typos and added bootstrap

doc/Projects/2019/Project1/html/._Project1-bs000.html

@@ -179,7 +179,7 @@ function</a>.  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
-<b>Scikit-Learn</b> if needed.
+<b>Scikit-Learn</b> if needed. You can alternatively write your own bootstrap code.
 
 <h3 id="___sec3" class="anchor">Part c): Bias-variance tradeoff </h3>
 
@@ -374,7 +374,7 @@ of data points, and possibly also your training and test data.
 
 <p>
 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!
 
 <h3 id="___sec4" class="anchor">Part d): Ridge Regression on the Franke function  with resampling </h3>

doc/Projects/2019/Project1/html/Project1-bs.html

@@ -179,7 +179,7 @@ function</a>.  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
-<b>Scikit-Learn</b> if needed.
+<b>Scikit-Learn</b> if needed. You can alternatively write your own bootstrap code.
 
 <h3 id="___sec3" class="anchor">Part c): Bias-variance tradeoff </h3>
 
@@ -374,7 +374,7 @@ of data points, and possibly also your training and test data.
 
 <p>
 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!
 
 <h3 id="___sec4" class="anchor">Part d): Ridge Regression on the Franke function  with resampling </h3>

doc/Projects/2019/Project1/html/Project1.html

@@ -134,7 +134,7 @@ function</a>.  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
-<b>Scikit-Learn</b> if needed.
+<b>Scikit-Learn</b> if needed. You can alternatively write your own bootstrap code.
 
 <h3 id="___sec3">Part c): Bias-variance tradeoff </h3>
 
@@ -329,7 +329,7 @@ of data points, and possibly also your training and test data.
 
 <p>
 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!
 
 <h3 id="___sec4">Part d): Ridge Regression on the Franke function  with resampling </h3>

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.}

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.}

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.}

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 ===