\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# split in training and test data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_test_split\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtest_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
- "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/sklearn/model_selection/_split.py\u001b[0m in \u001b[0;36mtrain_test_split\u001b[0;34m(*arrays, **options)\u001b[0m\n\u001b[1;32m 2125\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Invalid parameters passed: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2127\u001b[0;31m \u001b[0marrays\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mindexable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0marrays\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2128\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2129\u001b[0m \u001b[0mn_samples\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_num_samples\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marrays\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mindexable\u001b[0;34m(*iterables)\u001b[0m\n\u001b[1;32m 290\u001b[0m \"\"\"\n\u001b[1;32m 291\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0m_make_indexable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mX\u001b[0m \u001b[0;32min\u001b[0m \u001b[0miterables\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 292\u001b[0;31m \u001b[0mcheck_consistent_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 293\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 294\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_consistent_length\u001b[0;34m(*arrays)\u001b[0m\n\u001b[1;32m 253\u001b[0m \u001b[0muniques\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munique\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlengths\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 254\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0muniques\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 255\u001b[0;31m raise ValueError(\"Found input variables with inconsistent numbers of\"\n\u001b[0m\u001b[1;32m 256\u001b[0m \" samples: %r\" % [int(l) for l in lengths])\n\u001b[1;32m 257\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;31mValueError\u001b[0m: Found input variables with inconsistent numbers of samples: [1000, 100]"
- ]
- }
- ],
+ "outputs": [],
"source": [
"# split in training and test data\n",
- "X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)"
+ "# X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)"
]
},
{
@@ -4185,7 +4174,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 39,
"metadata": {
"collapsed": false,
"editable": true
@@ -4216,7 +4205,7 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 40,
"metadata": {
"collapsed": false,
"editable": true
@@ -4236,18 +4225,27 @@
"metadata": {},
"source": [
"where $y$ is the function we want to fit with a given polynomial.\n",
- "!bsubex\n",
- "Write a first code which sets up a design matrix $X$ defined by a fifth-order polynomial. Scale your data and split it in training and test data. \n",
- "!esubex\n",
"\n",
- "!bsubex\n",
- "Perform an ordinary least squares and compute the means squared error and the $R2$ factor for the training data and the test data, with and without scaling.\n",
- "!esubex\n",
"\n",
- "!bsubex\n",
- "Add now a model which allows you to make polynomials up to degree $15$. Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?\n",
+ "Write a first code which sets up a design matrix $X$ defined by a\n",
+ "fifth-order polynomial. Scale your data and split it in training and\n",
+ "test data.\n",
"\n",
- "!esubex"
+ "\n",
+ "\n",
+ "Perform an ordinary least squares and compute the means squared error\n",
+ "and the $R2$ factor for the training data and the test data, with and\n",
+ "without scaling.\n",
+ "\n",
+ "\n",
+ "\n",
+ "Add now a model which allows you to make polynomials up to degree\n",
+ "$15$. Perform a standard OLS fitting of the training data and compute\n",
+ "the MSE and $R2$ for the training and test data and plot both test and\n",
+ "training data MSE and $R2$ as functions of the polynomial\n",
+ "degree. Compare what you see with Figure 2.11 of Hastie et al. Comment\n",
+ "your results. For which polynomial degree do you find an optimal MSE\n",
+ "(smallest value)?"
]
}
],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.py b/doc/LectureNotes/_build/jupyter_execute/chapter1.py
index 7ff525383..b828ec607 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.py
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.py
@@ -483,11 +483,13 @@ ways of dealing with outliers.
The Huber cost function is defined as
$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\del\
-ta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2}& \text{for }|\boldsymbol{a}|\leq \delta\\ \delta (|\b\
+m{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
$$
-Here $a=\boldsymbol{y} - \boldsymbol{\tilde{y}}$.
+Here $\boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}}$.
+
+
We will discuss in more
detail these and other functions in the various lectures. We conclude this part with another example. Instead of
a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
@@ -2146,7 +2148,7 @@ It also common to split the data in a **training** set and a **testing** set. A
for testing. This can be done as follows with our design matrix $\boldsymbol{X}$ and data $\boldsymbol{y}$ (remember to import **scikit-learn**)
# split in training and test data
-X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)
+# X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)
Then we can use the standard scaler to scale our data as
@@ -2174,15 +2176,24 @@ x = np.linspace(-3, 3, n).reshape(-1, 1)
y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
where $y$ is the function we want to fit with a given polynomial.
-!bsubex
-Write a first code which sets up a design matrix $X$ defined by a fifth-order polynomial. Scale your data and split it in training and test data.
