Pythagorean Mean Rank Metrics

1 · Charles Tapley Hoyt · April 19, 2021, midnight
The mean rank (MR) and mean reciprocal rank (MRR) are among the most popular metrics reported for the evaluation of knowledge graph embedding models in the link prediction task. While they are reported on very different intervals ($\text{MR} \in [1,\infty)$ and $\text{MRR} \in (0,1]$, their deep theoretical connection can be elegantly described through the lens of Pythagorean means. This blog post describes ideas Max Berrendorf shared with me that I recently implemented in PyKEEN and later wrote...