# Data Imputation with Iterative Graph Reconstruction

arXiv: https://arxiv.org/abs/2212.02810 · HTML: https://mlsanity.com/paper/2212.02810/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [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)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Missing Data Imputation with Adversarially-trained Graph Convolutional Networks](https://mlsanity.com/paper/1905.01907/) (2019)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [GANS for Sequences of Discrete Elements with the Gumbel-softmax Distribution](https://mlsanity.com/paper/1611.04051/) (2016)
- [MIDA: Multiple Imputation using Denoising Autoencoders](https://mlsanity.com/paper/1705.02737/) (2017)
- [G2SAT: Learning to Generate SAT Formulas](https://mlsanity.com/paper/1910.13445/) (2019)
- [Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning](https://mlsanity.com/paper/1912.06989/) (2019)

## Built on by (most cited first, 15 of 15)

- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Self-Supervision Improves Diffusion Models for Tabular Data Imputation](https://mlsanity.com/paper/2407.18013/) (2024)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [On LLM-Enhanced Mixed-Type Data Imputation with High-Order Message Passing](https://mlsanity.com/paper/2501.02191/) (2025)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Sampling-guided Heterogeneous Graph Neural Network with Temporal Smoothing for Scalable Longitudinal Data Imputation](https://mlsanity.com/paper/2411.04899/) (2024)
- [MissDDIM: Deterministic and Efficient Conditional Diffusion for Tabular Data Imputation](https://mlsanity.com/paper/2508.03083/) (2025)
- [Towards Practical Benchmarking of Data Cleaning Techniques: On Generating Authentic Errors via Large Language Models](https://mlsanity.com/paper/2507.10934/) (2025)
- [IVGAE: Handling Incomplete Heterogeneous Data with a Variational Graph Autoencoder](https://mlsanity.com/paper/2511.22116/) (2025)
- [Federated Imputation under Heterogeneous Feature Spaces](https://mlsanity.com/paper/2605.16099/) (2026)
- [Enhancing Missing Data Imputation through Combined Bipartite Graph and Complete Directed Graph](https://mlsanity.com/paper/2411.04907/) (2024)
- [Missing Data Imputation using Neural Cellular Automata](https://mlsanity.com/paper/2509.00651/) (2025)
- [Nearly Optimal Bayesian Inference for Structural Missingness](https://mlsanity.com/paper/2601.18500/) (2026)
- [Imputation Meets Clustering: Exploiting Latent Subgroup Structure for Missing Data Recovery](https://mlsanity.com/paper/2607.06930/) (2026)
- [Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation](https://mlsanity.com/paper/2609.15284/) (2026)

## Abstract (arXiv)

Effective data imputation demands rich latent ``structure" discovery capabilities from ``plain" tabular data. Recent advances in graph neural networks-based data imputation solutions show their strong structure learning potential by directly translating tabular data as bipartite graphs. However, due to a lack of relations between samples, those solutions treat all samples equally which is against one important observation: ``similar sample should give more information about missing values." This paper presents a novel Iterative graph Generation and Reconstruction framework for Missing data imputation(IGRM). Instead of treating all samples equally, we introduce the concept: ``friend networks" to represent different relations among samples. To generate an accurate friend network with missing data, an end-to-end friend network reconstruction solution is designed to allow for continuous friend network optimization during imputation learning. The representation of the optimized friend network, in turn, is used to further optimize the data imputation process with differentiated message passing. Experiment results on eight benchmark datasets show that IGRM yields 39.13% lower mean absolute error compared with nine baselines and 9.04% lower than the second-best. Our code is available at https://github.com/G-AILab/IGRM.