\[ TPR = P(\textrm{модель:} + | \, \textrm{факт:} +) = {TP \over (TP + FN)} \]
\[ SPC = P(\textrm{модель:} - | \, \textrm{факт:} -) = {TN \over (FP + TN)} \] \[ PPV = P(\textrm{факт:} + | \, \textrm{модель:} +) = {TP \over (TP + FP)} \]
\[ NPV = P(\textrm{факт:} - | \, \textrm{модель:} -) = {TN \over (FN + TN)} \]
\[ FNR = 1 - TPR \]
\[ FPR = 1 - SPC \]
\[
FDR = 1 - PPV
\] \[
Acc = P(y_i = j \, | \, y_i \in \omega_j) = {(TP + TN) \over (TP + FP + TN + FN)}
\]
\[
F1 = {2 \cdot TP \over (2 \cdot TP + FP + FN)}
\]
\[ MCC = {TP \cdot TN - FP \cdot FN \over \sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} \]
\[ Info = TPR + SPC - 1 \] \[ Mark = PPV + NPV - 1 \]
\[ P(Y = 1 | X = x_0) = {P(X = x_0 | Y = 1) \cdot P(Y = 1) \over P(X = x_0)} \] \[ P(X) = {e^{\hat{\beta}_0 + \hat{\beta}_1 \cdot X} \over 1 + e^{\hat{\beta}_0 + \hat{\beta}_1 \cdot X}} \Leftrightarrow \\ \Leftrightarrow {P(X) \over 1 - P(X)} = e^{\hat{\beta}_0 + \hat{\beta}_1 \cdot X} \] \({P(X) \over 1 - P(X)} \in (0, \infty)\)
\[ \hat{\delta}_k(x) = x \cdot {\hat{\mu}_k \over \hat{\sigma}^2} - {\hat{\mu}_k^2 \over 2 \hat{\sigma}^2} + \mathrm{log}(\hat{\pi}_k) \rightarrow \mathrm{max}_k \]