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ROC curve equivalence using the Kolmogorov–Smirnov test

ROC curve equivalence using the Kolmogorov–Smirnov test. PRL, vol. 34, 470-475, 2013. Andrew P. Bradley Univ. of Queensland, Australia. ROC_1 » ROC_2  AUC_1 » AUC_2 AUC_1 » AUC_2  ROC_1 » ROC_2 AUC_1 » AUC_2  ROC_1 » ROC_2. The AUC problem.

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ROC curve equivalence using the Kolmogorov–Smirnov test

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  1. ROC curve equivalence using the Kolmogorov–Smirnov test PRL, vol. 34, 470-475, 2013 Andrew P. Bradley Univ. of Queensland, Australia ROC_1 » ROC_2  AUC_1 » AUC_2 AUC_1 »AUC_2  ROC_1 »ROC_2 AUC_1 »AUC_2  ROC_1 »ROC_2 Coffee Talk

  2. The AUC problem • The AUC is a fundamentally incoherent measure for comparing ROC curves (see David Hand, 2005, 2009, 2013) • Bradley: Don’t throw away the ROC because of this • Bradley: What we need is a test of the equivalence of two ROC curves: H0: ROC_1 » ROC_2 Use the Kolmogorov–Smirnov test by finding the two most different operating points. Coffee Talk

  3. The KS test for two distributions 1 H0: Fy(x) = Fz(x) Fz(x) Fy(x) D D = maxx|Fy(x)-Fz(x)| 0 If D > Z(p,n) : reject H0 Coffee Talk

  4. The KS test for two classifiers (Bradley) The classifier scores y and z have to be shifted to the same domain, e.g. by shifting z to the domain of y Coffee Talk

  5. Example AUCy = AUCz, ROCy ≠ ROCz Coffee Talk

  6. Conclusion Correct if in sy and szy are based on the same set of objects but just applied to different classifiers and some domain shift?? Coffee Talk

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