두 분류 분포를 위한 오즈 곡선 = Odds curve for two classification distributions

국문 초록 (Abstract)

이진분류모형의 성능을 탐색하는 시각적인 대표적인 방법인 ROC 곡선과 TOC 곡선 그리고 TROC 곡선은 혼동행렬을 구성하는 TP, TN, FP, FN 그리고 이들의 비율인 TPR, TNR, FPR, FNR으로 구현된다. 본 연구에서는 두 종류의 비율비인 오즈를 고려하여 단위면적인 정사각형에서의 구현하는 오즈 곡선을 제안하고, ROC 곡선과의 관계를 보인다. 오즈 곡선에서 판별력을 측정하는 두 종류의 측도를 제안하고, 오즈 곡선들의 형태를 바탕으로 두 종류의 측도를 이용하여 두 분류 분포의 판단 기준을 설정한다. 본 연구에서 제안한 오즈 곡선은 다른 시각적인 방법 등과 같이 유용하게 사용할 수 있으며, 오즈 곡선의 판별력을 측정하는 두 종류의 측도들은 분류 성능을 판단하는 대안적인 방법으로 같이 이용할 수 있다.

다국어 초록 (Multilingual Abstract)

The ROC, TOC, and TROC curves, which are visually descriptive methods of exploring the performance of the binary classification model, are implemented with TP, TN, FP, FN which consist of the confusion matrix, as well as their ratios TPR, TNR, FPR, FNR. In this study, we consider two types odds and then propose an odds curve representing these odds. And show the relationship between the odds curve and ROC curve. Based on the odds curve, we propose not only two statistics that measure the discriminant power of the odds curve but also the criteria for validation ratings of the odds curve. According to the shape of the odds curves, two classification distributions can be estimated and a criterion for validation ratings can be determined. The odds curve can be meaningfully used like other visual methods, and two kinds of measures for the discriminant power can be also applied together as an alternative criterion.

참고문헌 (Reference)

1 홍종선, "혼합분포에서 최적분류점" 한국통계학회 23 (23): 13-28, 2010

2 홍종선, "민감도와 특이도 직선을 이용한 부분 AUC" 한국통계학회 33 (33): 541-553, 2020

3 조민호, "Two optimal threshold criteria for ROC analysis" 한국데이터정보과학회 26 (26): 255-260, 2015

4 홍종선, "Three-way partial VUS" 한국데이터정보과학회 30 (30): 445-454, 2019

5 Bradley, A. P., "The use of the area under the ROC curve in the evaluation of machine learning algorithms" 30 : 1145-1159, 1997

6 Pontius Jr, R. G., "The total operating characteristic to measure diagnostic ability for multiple thresholds" 28 : 570-583, 2014

7 Stein, R. M., "The relationship between default prediction and lending profits : Integrating ROC analysis and loan pricing" 29 : 1213-1236, 2005

8 Hanley, J. A., "The meaning and use of the area under a receiver operating characteristic(ROC)curve" 143 : 29-36, 1982

9 Bamber, D., "The area above the ordinal dominance graph and the area below the receiver operating characteristic graph" 12 : 387-415, 1975

10 Pepe, M. S., "The Statistical Evaluation of Medical Tests for Classification and Prediction" Oxford University Press 2003

11 Tasche, D., "The Analytics of Risk Model Validation" Academic Press 169-196, 2008

12 Engelmann, B., "Testing rating accuracy" 16 : 82-86, 2003

13 홍종선, "TROC 곡선과 정확도 측도들" 한국데이터정보과학회 29 (29): 861-872, 2018

14 Metz, C. E., "Statistical significance tests for binormal ROC curves" 22 : 218-243, 1980

15 Centor, R. M., "Signal detectability : the use of ROC curves and their analyses" 11 : 102-106, 1991

16 Egan, J. P., "Signal Detection Theory and ROC-Analysis" Academic Press 1975

17 Green, D. M., "Signal Detection Theory and Psychophysics (Vol. 1)" Wiley 1966

18 Pepe, M. S., "Selecting differentially expressed genes from microarray experiments" 59 : 133-142, 2003

19 Provost, F., "Robust classification for imprecise environments" 42 : 203-231, 2001

20 Zweig, M. H., "Receiver-operating characteristic(ROC)plots : a fundamental evaluation tool in clinical medicine" 39 : 561-577, 1993

21 홍종선, "ROC 곡면에서 VUS의 판단기준" 한국통계학회 26 (26): 977-985, 2013

22 Fawcett, T., "ROC graphs : Notes and practical considerations for researchers" 31 : 1-38, 2004

23 Vuk, M., "ROC curve, lift chart and calibration plot" 3 : 89-, 2006

24 Sonego, P., "ROC analysis : applications to the classification of biological sequences and 3D structures" 9 : 198-209, 2008

25 홍종선, "Partial VUS and optimal thresholds" 한국데이터정보과학회 30 (30): 895-905, 2019

26 Hsieh, F., "Nonparametric and semiparametric estimation of the receiver operating characteristic curve" 24 : 25-40, 1996

27 Swets, J. A., "Measuring the accuracy of diagnostic systems" 240 : 1285-1293, 1988

28 홍종선, "Maximum absolute determinant of the confusion matrix" 한국데이터정보과학회 31 (31): 937-950, 2020

29 Jeni, L. A., "Facing imbalanced data–recommendations for the use of performance metrics" IEEE 245-251, 2013

30 Altman, D. G., "Diagnostic tests. 1: Sensitivity and specificity" 308 : 1552-, 1994

31 홍종선, "Confusion plot for the confusion matrix" 한국데이터정보과학회 32 (32): 427-437, 2021

32 Metz, C. E., "Basic principles of ROC analysis" WB Saunders 8 (8): 283-298, 1978

33 Provost, F., "Analysis and visualization of classifier performance with nonuniform class and cost distributions" 57-63, 1997

34 Fawcett, T., "An introduction to ROC analysis" 27 : 861-874, 2006

35 홍종선, "Alternative accuracy for multiple ROC analysis" 한국데이터정보과학회 25 (25): 1521-1530, 2014

36 Joseph, M. P., "A PD validation framework for Basel II internal ratings-based systems" 2005