# Handling Missing Data via Max-Entropy Regularized Graph Autoencoder

arXiv: https://arxiv.org/abs/2211.16771 · HTML: https://mlsanity.com/paper/2211.16771/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 68 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning](https://mlsanity.com/paper/1908.02441/) (2019)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [Graph Convolutional Networks for Graphs Containing Missing Features](https://mlsanity.com/paper/2007.04583/) (2020)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [Incomplete Graph Representation and Learning via Partial Graph Neural Networks](https://mlsanity.com/paper/2003.10130/) (2020)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependence](https://mlsanity.com/paper/1410.0438/) (2014)
- [Graph Autoencoders with Deconvolutional Networks](https://mlsanity.com/paper/2012.11898/) (2020)
- [Siamese Attribute-missing Graph Auto-encoder](https://mlsanity.com/paper/2112.04842/) (2021)

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

- [Parameter-Efficient Fine-Tuning with Discrete Fourier Transform](https://mlsanity.com/paper/2405.03003/) (2024)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Alleviating Over-smoothing for Unsupervised Sentence Representation](https://mlsanity.com/paper/2305.06154/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [stMCDI: Masked Conditional Diffusion Model with Graph Neural Network for Spatial Transcriptomics Data Imputation](https://mlsanity.com/paper/2403.10863/) (2024)
- [Deep Reinforcement Learning for Modelling Protein Complexes](https://mlsanity.com/paper/2405.02299/) (2024)
- [A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Models](https://mlsanity.com/paper/2405.17712/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Data Imputation from the Perspective of Graph Dirichlet Energy](https://mlsanity.com/paper/2304.04474/) (2023)
- [DPGAN: A Dual-Path Generative Adversarial Network for Missing Data Imputation in Graphs](https://mlsanity.com/paper/2404.17164/) (2024)
- [Reconciling Attribute and Structural Anomalies for Improved Graph Anomaly Detection](https://mlsanity.com/paper/2506.23469/) (2025)
- [Learning the Interaction Prior for Protein-Protein Interaction Prediction: A Model-Agnostic Approach](https://mlsanity.com/paper/2605.09964/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are popular weapons for modeling relational data. Existing GNNs are not specified for attribute-incomplete graphs, making missing attribute imputation a burning issue. Until recently, many works notice that GNNs are coupled with spectral concentration, which means the spectrum obtained by GNNs concentrates on a local part in spectral domain, e.g., low-frequency due to oversmoothing issue. As a consequence, GNNs may be seriously flawed for reconstructing graph attributes as graph spectral concentration tends to cause a low imputation precision. In this work, we present a regularized graph autoencoder for graph attribute imputation, named MEGAE, which aims at mitigating spectral concentration problem by maximizing the graph spectral entropy. Notably, we first present the method for estimating graph spectral entropy without the eigen-decomposition of Laplacian matrix and provide the theoretical upper error bound. A maximum entropy regularization then acts in the latent space, which directly increases the graph spectral entropy. Extensive experiments show that MEGAE outperforms all the other state-of-the-art imputation methods on a variety of benchmark datasets.