# Cardinality Estimation on Hyper-relational Knowledge Graphs

arXiv: https://arxiv.org/abs/2405.15231 · HTML: https://mlsanity.com/paper/2405.15231/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 76 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [Message Passing for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2009.10847/) (2020)
- [ReAcTable: Enhancing ReAct for Table Question Answering](https://mlsanity.com/paper/2310.00815/) (2023)
- [A Petri Dish for Histopathology Image Analysis](https://mlsanity.com/paper/2101.12355/) (2021)
- [On the representation and embedding of knowledge bases beyond binary relations](https://mlsanity.com/paper/1604.08642/) (2016)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [Role-Aware Modeling for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2104.09780/) (2021)
- [Link Prediction on N-ary Relational Facts: A Graph-based Approach](https://mlsanity.com/paper/2105.08476/) (2021)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [Query Embedding on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2106.08166/) (2021)
- [A Unified Deep Model of Learning from both Data and Queries for Cardinality Estimation](https://mlsanity.com/paper/2107.12295/) (2021)
- [An Analytical Study of Large SPARQL Query Logs](https://mlsanity.com/paper/1708.00363/) (2017)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Estimating the Cardinality of Conjunctive Queries over RDF Data Using Graph Summarisation](https://mlsanity.com/paper/1801.09619/) (2018)
- [LMKG: Learned Models for Cardinality Estimation in Knowledge Graphs](https://mlsanity.com/paper/2102.10588/) (2021)
- [Accurate Summary-based Cardinality Estimation Through the Lens of Cardinality Estimation Graphs](https://mlsanity.com/paper/2105.08878/) (2021)
- [Space-Efficient Random Walks on Streaming Graphs](https://mlsanity.com/paper/2209.06063/) (2022)
- [[Technical Report] Combining Sampling and Synopses with Worst-Case Optimal Runtime and Quality Guarantees for Graph Pattern Cardinality Estimation](https://mlsanity.com/paper/2103.13681/) (2021)

## Built on by (most cited first, 3 of 3)

- [Graph Neural Networks for Databases: A Survey](https://mlsanity.com/paper/2502.12908/) (2025)
- [Survey and Experiments on Mental Disorder Detection via Social Media: From Large Language Models and RAG to Agents](https://mlsanity.com/paper/2504.02800/) (2025)
- [OpenGLT: A Comprehensive Benchmark of Graph Neural Networks for Graph-Level Tasks](https://mlsanity.com/paper/2501.00773/) (2025)

## Abstract (arXiv)

Cardinality Estimation (CE) for query is to estimate the number of results without execution, which is an effective index in query optimization. Recently, CE for queries over knowlege graph (KGs) with triple facts has achieved great success. To more precisely represent facts, current researchers propose hyper-relational KGs (HKGs) to represent a triple fact with qualifiers providing additional context to the fact. However, existing CE methods, such as sampling and summary methods over KGs, perform unsatisfactorily on HKGs due to the complexity of qualifiers. Learning-based CE methods do not utilize qualifier information to learn query representation accurately, leading to poor performance. Also, there is only one limited CE benchmark for HKG query, which is not comprehensive and only covers limited patterns. The lack of querysets over HKG also becomes a bottleneck to comprehensively investigate CE problems on HKGs. In this work, we first construct diverse and unbiased hyper-relational querysets over three popular HKGs for investigating CE. Besides, we also propose a novel qualifier-aware graph neural network (GNN) model that effectively incorporates qualifier information and adaptively combines outputs from multiple GNN layers, to accurately predict the cardinality. Our experiments demonstrate that our model outperforms all state-of-the-art CE methods over three benchmarks on popular HKGs.