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Given a classifier and a dataset, let's say we want a) to find a classifier that separates classes such that F1 score is the best b) to find a classifier that separates classes such that AUC is best. Is the decision boundary in both cases same? Does finding the best AUC means that we already found best F1 score and Accuracy, or it isn't valid assumption?

I am training two classifiers, one that optimizes AUC and the other that optimizes F1 score. In both of these F1 score and AUC is the same.

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  • $\begingroup$ What do you mean by "decision boundary" for AUC? $\endgroup$ – Dave Aug 10 at 15:46
  • $\begingroup$ @Dave Let's say we train a LogisticRegression (linear classifier). Does the hyperplane (decision boundary) that bests splits the data same for the AUC and for the F1 score, or no matter what metric we want to improve we will always get the same hyperplane that separates the data? Is it valid for non-linear classifiers in terms of boundary? $\endgroup$ – Krushe Aug 10 at 15:51
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AUC, F1 score and accuracy are all different evaluation metrices and a good AUC score does not mean a good F1 or accuracy score. AUC score is area under the ROC curve which is different F1 score which is harmonic mean of precision and recall scores. Basically, your choice of evaluation metric depends on what you are trying to achieve in your problem.

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  • $\begingroup$ I know that they are, but can you explain to me why if I optimise classifier for F1 score I get the same AUC score as the classifier where I state I want to improve AUC score? $\endgroup$ – Krushe Aug 10 at 16:00
  • $\begingroup$ If you are trying to optimise F1 score, then there is no need to calculate AUC score. I'm not sure what's your concern exactly but if you are trying to achieve high F1 score then your AUC score may or may not be higher than F1. $\endgroup$ – Vivek Aug 10 at 18:22

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