  Cardinality Estimation (CE) for query is to estimate the number of results
without execution, which is an effective index in query optimization. Recently,
CE over has achieved great success in knowledge graphs (KGs) that consist of
triple facts. To more precisely represent facts, current researchers propose
hyper-relational KGs (HKGs) to represent a triple fact with qualifiers, where
qualifiers provide additional context to the fact. However, existing CE methods
over KGs achieve unsatisfying performance on HKGs due to the complexity of
qualifiers in HKGs. Also, there is only one dataset for HKG query cardinality
estimation, i.e., WD50K-QE, 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-attached
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 illustrate that the
proposed hyper-relational query encoder outperforms all state-of-the-art CE
methods over three popular HKGs on the diverse and unbiased benchmark.
