Papers › Adjust Pearson's r to Measure Arbitrary Monotone Dependence
Adjust Pearson's r to Measure Arbitrary Monotone Dependence
Xinbo Ai
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research challenges this notion, suggesting that Pearson's r should not be ruled out a priori for measuring nonlinear monotone relationships. Pearson's r is essentially a scaled covariance, rooted in the renowned Cauchy-Schwarz Inequality. Our findings reveal that different scaling bounds yield coefficients with different capture ranges, and interestingly, tighter bounds actually expand these ranges. We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's r, and propose a new correlation coefficient, i.e., rearrangement correlation. This coefficient is able to capture arbitrary monotone relationships, both linear and nonlinear ones. It reverts to Pearson's r in linear scenarios. Simulation experiments and real-life investigations show that the rearrangement correlation is more accurate in measuring nonlinear monotone dependence than the three classical correlation coefficients, and other recently proposed dependence measures.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections