# Distribution Matching for Graph Quantification Under Structural Covariate Shift

arXiv: https://arxiv.org/abs/2601.00864 · HTML: https://mlsanity.com/paper/2601.00864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Fisher consistency for prior probability shift](https://mlsanity.com/paper/1701.05512/) (2017)
- [QuaPy: A Python-Based Framework for Quantification](https://mlsanity.com/paper/2106.11057/) (2021)
- [Class Prior Estimation under Covariate Shift: No Problem?](https://mlsanity.com/paper/2206.02449/) (2022)
- [Kernel Density Estimation for Multiclass Quantification](https://mlsanity.com/paper/2401.00490/) (2023)
- [Unified Framework for Quantification](https://mlsanity.com/paper/1606.00868/) (2016)
- [Binary Quantification and Dataset Shift: An Experimental Investigation](https://mlsanity.com/paper/2310.04565/) (2023)
- [Adjusted Count Quantification Learning on Graphs](https://mlsanity.com/paper/2503.09395/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geometry-Aware Bayesian Quantification via Compositional Data Analysis](https://mlsanity.com/paper/2607.04977/) (2026)

## Abstract (arXiv)

Graphs are commonly used in machine learning to model relationships between instances. Consider the task of predicting the political preferences of users in a social network; to solve this task one should consider, both, the features of each individual user and the relationships between them. However, oftentimes one is not interested in the label of a single instance but rather in the distribution of labels over a set of instances; e.g., when predicting the political preferences of users, the overall prevalence of a given opinion might be of higher interest than the opinion of a specific person. This label prevalence estimation task is commonly referred to as quantification learning (QL). Current QL methods for tabular data are typically based on the so-called prior probability shift (PPS) assumption which states that the label-conditional instance distributions should remain equal across the training and test data. In the graph setting, PPS generally does not hold if the shift between training and test data is structural, i.e., if the training data comes from a different region of the graph than the test data. To address such structural shifts, an importance sampling variant of the popular adjusted count quantification approach has previously been proposed. In this work, we extend the idea of structural importance sampling to the state-of-the-art KDEy quantification approach. We show that our proposed method adapts to structural shifts and outperforms standard quantification approaches.