correcting typos

This commit is contained in:
Morten Hjorth-Jensen
2021-09-08 13:58:16 +02:00
parent 0f1d69e035
commit 0eb2d3d44e
6 changed files with 20 additions and 20 deletions
+4 -4
View File
@@ -436,13 +436,13 @@ Let us assume we have a data set with outputs/targets given by the vector
!bt
\[
\bm{y}=\begin{matrix}4 \\ 2 \\3\end{bmatrix},
\bm{y}=\begin{bmatrix}4 \\ 2 \\3\end{bmatrix},
\]
!et
and our inputs as a $3\times 2$ design matrix
!bt
\[
\bm{X}=\begin{matrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
\bm{X}=\begin{bmatrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
\]
!et
meaning that we have two features and two unknown parameters $\beta_0$ and $\beta_1$ to be determined either by ordinary least squares, Ridge or Lasso regression.
@@ -461,7 +461,7 @@ Inserting the above values we obtain that
!bt
\[
\hat{\bm{\beta}}^{\mathrm{OLS}}=\begin{matrix}\frac{11}{5} \\ 2\end{bmatrix},
\hat{\bm{\beta}}^{\mathrm{OLS}}=\begin{bmatrix}\frac{11}{5} \\ 2\end{bmatrix},
\]
!et
@@ -483,7 +483,7 @@ Inserting the above values we obtain that
!bt
\[
\hat{\bm{\beta}}^{\mathrm{Ridge}}=\begin{matrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix},
\hat{\bm{\beta}}^{\mathrm{Ridge}}=\begin{bmatrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix},
\]
!et