| Abstrakt: |
We derive the mapping between two of the most pervasive utility functions, the mean square error (MSE) and the concordance correlation coefficient (CCC, ρc). Despite its drawbacks, MSE is one of the most popular performance metrics and loss functions; along with lately ρc in many of the sequence prediction challenges. Despite the ever-growing simultaneous usage, e.g., inter-rater agreement, assay validation, a mapping between the two metrics is missing till date. While minimisation of Lp norm of the errors or of its positive powers (e.g., MSE) is indirectly aimed at ρc maximisation, we reason the often-witnessed ineffectiveness of MSE at ρc maximisation with graphical illustrations. The presented formulation uncovers not only the counterintuitive revelation that 'MSE1 < MSE2' does not imply 'ρc1 > ρc2 ', but also provides the precise range for the ρc metric for a given MSE. We derive the conditions for ρc optimisation for a given MSE. We extend the analysis to derive not only the span of valid {MSE, ρc} pairs, but also {MSE, ρ} span, where ρ is the correlation coefficient. The study inspires and anticipates a growing use of both covariance and error-based loss functions e.g., ρ -inspired | MSE σ X Y | , replacing the traditional solely error-based loss functions in multivariate regressions. The results are reproducible with easy-to-use scripts made available at github.com/vedhasua/mse_ccc_corollary. [ABSTRACT FROM AUTHOR] |