-!esubex
-!bsubex
-Perform an ordinary least squares and compute the means squared error and the $R2$ factor for the training data and the test data, with and without scaling.
-!esubex
-!bsubex
-Add now a model which allows you to make polynomials up to degree $15$. Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
+Write a first code which sets up a design matrix $X$ defined by a
+fifth-order polynomial. Scale your data and split it in training and
+test data.
-!esubex
\ No newline at end of file
+
+
+Perform an ordinary least squares and compute the means squared error
+and the $R2$ factor for the training data and the test data, with and
+without scaling.
+
+
+
+Add now a model which allows you to make polynomials up to degree
+$15$. Perform a standard OLS fitting of the training data and compute
+the MSE and $R2$ for the training and test data and plot both test and
+training data MSE and $R2$ as functions of the polynomial
+degree. Compare what you see with Figure 2.11 of Hastie et al. Comment
+your results. For which polynomial degree do you find an optimal MSE
+(smallest value)?
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_11_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_11_0.png
index f67778338..d56e1d6d0 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_11_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_11_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_13_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_13_1.png
index a2e04aaa5..3fd1831e1 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_13_1.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_13_1.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_27_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_27_0.png
index c1228b486..ab7dda310 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_27_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_27_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_3_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_3_0.png
index c7183345f..4ad4c8690 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_3_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_3_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_61_10.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_61_10.png
index 97a6c4434..16b5dca78 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter1_61_10.png and b/doc/LectureNotes/_build/jupyter_execute/chapter1_61_10.png differ
diff --git a/doc/LectureNotes/chapter1.ipynb b/doc/LectureNotes/chapter1.ipynb
index 6209e3881..756ce7708 100644
--- a/doc/LectureNotes/chapter1.ipynb
+++ b/doc/LectureNotes/chapter1.ipynb
@@ -629,8 +629,8 @@
"metadata": {},
"source": [
"$$\n",
- "H_{\\delta}(a)=\\left\\{\\begin{array}\\frac{1}{2}a^{2}&{\\text{for }}|a|\\leq \\delta ,\\\\ \\delta (|a|-\\frac {1}{2}\\del\\\n",
- "ta ),&{\\text{otherwise.}\\end{array}\\right.\n",
+ "H_{\\delta}(\\boldsymbol{a})=\\left\\{\\begin{array}{cc}\\frac{1}{2} \\boldsymbol{a}^{2}& \\text{for }|\\boldsymbol{a}|\\leq \\delta\\\\ \\delta (|\\b\\\n",
+ "m{a}|-\\frac{1}{2}\\delta ),&\\text{otherwise}.\\end{array}\\right.\n",
"$$"
]
},
@@ -638,7 +638,9 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Here $a=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n",
+ "Here $\\boldsymbol{a}=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n",
+ "\n",
+ "\n",
"We will discuss in more\n",
"detail these and other functions in the various lectures. We conclude this part with another example. Instead of \n",
"a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn."
@@ -3412,7 +3414,7 @@
"outputs": [],
"source": [
"# split in training and test data\n",
- "X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)"
+ "# X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2)"
]
},
{
@@ -3475,18 +3477,27 @@
"metadata": {},
"source": [
"where $y$ is the function we want to fit with a given polynomial.\n",
- "!bsubex\n",
- "Write a first code which sets up a design matrix $X$ defined by a fifth-order polynomial. Scale your data and split it in training and test data. \n",
- "!esubex\n",
"\n",
- "!bsubex\n",
- "Perform an ordinary least squares and compute the means squared error and the $R2$ factor for the training data and the test data, with and without scaling.\n",
- "!esubex\n",
"\n",
- "!bsubex\n",
- "Add now a model which allows you to make polynomials up to degree $15$. Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?\n",
+ "Write a first code which sets up a design matrix $X$ defined by a\n",
+ "fifth-order polynomial. Scale your data and split it in training and\n",
+ "test data.\n",
"\n",
- "!esubex"
+ "\n",
+ "\n",
+ "Perform an ordinary least squares and compute the means squared error\n",
+ "and the $R2$ factor for the training data and the test data, with and\n",
+ "without scaling.\n",
+ "\n",
+ "\n",
+ "\n",
+ "Add now a model which allows you to make polynomials up to degree\n",
+ "$15$. Perform a standard OLS fitting of the training data and compute\n",
+ "the MSE and $R2$ for the training and test data and plot both test and\n",
+ "training data MSE and $R2$ as functions of the polynomial\n",
+ "degree. Compare what you see with Figure 2.11 of Hastie et al. Comment\n",
+ "your results. For which polynomial degree do you find an optimal MSE\n",
+ "(smallest value)?"
