diff --git a/doc/Projects/2019/Project1/html/._Project1-bs000.html b/doc/Projects/2019/Project1/html/._Project1-bs000.html
index 114f1b35f..0e1c861c4 100644
--- a/doc/Projects/2019/Project1/html/._Project1-bs000.html
+++ b/doc/Projects/2019/Project1/html/._Project1-bs000.html
@@ -179,7 +179,7 @@ function. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -196,7 +196,7 @@ $$
The function will be defined for \( x,y\in [0,1] \). Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an \( x \) and \( y \) dependence of the form \( [x, y,
-x^2, y^2, xy, \dots] \). We will also include cross-validation as
+x^2, y^2, xy, \dots] \). We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for \( x \) and \( y \), or as in
the example below just a set of fixed
@@ -316,7 +316,7 @@ approximately \( 2/3 \) to \( 4/5 \) of the data as training data.
Implement the \( k \)-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-Scikit-Learn if needed.
+Scikit-Learn if needed. You can alternatively write your own bootstrap code.
Part c): Bias-variance tradeoff
@@ -374,7 +374,7 @@ of data points, and possibly also your training and test data.
Try to make a figure similar to Fig. 2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
Part d): Ridge Regression on the Franke function with resampling
diff --git a/doc/Projects/2019/Project1/html/Project1-bs.html b/doc/Projects/2019/Project1/html/Project1-bs.html
index 114f1b35f..0e1c861c4 100644
--- a/doc/Projects/2019/Project1/html/Project1-bs.html
+++ b/doc/Projects/2019/Project1/html/Project1-bs.html
@@ -179,7 +179,7 @@ function. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -196,7 +196,7 @@ $$
The function will be defined for \( x,y\in [0,1] \). Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an \( x \) and \( y \) dependence of the form \( [x, y,
-x^2, y^2, xy, \dots] \). We will also include cross-validation as
+x^2, y^2, xy, \dots] \). We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for \( x \) and \( y \), or as in
the example below just a set of fixed
@@ -316,7 +316,7 @@ approximately \( 2/3 \) to \( 4/5 \) of the data as training data.
Implement the \( k \)-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-Scikit-Learn if needed.
+Scikit-Learn if needed. You can alternatively write your own bootstrap code.
Part c): Bias-variance tradeoff
@@ -374,7 +374,7 @@ of data points, and possibly also your training and test data.
Try to make a figure similar to Fig. 2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
Part d): Ridge Regression on the Franke function with resampling
diff --git a/doc/Projects/2019/Project1/html/Project1.html b/doc/Projects/2019/Project1/html/Project1.html
index f350ddddb..f84e992cd 100644
--- a/doc/Projects/2019/Project1/html/Project1.html
+++ b/doc/Projects/2019/Project1/html/Project1.html
@@ -134,7 +134,7 @@ function. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -151,7 +151,7 @@ $$
The function will be defined for \( x,y\in [0,1] \). Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an \( x \) and \( y \) dependence of the form \( [x, y,
-x^2, y^2, xy, \dots] \). We will also include cross-validation as
+x^2, y^2, xy, \dots] \). We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for \( x \) and \( y \), or as in
the example below just a set of fixed
@@ -271,7 +271,7 @@ approximately \( 2/3 \) to \( 4/5 \) of the data as training data.
Implement the \( k \)-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-Scikit-Learn if needed.
+Scikit-Learn if needed. You can alternatively write your own bootstrap code.
Part c): Bias-variance tradeoff
@@ -329,7 +329,7 @@ of data points, and possibly also your training and test data.
Try to make a figure similar to Fig. 2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
Part d): Ridge Regression on the Franke function with resampling
diff --git a/doc/Projects/2019/Project1/ipynb/ipynb-Project1-src.tar.gz b/doc/Projects/2019/Project1/ipynb/ipynb-Project1-src.tar.gz
index 4cae777dd..44c25d08c 100644
Binary files a/doc/Projects/2019/Project1/ipynb/ipynb-Project1-src.tar.gz and b/doc/Projects/2019/Project1/ipynb/ipynb-Project1-src.tar.gz differ
diff --git a/doc/Projects/2019/Project1/pdf/Project1.p.tex b/doc/Projects/2019/Project1/pdf/Project1.p.tex
index ee1530565..6c4d050b5 100644
--- a/doc/Projects/2019/Project1/pdf/Project1.p.tex
+++ b/doc/Projects/2019/Project1/pdf/Project1.p.tex
@@ -175,7 +175,7 @@ function}. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -189,7 +189,7 @@ f(x,y) &= \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}
The function will be defined for $x,y\in [0,1]$. Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,
-x^2, y^2, xy, \dots]$. We will also include cross-validation as
+x^2, y^2, xy, \dots]$. We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for $x$ and $y$, or as in
the example below just a set of fixed
@@ -300,7 +300,7 @@ approximately $2/3$ to $4/5$ of the data as training data.
Implement the $k$-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-\textbf{Scikit-Learn} if needed.
+\textbf{Scikit-Learn} if needed. You can alternatively write your own bootstrap code.
@@ -351,7 +351,7 @@ of your model complexity (the degree of the polynomial) and the number
of data points, and possibly also your training and test data.
