  Most knowledge graphs (KGs) are incomplete, which motivates one important
research topic on automatically complementing knowledge graphs. However,
evaluation of knowledge graph completion (KGC) models often ignores the
incompleteness -- facts in the test set are ranked against all unknown triplets
which may contain a large number of missing facts not included in the KG yet.
Treating all unknown triplets as false is called the closed-world assumption.
This closed-world assumption might negatively affect the fairness and
consistency of the evaluation metrics. In this paper, we study KGC evaluation
under a more realistic setting, namely the open-world assumption, where unknown
triplets are considered to include many missing facts not included in the
training or test sets. For the currently most used metrics such as mean
reciprocal rank (MRR) and Hits@K, we point out that their behavior may be
unexpected under the open-world assumption. Specifically, with not many missing
facts, their numbers show a logarithmic trend with respect to the true strength
of the model, and thus, the metric increase could be insignificant in terms of
reflecting the true model improvement. Further, considering the variance, we
show that the degradation in the reported numbers may result in incorrect
comparisons between different models, where stronger models may have lower
metric numbers. We validate the phenomenon both theoretically and
experimentally. Finally, we suggest possible causes and solutions for this
problem. Our code and data are available at
https://github.com/GraphPKU/Open-World-KG .