]
}
],
diff --git a/doc/pub/week34/html/._week34-bs038.html b/doc/pub/week34/html/._week34-bs038.html
index ee1073033..377a254ab 100644
--- a/doc/pub/week34/html/._week34-bs038.html
+++ b/doc/pub/week34/html/._week34-bs038.html
@@ -640,13 +640,16 @@ ways of dealing with outliers.
The Huber cost function is defined as
$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2}& \text{for }|\boldsymbol{a}|\leq \delta\\ \delta (|\boldsymbol{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
$$
-Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear \( x \)-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
+Here \( \boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
+
+
+We will discuss in more detail these and other functions in the
+various lectures. We conclude this part with another example. Instead
+of a linear \( x \)-dependence we study now a cubic polynomial and use the
+polynomial regression analysis tools of scikit-learn.
diff --git a/doc/pub/week34/html/._week34-bs066.html b/doc/pub/week34/html/._week34-bs066.html
index 5e3e40188..70c35b11e 100644
--- a/doc/pub/week34/html/._week34-bs066.html
+++ b/doc/pub/week34/html/._week34-bs066.html
@@ -656,27 +656,6 @@ Perform an ordinary least squares and compute the means squared error and the \(
c)
Add now a model which allows you to make polynomials up to degree \( 15 \). Perform a standard OLS fitting of the training data and compute the MSE and \( R2 \) for the training and test data and plot both test and training data MSE and \( R2 \) as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
-
-
-
-
-
-
-Solution.
-
-
-
-
-
-Here you simply need to change the degree of the polynomial in the above code to \( n=15 \).
-
-
-
-
diff --git a/doc/pub/week34/html/week34-reveal.html b/doc/pub/week34/html/week34-reveal.html
index 3a2da7cec..07e207628 100644
--- a/doc/pub/week34/html/week34-reveal.html
+++ b/doc/pub/week34/html/week34-reveal.html
@@ -1743,14 +1743,17 @@ ways of dealing with outliers.
The Huber cost function is defined as
$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2}& \text{for }|\boldsymbol{a}|\leq \delta\\ \delta (|\boldsymbol{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
$$
-Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear \( x \)-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
+Here \( \boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
+
+
+We will discuss in more detail these and other functions in the
+various lectures. We conclude this part with another example. Instead
+of a linear \( x \)-dependence we study now a cubic polynomial and use the
+polynomial regression analysis tools of scikit-learn.
@@ -3579,12 +3582,6 @@ Perform an ordinary least squares and compute the means squared error and the \(
c)
Add now a model which allows you to make polynomials up to degree \( 15 \). Perform a standard OLS fitting of the training data and compute the MSE and \( R2 \) for the training and test data and plot both test and training data MSE and \( R2 \) as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
-
-
-Solution.
-Here you simply need to change the degree of the polynomial in the above code to \( n=15 \).
-
-
diff --git a/doc/pub/week34/html/week34-solarized.html b/doc/pub/week34/html/week34-solarized.html
index fb074240f..537a3b7fa 100644
--- a/doc/pub/week34/html/week34-solarized.html
+++ b/doc/pub/week34/html/week34-solarized.html
@@ -1826,13 +1826,16 @@ ways of dealing with outliers.
The Huber cost function is defined as
$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2}& \text{for }|\boldsymbol{a}|\leq \delta\\ \delta (|\boldsymbol{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
$$
-Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear \( x \)-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
+Here \( \boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
+
+
+We will discuss in more detail these and other functions in the
+various lectures. We conclude this part with another example. Instead
+of a linear \( x \)-dependence we study now a cubic polynomial and use the
+polynomial regression analysis tools of scikit-learn.
@@ -3562,12 +3565,6 @@ Perform an ordinary least squares and compute the means squared error and the \(
c)
Add now a model which allows you to make polynomials up to degree \( 15 \). Perform a standard OLS fitting of the training data and compute the MSE and \( R2 \) for the training and test data and plot both test and training data MSE and \( R2 \) as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
-
-
-Solution.
-Here you simply need to change the degree of the polynomial in the above code to \( n=15 \).
-
-
diff --git a/doc/pub/week34/html/week34.html b/doc/pub/week34/html/week34.html
index 2c5788986..808fa980d 100644
--- a/doc/pub/week34/html/week34.html
+++ b/doc/pub/week34/html/week34.html
@@ -1831,13 +1831,16 @@ ways of dealing with outliers.
The Huber cost function is defined as
$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2}& \text{for }|\boldsymbol{a}|\leq \delta\\ \delta (|\boldsymbol{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
$$
-Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear \( x \)-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
+Here \( \boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
+
+
+We will discuss in more detail these and other functions in the
+various lectures. We conclude this part with another example. Instead
+of a linear \( x \)-dependence we study now a cubic polynomial and use the
+polynomial regression analysis tools of scikit-learn.
