lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

update week 36

Browse Source
This commit is contained in:
Morten Hjorth-Jensen
2021-09-09 15:11:20 +02:00
parent a1fd51e4c4
commit 419f83c93a
7 changed files with 2376 additions and 320 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/pub/week36/html/week36-reveal.html
+11 -6
View File
@@ -162,7 +162,7 @@ MathJax.Hub.Config({
<h2 id="plans-for-week-36">Plans for week 36 </h2>
<ul>
<p><li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression</li>
<p><li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember9.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a>.</li>
<p><li> Friday: Linear Regression and links with Statistics, Resampling methods and presentation of first project.</li>
</ul>
<p>
@@ -769,11 +769,7 @@ $$
<p>&nbsp;<br>
<p>
Plotting these results (figure in handwritten notes for week 36) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
<p>
We will now couple the discussions of ordinary least squares, Ridge and Lasso regression with a statistical interpretation, that is we move from a linear algebra analysis to a statistical analysis. In particular, we will focus on what the regularization terms can result in.
We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters \( \beta \).
Plotting these results (<a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf" target="_blank">figure in handwritten notes for week 36</a>) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
</section>
@@ -1195,6 +1191,15 @@ plt.show()
<section>
<h2 id="linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation </h2>
<p>
We will now couple the discussions of ordinary least squares, Ridge
and Lasso regression with a statistical interpretation, that is we
move from a linear algebra analysis to a statistical analysis. In
particular, we will focus on what the regularization terms can result
in. We will amongst other things show that the regularization
parameter can reduce considerably the variance of the parameters
\( \beta \).
<p>
The
advantage of doing linear regression is that we actually end up with
doc/pub/week36/html/week36-solarized.html
+11 -6
View File
@@ -303,7 +303,7 @@ MathJax.Hub.Config({
<h2 id="plans-for-week-36">Plans for week 36 </h2>
<ul>
<li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression</li>
<li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember9.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a>.</li>
<li> Friday: Linear Regression and links with Statistics, Resampling methods and presentation of first project.</li>
</ul>
@@ -827,11 +827,7 @@ $$
$$
<p>
Plotting these results (figure in handwritten notes for week 36) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
<p>
We will now couple the discussions of ordinary least squares, Ridge and Lasso regression with a statistical interpretation, that is we move from a linear algebra analysis to a statistical analysis. In particular, we will focus on what the regularization terms can result in.
We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters \( \beta \).
Plotting these results (<a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf" target="_blank">figure in handwritten notes for week 36</a>) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1216,6 +1212,15 @@ plt.show()
<h2 id="linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation </h2>
<p>
We will now couple the discussions of ordinary least squares, Ridge
and Lasso regression with a statistical interpretation, that is we
move from a linear algebra analysis to a statistical analysis. In
particular, we will focus on what the regularization terms can result
in. We will amongst other things show that the regularization
parameter can reduce considerably the variance of the parameters
\( \beta \).
<p>
The
advantage of doing linear regression is that we actually end up with
doc/pub/week36/html/week36.html
+11 -6
View File
@@ -308,7 +308,7 @@ MathJax.Hub.Config({
<h2 id="plans-for-week-36">Plans for week 36 </h2>
<ul>
<li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression</li>
<li> Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember9.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a>.</li>
<li> Friday: Linear Regression and links with Statistics, Resampling methods and presentation of first project.</li>
</ul>
@@ -832,11 +832,7 @@ $$
$$
<p>
Plotting these results (figure in handwritten notes for week 36) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
<p>
We will now couple the discussions of ordinary least squares, Ridge and Lasso regression with a statistical interpretation, that is we move from a linear algebra analysis to a statistical analysis. In particular, we will focus on what the regularization terms can result in.
We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters \( \beta \).
Plotting these results (<a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf" target="_blank">figure in handwritten notes for week 36</a>) shows clearly that Lasso regression suppresses (sets to zero) values of \( \beta_i \) for specific values of \( \lambda \). Ridge regression reduces on the other hand the values of \( \beta_i \) as function of \( \lambda \).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -1221,6 +1217,15 @@ plt<span style="color: #666666">.</span>show()
<h2 id="linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation </h2>
<p>
We will now couple the discussions of ordinary least squares, Ridge
and Lasso regression with a statistical interpretation, that is we
move from a linear algebra analysis to a statistical analysis. In
particular, we will focus on what the regularization terms can result
in. We will amongst other things show that the regularization
parameter can reduce considerably the variance of the parameters
\( \beta \).
<p>
The
advantage of doing linear regression is that we actually end up with
doc/pub/week36/ipynb/ipynb-week36-src.tar.gz
BIN
View File
Binary file not shown.
doc/pub/week36/ipynb/week36.ipynb
+84 -295
View File
File diff suppressed because one or more lines are too long
doc/src/week36/add.do.txt
+2249
View File
File diff suppressed because it is too large Load Diff
doc/src/week36/week36.do.txt
+10 -7
View File
@@ -6,7 +6,7 @@ DATE: today
!split
===== Plans for week 36 =====
* Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression
* Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression. "Video of Lecture":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember9.mp4?vrtx=view-as-webpage".
* Friday: Linear Regression and links with Statistics, Resampling methods and presentation of first project.
Recommended Reading:
@@ -523,10 +523,8 @@ which leads to
\]
!et
Plotting these results (figure in handwritten notes for week 36) shows clearly that Lasso regression suppresses (sets to zero) values of $\beta_i$ for specific values of $\lambda$. Ridge regression reduces on the other hand the values of $\beta_i$ as function of $\lambda$.
Plotting these results ("figure in handwritten notes for week 36":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2021/NotesSeptember9.pdf") shows clearly that Lasso regression suppresses (sets to zero) values of $\beta_i$ for specific values of $\lambda$. Ridge regression reduces on the other hand the values of $\beta_i$ as function of $\lambda$.
We will now couple the discussions of ordinary least squares, Ridge and Lasso regression with a statistical interpretation, that is we move from a linear algebra analysis to a statistical analysis. In particular, we will focus on what the regularization terms can result in.
We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters $\beta$.
!split
@@ -896,15 +894,20 @@ plt.ylabel('MSE')
plt.legend()
plt.show()
!ec
!split
===== Linking the regression analysis with a statistical interpretation =====
We will now couple the discussions of ordinary least squares, Ridge
and Lasso regression with a statistical interpretation, that is we
move from a linear algebra analysis to a statistical analysis. In
particular, we will focus on what the regularization terms can result
in. We will amongst other things show that the regularization
parameter can reduce considerably the variance of the parameters
$\beta$.
The
advantage of doing linear regression is that we actually end up with