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What is F-beta score and when is F1 not enough?

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Answer

  • Fβ  =  (1  +  β2)    P    R  /  (β2    P  +  R)F_{\beta}\; = \;(1\; + \;\beta^{2})\; \cdot \;P\; \cdot \;R\; / \;(\beta^{2}\; \cdot \;P\; + \;R) generalizes F1 with a weight on recall vs precision. β  =  1\beta\; = \;1 → F1 (equal). β  =  2\beta\; = \;2 (F2) → recall matters 4x more than precision — appropriate for medical screening where missing positives is very costly. β  =  0.5\beta\; = \;0.5 (F0.5) → precision matters 4x more — for a spam filter where false positives annoy users.
  • F1's implicit assumption is that precision and recall are equally important — often they aren't.
Check yourself — multiple choice
  • F-beta is always equal to F1
  • F-beta weights recall vs precision; beta > 1 favors recall, beta < 1 favors precision
  • F-beta only works for regression
  • F-beta requires balanced classes

F-beta weights recall vs precision via β. F2 favors recall; F0.5 favors precision.

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