$$
-\boldsymbol{y}=\begin{matrix}4 \\ 2 \\3\end{bmatrix},
+\boldsymbol{y}=\begin{bmatrix}4 \\ 2 \\3\end{bmatrix},
$$
and our inputs as a \( 3\times 2 \) design matrix
$$
-\boldsymbol{X}=\begin{matrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
+\boldsymbol{X}=\begin{bmatrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
$$
@@ -701,7 +701,7 @@ Inserting the above values we obtain that
$$
-\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{matrix}\frac{11}{5} \\ 2\end{bmatrix},
+\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{bmatrix}\frac{11}{5} \\ 2\end{bmatrix},
$$
@@ -729,7 +729,7 @@ Inserting the above values we obtain that
$$
-\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{matrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix},
+\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{bmatrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix},
$$
diff --git a/doc/pub/week36/html/week36-solarized.html b/doc/pub/week36/html/week36-solarized.html
index d1e88fd64..dd08803f0 100644
--- a/doc/pub/week36/html/week36-solarized.html
+++ b/doc/pub/week36/html/week36-solarized.html
@@ -688,12 +688,12 @@ We will amongst other things show that the regularization parameter can reduce c
Let us assume we have a data set with outputs/targets given by the vector
$$
-\boldsymbol{y}=\begin{matrix}4 \\ 2 \\3\end{bmatrix},
+\boldsymbol{y}=\begin{bmatrix}4 \\ 2 \\3\end{bmatrix},
$$
and our inputs as a \( 3\times 2 \) design matrix
$$
-\boldsymbol{X}=\begin{matrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
+\boldsymbol{X}=\begin{bmatrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix},
$$
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.
@@ -713,7 +713,7 @@ $$
Inserting the above values we obtain that
$$
-\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{matrix}\frac{11}{5} \\ 2\end{bmatrix},
+\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{bmatrix}\frac{11}{5} \\ 2\end{bmatrix},
$$
@@ -737,7 +737,7 @@ $$ Inserting the above values we obtain that $$ -\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{matrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix}, +\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{bmatrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix}, $$
diff --git a/doc/pub/week36/html/week36.html b/doc/pub/week36/html/week36.html index d117d30dd..db69c4b73 100644 --- a/doc/pub/week36/html/week36.html +++ b/doc/pub/week36/html/week36.html @@ -693,12 +693,12 @@ We will amongst other things show that the regularization parameter can reduce c Let us assume we have a data set with outputs/targets given by the vector $$ -\boldsymbol{y}=\begin{matrix}4 \\ 2 \\3\end{bmatrix}, +\boldsymbol{y}=\begin{bmatrix}4 \\ 2 \\3\end{bmatrix}, $$ and our inputs as a \( 3\times 2 \) design matrix $$ -\boldsymbol{X}=\begin{matrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix}, +\boldsymbol{X}=\begin{bmatrix}2 & 0\\ 0 & 1 \\ 1 & 0\end{bmatrix}, $$ 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. @@ -718,7 +718,7 @@ $$ Inserting the above values we obtain that $$ -\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{matrix}\frac{11}{5} \\ 2\end{bmatrix}, +\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{bmatrix}\frac{11}{5} \\ 2\end{bmatrix}, $$
@@ -742,7 +742,7 @@ $$ Inserting the above values we obtain that $$ -\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{matrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix}, +\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}=\begin{bmatrix}\frac{11}{5+\lambda} \\ \frac{2}{1+\lambda}\end{bmatrix}, $$
diff --git a/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz b/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz index 4fbe9544c..e9efb4e29 100644 Binary files a/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz and b/doc/pub/week36/ipynb/ipynb-week36-src.tar.gz differ diff --git a/doc/pub/week36/ipynb/week36.ipynb b/doc/pub/week36/ipynb/week36.ipynb index 1aa22c4c9..8be9302f1 100644 --- a/doc/pub/week36/ipynb/week36.ipynb +++ b/doc/pub/week36/ipynb/week36.ipynb @@ -788,7 +788,7 @@ "metadata": {}, "source": [ "$$\n", - "\\boldsymbol{y}=\\begin{matrix}4 \\\\ 2 \\\\3\\end{bmatrix},\n", + "\\boldsymbol{y}=\\begin{bmatrix}4 \\\\ 2 \\\\3\\end{bmatrix},\n", "$$" ] }, @@ -804,7 +804,7 @@ "metadata": {}, "source": [ "$$\n", - "\\boldsymbol{X}=\\begin{matrix}2 & 0\\\\ 0 & 1 \\\\ 1 & 0\\end{bmatrix},\n", + "\\boldsymbol{X}=\\begin{bmatrix}2 & 0\\\\ 0 & 1 \\\\ 1 & 0\\end{bmatrix},\n", "$$" ] }, @@ -840,7 +840,7 @@ "metadata": {}, "source": [ "$$\n", - "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\begin{matrix}\\frac{11}{5} \\\\ 2\\end{bmatrix},\n", + "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\begin{bmatrix}\\frac{11}{5} \\\\ 2\\end{bmatrix},\n", "$$" ] }, @@ -878,7 +878,7 @@ "metadata": {}, "source": [ "$$\n", - "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}}=\\begin{matrix}\\frac{11}{5+\\lambda} \\\\ \\frac{2}{1+\\lambda}\\end{bmatrix},\n", + "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}}=\\begin{bmatrix}\\frac{11}{5+\\lambda} \\\\ \\frac{2}{1+\\lambda}\\end{bmatrix},\n", "$$" ] }, diff --git a/doc/src/week36/week36.do.txt b/doc/src/week36/week36.do.txt index dd3573afa..4a47a5747 100644 --- a/doc/src/week36/week36.do.txt +++ b/doc/src/week36/week36.do.txt @@ -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