From 3e949627801cad01b9a4dcb2c6f586c15dfb6cbd Mon Sep 17 00:00:00 2001 From: Dhanunjaya-Elluri Date: Mon, 9 Dec 2024 12:54:05 +0100 Subject: [PATCH] Added Explained Variance Score Formula --- book/2-regression.tex | 21 ++++++++++++++++----- 1 file changed, 16 insertions(+), 5 deletions(-) diff --git a/book/2-regression.tex b/book/2-regression.tex index c344685..bff7dac 100644 --- a/book/2-regression.tex +++ b/book/2-regression.tex @@ -544,9 +544,9 @@ \subsection{Mean Poisson Deviance} $ } }; - \draw[-latex,nmlred, semithick] ($(a.south)+(-2.2,0)$) to[bend left=15] node[pos=1, left] {number of samples} +(-1,-1); - \draw[-latex,nmlpurple, semithick] ($(a.north)+(0,0.0)$) to[bend left=15] node[pos=1, right] {actual value} +(1.5,.5); - \draw[-latex,nmlcyan, semithick] ($(a.south)+(1.3,0)$) to[bend right=15] node[pos=1, right] {predicted value} +(1.5,-1); + \draw[-latex,nmlred, semithick] ($(a.south)+(-2.2,0.2)$) to[bend left=15] node[pos=1, left] {number of samples} +(-1,-0.5); + \draw[-latex,nmlpurple, semithick] ($(a.north)+(1.3,0.0)$) to[bend left=15] node[pos=1, right] {actual value} +(1,.5); + \draw[-latex,nmlcyan, semithick] ($(a.south)+(1.3,0)$) to[bend right=15] node[pos=1, right] {predicted value} +(1,-0.5); } \end{center} @@ -809,12 +809,23 @@ \subsection{Pinball Loss } \section{Explained Variance Score} \subsection{Explained Variance Score} -The Explained Variance Score is a regression evaluation metric that measures the proportion of variance in the target variable that is captured by the model’s predictions. +The Explained Variance Score (EVS) is a regression evaluation metric that measures the proportion of variance in the target variable that is captured by the model’s predictions. It focuses specifically on how well the variability of the data is explained, rather than penalizing systematic biases or a lack of correlation between true and predicted values. % formula \begin{center} - [FORMULA GOES HERE] + \tikz{ + \node[inner sep=2pt, font=\Large] (a) { + { + $\displaystyle + EVS = 1 - \frac{Var({\color{nmlcyan}Y} - {\color{nmlpurple}\hat{Y}})}{Var({\color{nmlcyan}Y})} + $ + } + }; + + \draw[-latex,nmlcyan, semithick] ($(a.north)+(1.2,0)$) to[bend right=15] node[pos=1, left] {actual value} +(-1,.5); + \draw[-latex,nmlpurple, semithick] ($(a.north)+(2.3,0)$) to[bend left=15] node[pos=1, right] {predicted value} +(1,.5); + } \end{center} Explained Variance Score ranges from -infinity to 1, with 1 indicating that the model explains all variability in the target variable. Negative values suggest the model performs worse