The accuracy, or proportion of correct predictions is estimated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$acc = \frac{1}{n_{{test}}}\sum\limits_{i=1}^{n_{t}est}I\left(y_{i}=\hat{y}_{i}\right), $$ \end{document}acc=1ntest∑i=1ntestIyi=ŷi, where I(.) denotes the indicator function (I(A)=1 if A holds, I(A)=0 otherwise). The Area Under Curve (AUC), or probability that the classifier ranks a randomly chosen observation with Y=1 higher than a randomly chosen observation with Y=0 is estimated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$auc = \frac{1}{n_{0,test}n_{1,test}}\sum_{i:y_{i}=1}\sum_{j:y_{j}=0} I\left(\hat{p}_{i}>\hat{p}_{j}\right), $$ \end{document}auc=1n0,testn1,test∑i:yi=1∑j:yj=0Ip^i>p^j, where n0,test and n1,test are the numbers of observations in the test set with yi=0 and yi=1, respectively. The Brier score is a commonly and increasingly used performance measure [22, 23]. It measures the deviation between true class and predicted probability and is estimated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$brier = \frac{1}{n_{{test}}}\sum_{i=1}^{n_{{test}}} \left(\hat{p}_{i}-y_{i}\right)^{2}. $$ \end{document}brier=1ntest∑i=1ntestp^i−yi2.