@@ -3567,12 +3570,6 @@ Perform an ordinary least squares and compute the means squared error and the \(
c)
Add now a model which allows you to make polynomials up to degree \( 15 \). Perform a standard OLS fitting of the training data and compute the MSE and \( R2 \) for the training and test data and plot both test and training data MSE and \( R2 \) as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
-
-
-Solution.
-Here you simply need to change the degree of the polynomial in the above code to \( n=15 \).
-
-
diff --git a/doc/pub/week34/ipynb/ipynb-week34-src.tar.gz b/doc/pub/week34/ipynb/ipynb-week34-src.tar.gz
index e3b48e526..b42740f87 100644
Binary files a/doc/pub/week34/ipynb/ipynb-week34-src.tar.gz and b/doc/pub/week34/ipynb/ipynb-week34-src.tar.gz differ
diff --git a/doc/pub/week34/ipynb/week34.ipynb b/doc/pub/week34/ipynb/week34.ipynb
index 5f52865d4..a72987afc 100644
--- a/doc/pub/week34/ipynb/week34.ipynb
+++ b/doc/pub/week34/ipynb/week34.ipynb
@@ -1860,7 +1860,7 @@
"metadata": {},
"source": [
"$$\n",
- "H_{\\delta}(a)=\\left\\{\\begin{array}\\frac{1}{2}a^{2}&{\\text{for }}|a|\\leq \\delta ,\\\\ \\delta (|a|-\\frac {1}{2}\\delta ),&{\\text{otherwise.}\\end{array}\\right.\n",
+ "H_{\\delta}(\\boldsymbol{a})=\\left\\{\\begin{array}{cc}\\frac{1}{2} \\boldsymbol{a}^{2}& \\text{for }|\\boldsymbol{a}|\\leq \\delta\\\\ \\delta (|\\boldsymbol{a}|-\\frac{1}{2}\\delta ),&\\text{otherwise}.\\end{array}\\right.\n",
"$$"
]
},
@@ -1868,10 +1868,13 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Here $a=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n",
- "We will discuss in more\n",
- "detail these and other functions in the various lectures. We conclude this part with another example. Instead of \n",
- "a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn."
+ "Here $\\boldsymbol{a}=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n",
+ "\n",
+ "\n",
+ "We will discuss in more detail these and other functions in the\n",
+ "various lectures. We conclude this part with another example. Instead\n",
+ "of a linear $x$-dependence we study now a cubic polynomial and use the\n",
+ "polynomial regression analysis tools of scikit-learn."
]
},
{
@@ -4396,12 +4399,6 @@
"Add now a model which allows you to make polynomials up to degree $15$. Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?\n",
"\n",
"\n",
- "\n",
- "**Solution.**\n",
- "Here you simply need to change the degree of the polynomial in the above code to $n=15$.\n",
- "\n",
- "\n",
- "\n",
""
]
}
diff --git a/doc/src/week34/week34.do.txt b/doc/src/week34/week34.do.txt
index 39c829685..ad6c46f02 100644
--- a/doc/src/week34/week34.do.txt
+++ b/doc/src/week34/week34.do.txt
@@ -1285,13 +1285,16 @@ ways of dealing with outliers.
The Huber cost function is defined as
!bt
\[
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
+H_{\delta}(\bm{a})=\left\{\begin{array}{cc}\frac{1}{2} \bm{a}^{2}& \text{for }|\bm{a}|\leq \delta\\ \delta (|\bm{a}|-\frac{1}{2}\delta ),&\text{otherwise}.\end{array}\right.
\]
!et
-Here $a=\bm{y} - \bm{\tilde{y}}$.
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
+Here $\bm{a}=\bm{y} - \bm{\tilde{y}}$.
+
+
+We will discuss in more detail these and other functions in the
+various lectures. We conclude this part with another example. Instead
+of a linear $x$-dependence we study now a cubic polynomial and use the
+polynomial regression analysis tools of scikit-learn.
!bc pycod
import matplotlib.pyplot as plt
@@ -2872,9 +2875,7 @@ Perform an ordinary least squares and compute the means squared error and the $R
!bsubex
Add now a model which allows you to make polynomials up to degree $15$. Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?
-!bsol
-Here you simply need to change the degree of the polynomial in the above code to $n=15$.
-!esol
+
!esubex
@@ -844,11 +844,11 @@ ways of dealing with outliers.
-
@@ -2330,13 +2332,13 @@ but now splitting the data into a training set and a test set.