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I am currently trying to understand the MSE of ridge regression. First, I am calculating the MSE mathematically, but I found it quite vague. After reviewing some books and articles I understood that

$$ \begin{aligned} \text{MSE}(\hat{\beta_R}) &= E[||\hat{\beta}_R-{\beta}||^2] \\ \Rightarrow\hat{\beta_{R}}-\beta &= ((X^TX+\lambda)^{-1}X^TX-I)\beta+e \\ \Rightarrow||\hat{\beta}_R-{\beta}||^2 &= (\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta}) \end{aligned} $$

After that I got stuck because of the norm and expectation calculation. I tried to solve it, but it becomes so complicated.

I checked books like: "The Elements of Statistical Learning" and "An Introduction to Statistical Learning".

Can anyone please clarify MSE of ridge regression or guide me to a good source?

I am currently trying to understand the MSE of ridge regression. First, I am calculating the MSE mathematically, but I found it quite vague. After reviewing some books and articles I understood that

$$ \begin{aligned} \text{MSE}(\hat{\beta_R}) &= E[||\hat{\beta}_R-{\beta}||^2] \\ \Rightarrow\hat{\beta_{R}}-\beta &= ((X^TX+\lambda)^{-1}X^TX-I)\beta+e \\ \Rightarrow||\hat{\beta}_R-{\beta}||^2 &= (\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta}) \end{aligned} $$

After that I got stuck because of the norm and expectation calculation. I tried to solve it, but it becomes so complicated.

I have checked books like: "The Elements of Statistical Learning" and "An Introduction to Statistical Learning".

Can anyone please clarify MSE of ridge regression or guide me to a good source?

I am currently trying to understand the MSE of ridge regression. First, I am calculating the MSE mathematically, but I found it quite vague. After reviewing some books and articles I understood that

$$ \begin{aligned} \text{MSE}(\hat{\beta_R}) &= E[||\hat{\beta}_R-{\beta}||^2] \\ \Rightarrow\hat{\beta_{R}}-\beta &= ((X^TX+\lambda)^{-1}X^TX-I)\beta+e \\ \Rightarrow||\hat{\beta}_R-{\beta}||^2 &= (\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta}) \end{aligned} $$

After that I got stuck because of the norm and expectation. I tried to solve it, but it becomes so complicated.

I checked books like: "The Elements of Statistical Learning" and "An Introduction to Statistical Learning".

Can anyone please clarify MSE of ridge regression or guide me to a good source?

I am currently trying to understand the MSE of ridge regression. First, I am calculating the MSE mathematically, but I found it quite vague. After reviewing some books and articles I understood that

$$ \begin{aligned} \text{MSE}(\hat{\beta_R}) &= E[||\hat{\beta}_R-{\beta}||^2] \\ \Rightarrow\hat{\beta_{R}}-\beta &= ((X^TX+\lambda)^{-1}X^TX-I)\beta+e \\ \Rightarrow||\hat{\beta}_R-{\beta}||^2 &= (\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta}) \end{aligned} $$

After that I got stuck because of the norm and expectation calculation. I tried to solve it, but it becomes so complicated.

I checked books like: "The Elements of Statistical Learning" and "An Introduction to Statistical Learning".

Can anyone please clarify MSE of ridge regression or guide me to a good source?

I am currently trying to understand the MSE of ridge regression.

  First, I am calculating the MSE mathematically, but I found it quite vague.

  After, reviewing some books and articles I understood that

$$MSE(\hat{\beta_R})=E[||\hat{\beta}_R-{\beta}||^2]$$ $$\Rightarrow\hat{\beta_{R}}-\beta=((X^TX+\lambda)^{-1}X^TX-I)\beta+e$$ $$\Rightarrow||\hat{\beta}_R-{\beta}||^2=(\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta})$$

After that I stuck because of the norm and expectation , I tried to solve it, but it becomes so complicated.

I checked books like: the elements of statistical learning and an introduction to statistical learning.

Can anyone please clarify MSE of ridge regression or guide me to a good source?

Many thanks.

I am currently trying to understand the MSE of ridge regression. First, I am calculating the MSE mathematically, but I found it quite vague. After reviewing some books and articles I understood that

$$ \begin{aligned} \text{MSE}(\hat{\beta_R}) &= E[||\hat{\beta}_R-{\beta}||^2] \\ \Rightarrow\hat{\beta_{R}}-\beta &= ((X^TX+\lambda)^{-1}X^TX-I)\beta+e \\ \Rightarrow||\hat{\beta}_R-{\beta}||^2 &= (\hat{\beta_R}-{\beta})^T(\hat{\beta_R}-{\beta}) \end{aligned} $$

After that I got stuck because of the norm and expectation. I tried to solve it, but it becomes so complicated.

I checked books like: "The Elements of Statistical Learning" and "An Introduction to Statistical Learning".

Can anyone please clarify MSE of ridge regression or guide me to a good source?