Hyb Error: A Hybrid Metric Combining Absolute and Relative Error Measurements
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Summary
This academic paper introduces 'Hyb Error,' a novel error metric that combines absolute and relative errors by taking the harmonic mean of both. The metric is defined as |x-y|/(1+|y|) and addresses limitations of traditional error measurements by approaching absolute error when |y| is near zero and relative error when |y| is large. The paper demonstrates that Hyb Error corresponds to the decision boundary of common floating-point equality functions and proposes Maximum Element-wise Hyb Error (MEHE) for sequence analysis.
Key quotes
· 3 pulledThis metric equals half the harmonic mean of absolute error and relative error, effectively combining their advantages while mitigating their limitations.
Hyb Error approaches absolute error as |y| approaches 0, thereby avoiding the exaggeration of relative error, and approaches relative error as |y| approaches infinity, thereby avoiding the exaggeration of absolute error.
The Hyb Error of ε is equivalent to |x-y|=ε+ε|y|, which implies isclose(x,y,ε,ε)=True, where 'isclose' is a common floating-point equality check function in numerical libraries.
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