
- [On Node Features for Graph Neural Networks](https://mlsanity.com/paper/1911.08795/) (2019)
- [Large-scale Log-determinant Computation through Stochastic Chebyshev Expansions](https://mlsanity.com/paper/1503.06394/) (2015)

## Built on by (most cited first, 12 of 12)

- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning](https://mlsanity.com/paper/2211.01214/) (2022)
- [Revisiting Initializing Then Refining: An Incomplete and Missing Graph Imputation Network](https://mlsanity.com/paper/2302.07524/) (2023)
- [Accurate Link Prediction for Edge-Incomplete Graphs via PU Learning](https://mlsanity.com/paper/2405.11911/) (2024)
- [AmGCL: Feature Imputation of Attribute Missing Graph via Self-supervised Contrastive Learning](https://mlsanity.com/paper/2305.03741/) (2023)
- [An Additive Autoencoder for Dimension Estimation](https://mlsanity.com/paper/2210.06773/) (2022)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Scalable Attribute-Missing Graph Clustering via Neighborhood Differentiation](https://mlsanity.com/paper/2507.13368/) (2025)
- [Clustering-Oriented Generative Attribute Graph Imputation](https://mlsanity.com/paper/2507.19085/) (2025)
- [Topology-Driven Attribute Recovery for Attribute Missing Graph Learning in Social Internet of Things](https://mlsanity.com/paper/2501.10151/) (2025)
- [Divide-Then-Rule: A Cluster-Driven Hierarchical Interpolator for Attribute-Missing Graphs](https://mlsanity.com/paper/2507.10595/) (2025)
- [FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation](https://mlsanity.com/paper/2601.18938/) (2026)

## Abstract (arXiv)

Given a graph with partial observations of node features, how can we estimate the missing features accurately? Feature estimation is a crucial problem for analyzing real-world graphs whose features are commonly missing during the data collection process. Accurate estimation not only provides diverse information of nodes but also supports the inference of graph neural networks that require the full observation of node features. However, designing an effective approach for estimating high-dimensional features is challenging, since it requires an estimator to have large representation power, increasing the risk of overfitting. In this work, we propose SVGA (Structured Variational Graph Autoencoder), an accurate method for feature estimation. SVGA applies strong regularization to the distribution of latent variables by structured variational inference, which models the prior of variables as Gaussian Markov random field based on the graph structure. As a result, SVGA combines the advantages of probabilistic inference and graph neural networks, achieving state-of-the-art performance in real datasets.