Update on project 1

2018-09-14 06:13:23 +02:00
parent 81a5432b78
commit 546b0bf220
7 changed files with 20 additions and 20 deletions
@@ -151,7 +151,7 @@ MathJax.Hub.Config({
 <center><b>Department of Physics, University of Oslo, Norway</b></center>
 <br>
 <p>
-<center><h4>Sep 12, 2018</h4></center> <!-- date -->
+<center><h4>Sep 14, 2018</h4></center> <!-- date -->
 <br>
 <p>
 </div> <!-- end jumbotron -->
@@ -171,7 +171,7 @@ to fit polynomials to a specific two-dimensional function called
 function</a>.  This
 is a function which has been widely used when testing various  interpolation and fitting
 algorithms. Furthermore, after having etsablished the model and the
-method, we will employ resamling techniques such as the  cross-validation and
+method, we will employ resamling techniques such as the  cross-validation and/or
 the bootstrap methods, in order to perform a proper assessment of our models.

 <p>
@@ -276,8 +276,8 @@ $$
 $$

 <p>
-Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and the bootstrap algorithm
-and evaluate again the MSE and the \( R^2 \) functions resulting from the test data.
+Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and/or the bootstrap algorithm
+and evaluate again the MSE and the \( R^2 \) functions resulting from the test data. Evaluate also the bias and variance of the final models using for example equation (7.9) in the textbook of Hastie <em>et al.</em>

 <h3 id="___sec2" class="anchor">Part b): Ridge Regression on the Franke function  with resampling </h3>

@@ -151,7 +151,7 @@ MathJax.Hub.Config({
 <center><b>Department of Physics, University of Oslo, Norway</b></center>
 <br>
 <p>
-<center><h4>Sep 12, 2018</h4></center> <!-- date -->
+<center><h4>Sep 14, 2018</h4></center> <!-- date -->
 <br>
 <p>
 </div> <!-- end jumbotron -->
@@ -171,7 +171,7 @@ to fit polynomials to a specific two-dimensional function called
 function</a>.  This
 is a function which has been widely used when testing various  interpolation and fitting
 algorithms. Furthermore, after having etsablished the model and the
-method, we will employ resamling techniques such as the  cross-validation and
+method, we will employ resamling techniques such as the  cross-validation and/or
 the bootstrap methods, in order to perform a proper assessment of our models.

 <p>
@@ -276,8 +276,8 @@ $$
 $$

 <p>
-Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and the bootstrap algorithm
-and evaluate again the MSE and the \( R^2 \) functions resulting from the test data.
+Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and/or the bootstrap algorithm
+and evaluate again the MSE and the \( R^2 \) functions resulting from the test data. Evaluate also the bias and variance of the final models using for example equation (7.9) in the textbook of Hastie <em>et al.</em>

 <h3 id="___sec2" class="anchor">Part b): Ridge Regression on the Franke function  with resampling </h3>

@@ -110,7 +110,7 @@ MathJax.Hub.Config({
 <center><b>Department of Physics, University of Oslo, Norway</b></center>
 <br>
 <p>
-<center><h4>Sep 12, 2018</h4></center> <!-- date -->
+<center><h4>Sep 14, 2018</h4></center> <!-- date -->
 <br>

 <h2 id="___sec0">Regression analysis and resampling methods  </h2>
@@ -128,7 +128,7 @@ to fit polynomials to a specific two-dimensional function called
 function</a>.  This
 is a function which has been widely used when testing various  interpolation and fitting
 algorithms. Furthermore, after having etsablished the model and the
-method, we will employ resamling techniques such as the  cross-validation and
+method, we will employ resamling techniques such as the  cross-validation and/or
 the bootstrap methods, in order to perform a proper assessment of our models.

 <p>
@@ -233,8 +233,8 @@ $$
 $$

 <p>
-Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and the bootstrap algorithm
-and evaluate again the MSE and the \( R^2 \) functions resulting from the test data.
+Perform a resampling of the data where you split the data in training data and test data. Implement the \( k \)-fold cross-validation algorithm and/or the bootstrap algorithm
+and evaluate again the MSE and the \( R^2 \) functions resulting from the test data. Evaluate also the bias and variance of the final models using for example equation (7.9) in the textbook of Hastie <em>et al.</em>

 <h3 id="___sec2">Part b): Ridge Regression on the Franke function  with resampling </h3>

@@ -125,7 +125,7 @@ Project 1 on Machine Learning, deadline October 1

 % --- begin date ---
 \begin{center}
-Sep 12, 2018
+Sep 14, 2018
 \end{center}
 % --- end date ---

@@ -145,7 +145,7 @@ to fit polynomials to a specific two-dimensional function called
 function}.  This
 is a function which has been widely used when testing various  interpolation and fitting
 algorithms. Furthermore, after having etsablished the model and the
-method, we will employ resamling techniques such as the  cross-validation and
+method, we will employ resamling techniques such as the  cross-validation and/or
 the bootstrap methods, in order to perform a proper assessment of our models.


@@ -240,8 +240,8 @@ where we have defined the mean value  of $\hat{y}$ as
 \bar{y} =  \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
 \]

-Perform a resampling of the data where you split the data in training data and test data. Implement the $k$-fold cross-validation algorithm and the bootstrap algorithm
-and evaluate again the MSE and the $R^2$ functions resulting from the test data. 
+Perform a resampling of the data where you split the data in training data and test data. Implement the $k$-fold cross-validation algorithm and/or the bootstrap algorithm
+and evaluate again the MSE and the $R^2$ functions resulting from the test data. Evaluate also the bias and variance of the final models using for example equation (7.9) in the textbook of Hastie \emph{et al.}



@@ -258,7 +258,7 @@ We are going to download digital terrain data from the website \href{{https://ea
 In order to obtain data for a specific region, you need to register as a user (free) at this website and then decide upon which area you want to fetch the digital terrain data from.  In order to be able to read the data properly, you need to specify that the format should be \textbf{SRTM Arc-Second Global} and download the data as a \textbf{GeoTIF} file.
 The files are then stored in \emph{tif} format which can be imported into a Python program using
 \begin{verbatim}
-from imageio import imread
+scipy.misc.imread
 \end{verbatim}

 Here is a simple part of a Python code which reads and plots the data from such files
@@ -16,7 +16,7 @@ to fit polynomials to a specific two-dimensional function called
 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 etsablished the model and the
-method, we will employ resamling techniques such as the  cross-validation and
+method, we will employ resamling techniques such as the  cross-validation and/or
 the bootstrap methods, in order to perform a proper assessment of our models.


@@ -120,8 +120,8 @@ where we have defined the mean value  of $\hat{y}$ as
 \]
 !et

-Perform a resampling of the data where you split the data in training data and test data. Implement the $k$-fold cross-validation algorithm and the bootstrap algorithm
-and evaluate again the MSE and the $R^2$ functions resulting from the test data. 
+Perform a resampling of the data where you split the data in training data and test data. Implement the $k$-fold cross-validation algorithm and/or the bootstrap algorithm
+and evaluate again the MSE and the $R^2$ functions resulting from the test data. Evaluate also the bias and variance of the final models using for example equation (7.9) in the textbook of Hastie *et al.*