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$AUC$ is the area under the receiver operating characteristic curve. It's said that a loss function set to $1-AUC$ can be minimized by maximizing $AUC$. How does this tie into logit (logistic) regression, if at all, and does logit regression maximize $AUC$ directly/indirectly somehow?

described mathematically for both the discrete-class and probability-based logit regression would be nice. Also, what is a rank loss function?

develarist
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  • Suppose you're minimizing some loss $\mathcal{L}(\theta)$. This is the same as **maximizing** $-\mathcal{L}(\theta)$. That's all the claim about $1- AUC$ is saying. – Sycorax Apr 29 '20 at 04:17
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    Does this answer your question? [Does a logistic regression maximizing likelihood necessarily also maximize AUC over linear models?](https://stats.stackexchange.com/questions/422784/does-a-logistic-regression-maximizing-likelihood-necessarily-also-maximize-auc-o) I believe this answers the rest. – Sycorax Apr 29 '20 at 04:17
  • No i saw that first and theyre only discussing the regression coefficient there despite the title – develarist Apr 29 '20 at 05:59
  • I'm not sure what distinction you're drawing between a logistic regression model and the coefficients which maximize the likelihood used in logistic regression. You ask if logistic regression maximizes AUC, and the answer shows that there are circumstances where the MLE solution to logistic regression does not correspond to maximizing AUC. How is your question different? What part of your question is not addressed in the linked thread? – Sycorax Apr 29 '20 at 06:09

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