# Confidence-Based Feature Imputation for Graphs with Partially Known Features

arXiv: https://arxiv.org/abs/2305.16618 · HTML: https://mlsanity.com/paper/2305.16618/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 54 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning](https://mlsanity.com/paper/2010.16103/) (2020)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features](https://mlsanity.com/paper/2111.12128/) (2021)
- [Graph Convolutional Networks for Graphs Containing Missing Features](https://mlsanity.com/paper/2007.04583/) (2020)
- [Learning on Attribute-Missing Graphs](https://mlsanity.com/paper/2011.01623/) (2020)
- [Optimizing Generalized PageRank Methods for Seed-Expansion Community Detection](https://mlsanity.com/paper/1905.10881/) (2019)
- [HAGEN: Homophily-Aware Graph Convolutional Recurrent Network for Crime Forecasting](https://mlsanity.com/paper/2109.12846/) (2021)
- [Incomplete Graph Representation and Learning via Partial Graph Neural Networks](https://mlsanity.com/paper/2003.10130/) (2020)
- [Class-Attentive Diffusion Network for Semi-Supervised Classification](https://mlsanity.com/paper/2006.10222/) (2020)

## Built on by (most cited first, 14 of 14)

- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Uncertainty-Aware Graph Structure Learning](https://mlsanity.com/paper/2502.12618/) (2025)
- [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)
- [Rethinking GNNs and Missing Features: Challenges, Evaluation and a Robust Solution](https://mlsanity.com/paper/2601.04855/) (2026)
- [MDS-GNN: A Mutual Dual-Stream Graph Neural Network on Graphs with Incomplete Features and Structure](https://mlsanity.com/paper/2408.04845/) (2024)
- [Enhancing Missing Data Imputation through Combined Bipartite Graph and Complete Directed Graph](https://mlsanity.com/paper/2411.04907/) (2024)
- [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)
- [Mitigating Structural Overfitting: A Distribution-Aware Rectification Framework for Missing Feature Imputation](https://mlsanity.com/paper/2512.06356/) (2025)
- [FSD-CAP: Fractional Subgraph Diffusion with Class-Aware Propagation for Graph Feature Imputation](https://mlsanity.com/paper/2601.18938/) (2026)
- [Drop the mask! GAMM-A Taxonomy for Graph Attributes Missing Mechanisms](https://mlsanity.com/paper/2602.08407/) (2026)
- [GAD in the Wild: Benchmarking Graph Anomaly Detection under Realistic Deployment Challenges](https://mlsanity.com/paper/2605.07133/) (2026)
- [When Missingness Follows the Graph: Beyond Feature Propagation for Missing Features](https://mlsanity.com/paper/2610.18113/) (2026)

## Abstract (arXiv)

This paper investigates a missing feature imputation problem for graph learning tasks. Several methods have previously addressed learning tasks on graphs with missing features. However, in cases of high rates of missing features, they were unable to avoid significant performance degradation. To overcome this limitation, we introduce a novel concept of channel-wise confidence in a node feature, which is assigned to each imputed channel feature of a node for reflecting certainty of the imputation. We then design pseudo-confidence using the channel-wise shortest path distance between a missing-feature node and its nearest known-feature node to replace unavailable true confidence in an actual learning process. Based on the pseudo-confidence, we propose a novel feature imputation scheme that performs channel-wise inter-node diffusion and node-wise inter-channel propagation. The scheme can endure even at an exceedingly high missing rate (e.g., 99.5%) and it achieves state-of-the-art accuracy for both semi-supervised node classification and link prediction on various datasets containing a high rate of missing features. Codes are available at https://github.com/daehoum1/pcfi.