Try to make a figure similar to Fig.~2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
\paragraph{Part d): Ridge Regression on the Franke function with resampling.}
diff --git a/doc/Projects/2019/Project1/pdf/Project1.pdf b/doc/Projects/2019/Project1/pdf/Project1.pdf
index 963505aa0..0380e19af 100644
Binary files a/doc/Projects/2019/Project1/pdf/Project1.pdf and b/doc/Projects/2019/Project1/pdf/Project1.pdf differ
diff --git a/doc/Projects/2019/Project1/pdf/Project1.tex b/doc/Projects/2019/Project1/pdf/Project1.tex
index 57ee02c4e..d24675702 100644
--- a/doc/Projects/2019/Project1/pdf/Project1.tex
+++ b/doc/Projects/2019/Project1/pdf/Project1.tex
@@ -145,7 +145,7 @@ function}. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -159,7 +159,7 @@ f(x,y) &= \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}
The function will be defined for $x,y\in [0,1]$. Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,
-x^2, y^2, xy, \dots]$. We will also include cross-validation as
+x^2, y^2, xy, \dots]$. We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for $x$ and $y$, or as in
the example below just a set of fixed
@@ -270,7 +270,7 @@ approximately $2/3$ to $4/5$ of the data as training data.
Implement the $k$-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-\textbf{Scikit-Learn} if needed.
+\textbf{Scikit-Learn} if needed. You can alternatively write your own bootstrap code.
@@ -321,7 +321,7 @@ of your model complexity (the degree of the polynomial) and the number
of data points, and possibly also your training and test data.
Try to make a figure similar to Fig.~2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
\paragraph{Part d): Ridge Regression on the Franke function with resampling.}
diff --git a/doc/Projects/2019/Project1/pdf/Project1.tex~ b/doc/Projects/2019/Project1/pdf/Project1.tex~
index 0c4ffdbbd..9253df903 100644
--- a/doc/Projects/2019/Project1/pdf/Project1.tex~
+++ b/doc/Projects/2019/Project1/pdf/Project1.tex~
@@ -145,7 +145,7 @@ function}. This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -159,7 +159,7 @@ f(x,y) &= \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}
The function will be defined for $x,y\in [0,1]$. Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,
-x^2, y^2, xy, \dots]$. We will also include cross-validation as
+x^2, y^2, xy, \dots]$. We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for $x$ and $y$, or as in
the example below just a set of fixed
@@ -270,7 +270,7 @@ approximately $2/3$ to $4/5$ of the data as training data.
Implement the $k$-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-\textbf{Scikit-Learn} if needed.
+\textbf{Scikit-Learn} if needed. You can alternatively write your own bootstrap code.
@@ -321,7 +321,7 @@ of your model complexity (the degree of the polynomial) and the number
of data points, and possibly also your training and test data.
Try to make a figure similar to Fig.~2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
\paragraph{Part d): Ridge Regression on the Franke function with resampling.}
diff --git a/doc/src/Projects/2019/Project1/Project1.do.txt b/doc/src/Projects/2019/Project1/Project1.do.txt
index 237f1d6bf..b1accc914 100644
--- a/doc/src/Projects/2019/Project1/Project1.do.txt
+++ b/doc/src/Projects/2019/Project1/Project1.do.txt
@@ -17,7 +17,7 @@ function":"http://www.dtic.mil/dtic/tr/fulltext/u2/a081688.pdf". This
is a function which has been widely used when testing various
interpolation and fitting algorithms. Furthermore, after having
established the model and the method, we will employ resamling
-techniques such as cross-validation in order to perform a
+techniques such as cross-validation and/or bootstrap in order to perform a
proper assessment of our models. We will also study in detail the
so-called Bias-Variance trade off.
@@ -33,7 +33,7 @@ f(x,y) &= \frac{3}{4}\exp{\left(-\frac{(9x-2)^2}{4} - \frac{(9y-2)^2}{4}\right)}
The function will be defined for $x,y\in [0,1]$. Our first step will
be to perform an OLS regression analysis of this function, trying out
a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,
-x^2, y^2, xy, \dots]$. We will also include cross-validation as
+x^2, y^2, xy, \dots]$. We will also include cross-validation (or bootstrap) as
resampling technique. As in homeworks 1 and 2, we can use a uniform
distribution to set up the arrays of values for $x$ and $y$, or as in
the example below just a set of fixed
@@ -153,7 +153,7 @@ approximately $2/3$ to $4/5$ of the data as training data.
Implement the $k$-fold cross-validation algorithm (write your own
code) and evaluate again the MSE function resulting
from the test data. You can compare your own code with that from
-_Scikit-Learn_ if needed.
+_Scikit-Learn_ if needed. You can alternatively write your own bootstrap code.
@@ -211,7 +211,7 @@ of your model complexity (the degree of the polynomial) and the number
of data points, and possibly also your training and test data.
Try to make a figure similar to Fig. 2.11 of Hastie, Tibshirani, and
-Friedman, see the references below. You will most likely not get an
+Friedman, see the references below. You should include an analysis of the bias and variance for the test results. Figure 2.11 displays only the test and training MSEs while indicating regions of low/high bias and variance. You will most likely not get an
equally smooth curve!
=== Part d): Ridge Regression on the Franke function with resampling ===