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Adding Balanced Accuracy formula #153

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b4f3cdc
Adding Balanced Accuracy formula into the book
nakul-py Dec 12, 2024
aba2123
Adding Balanced-Accuracy Formula
nakul-py Dec 13, 2024
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17 changes: 16 additions & 1 deletion book/3-classification.tex
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Expand Up @@ -344,7 +344,22 @@ \subsection{Balanced Accuracy}

% formula
\begin{center}
[FORMULA GOES HERE]
\tikz{
\node[inner sep=2pt, font=\Large] (a) {
{
$\displaystyle
Balanced-Accuracy = \frac{1}{2} \left(
\frac{\textcolor{nmlred}{TP}}{\textcolor{nmlred}{TP} + \textcolor{nmlgreen}{FN}} +
\frac{\textcolor{nmlcyan}{TN}}{\textcolor{nmlcyan}{TN} + \textcolor{nmlpurple}{FP}}
\right)
$
}
};
\draw[-latex, nmlgreen, semithick] ($(a.south)+(2.1,0.04)$) to[bend left=25] node[pos=1, left] {\color{nmlgreen} false negative} +(-.8, -.5);
\draw[-latex, nmlpurple, semithick] ($(a.south)+(5.1,0.04)$) to[bend left=-25] node[pos=1, right] {\color{nmlpurple} false positive} +(.8, -.7);
\draw[-latex, nmlred, semithick] ($(a.south)+(1.5, 1.3)$) to[bend right=25] node[pos=1, left] {\color{nmlred} true positive} +(-0.9, .6);
\draw[-latex, nmlcyan, semithick] ($(a.south)+(4.5, 1.3)$) to[bend left=25] node[pos=1, right] {\color{nmlcyan} true negative} +(0.9, .6);
}
\end{center}

It is particularly useful when working with datasets where some classes are significantly underrepresented, ensuring that the performance of all classes is treated equally.
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