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updating p3

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Morten Hjorth-Jensen
2021-11-14 16:25:43 +01:00
parent d8ba00749c
commit 00def199d3
9 changed files with 290 additions and 71 deletions
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doc/Projects/2021/Project3/html/._Project3-bs000.html
+39 -5
View File
@@ -65,6 +65,11 @@ doconce format html Project3.do.txt --html_style=bootstrap --pygments_html_style
None,
'part-d-solving-eigenvalue-problems'),
('Part e)', 3, None, 'part-e'),
('Additonal (optional) exercise, adding 30 more points to final '
'score',
2,
None,
'additonal-optional-exercise-adding-30-more-points-to-final-score'),
('Introduction to numerical projects',
2,
None,
@@ -129,6 +134,7 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="#part-c-neural-networks" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part c) Neural networks</a></li>
<!-- navigation toc: --> <li><a href="#part-d-solving-eigenvalue-problems" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part d) Solving eigenvalue problems</a></li>
<!-- navigation toc: --> <li><a href="#part-e" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part e)</a></li>
<!-- navigation toc: --> <li><a href="#additonal-optional-exercise-adding-30-more-points-to-final-score" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Additonal (optional) exercise, adding 30 more points to final score</a></li>
<!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
<!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
<!-- navigation toc: --> <li><a href="#format-for-electronic-delivery-of-report-and-programs" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Format for electronic delivery of report and programs</a></li>
@@ -159,7 +165,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Nov 13, 2021</h4>
<h4>Nov 14, 2021</h4>
</center> <!-- date -->
<br>
@@ -172,10 +178,11 @@ MathJax.Hub.Config({
<ol>
<li> <a href="https://www.kaggle.com/datasets" target="_self">Kaggle</a></li>
<li> The <a href="https://archive.ics.uci.edu/ml/index.php" target="_self">University of California at Irvine (UCI) with its machine learning repository</a>.</li>
<li> Or other sources.</li>
</ol>
<p>The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:</p>
<ol>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests</b>, <b>Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so.</li>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Adversarial Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests, Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as <b>Principal Component Analysis</b> and <b>k-means Clustering</b>.</li>
</ol>
<p>For Boosting, feel also free to write your own codes.</p>
@@ -186,11 +193,13 @@ MathJax.Hub.Config({
<li> If possible, you should link the data sets with exisiting research and analyses thereof. Scientific articles which have used Machine Learning algorithms to analyze the data are highly welcome. Perhaps you can improve previous analyses and even publish a new article?</li>
<li> A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.</li>
</ol>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc.. </p>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..</p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.. </p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html" target="_self">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_self">Yadav et al</a>.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html" target="_self">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_self">Yadav et al</a>.</p>
<p><b>Note</b>: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise. </p>
<h2 id="the-basic-structure-of-your-project" class="anchor">The basic structure of your project </h2>
<p>Here follows a set up on how to structure your report and analyze the data you have opted for.</p>
@@ -326,6 +335,31 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
<h3 id="part-e" class="anchor">Part e) </h3>
<p>Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods. </p>
<h2 id="additonal-optional-exercise-adding-30-more-points-to-final-score" class="anchor">Additonal (optional) exercise, adding 30 more points to final score </h2>
<p>This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like <b>Scikit-Learn</b>, <b>Tensorflow</b> or similar.
</p>
<p>Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
</p>
<p>Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
</p>
<h2 id="introduction-to-numerical-projects" class="anchor">Introduction to numerical projects </h2>
<p>Here follows a brief recipe and recommendation on how to write a report for each
doc/Projects/2021/Project3/html/Project3-bs.html
+39 -5
View File
@@ -65,6 +65,11 @@ doconce format html Project3.do.txt --html_style=bootstrap --pygments_html_style
None,
'part-d-solving-eigenvalue-problems'),
('Part e)', 3, None, 'part-e'),
('Additonal (optional) exercise, adding 30 more points to final '
'score',
2,
None,
'additonal-optional-exercise-adding-30-more-points-to-final-score'),
('Introduction to numerical projects',
2,
None,
@@ -129,6 +134,7 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="#part-c-neural-networks" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part c) Neural networks</a></li>
<!-- navigation toc: --> <li><a href="#part-d-solving-eigenvalue-problems" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part d) Solving eigenvalue problems</a></li>
<!-- navigation toc: --> <li><a href="#part-e" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part e)</a></li>
<!-- navigation toc: --> <li><a href="#additonal-optional-exercise-adding-30-more-points-to-final-score" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Additonal (optional) exercise, adding 30 more points to final score</a></li>
<!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
<!-- navigation toc: --> <li><a href="#introduction-to-numerical-projects" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Introduction to numerical projects</a></li>
<!-- navigation toc: --> <li><a href="#format-for-electronic-delivery-of-report-and-programs" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Format for electronic delivery of report and programs</a></li>
@@ -159,7 +165,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Nov 13, 2021</h4>
<h4>Nov 14, 2021</h4>
</center> <!-- date -->
<br>
@@ -172,10 +178,11 @@ MathJax.Hub.Config({
<ol>
<li> <a href="https://www.kaggle.com/datasets" target="_self">Kaggle</a></li>
<li> The <a href="https://archive.ics.uci.edu/ml/index.php" target="_self">University of California at Irvine (UCI) with its machine learning repository</a>.</li>
<li> Or other sources.</li>
</ol>
<p>The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:</p>
<ol>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests</b>, <b>Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so.</li>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Adversarial Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests, Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as <b>Principal Component Analysis</b> and <b>k-means Clustering</b>.</li>
</ol>
<p>For Boosting, feel also free to write your own codes.</p>
@@ -186,11 +193,13 @@ MathJax.Hub.Config({
<li> If possible, you should link the data sets with exisiting research and analyses thereof. Scientific articles which have used Machine Learning algorithms to analyze the data are highly welcome. Perhaps you can improve previous analyses and even publish a new article?</li>
<li> A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.</li>
</ol>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc.. </p>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..</p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.. </p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html" target="_self">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_self">Yadav et al</a>.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html" target="_self">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_self">Yadav et al</a>.</p>
<p><b>Note</b>: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise. </p>
<h2 id="the-basic-structure-of-your-project" class="anchor">The basic structure of your project </h2>
<p>Here follows a set up on how to structure your report and analyze the data you have opted for.</p>
@@ -326,6 +335,31 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
<h3 id="part-e" class="anchor">Part e) </h3>
<p>Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods. </p>
<h2 id="additonal-optional-exercise-adding-30-more-points-to-final-score" class="anchor">Additonal (optional) exercise, adding 30 more points to final score </h2>
<p>This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like <b>Scikit-Learn</b>, <b>Tensorflow</b> or similar.
</p>
<p>Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
</p>
<p>Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
</p>
<h2 id="introduction-to-numerical-projects" class="anchor">Introduction to numerical projects </h2>
<p>Here follows a brief recipe and recommendation on how to write a report for each
doc/Projects/2021/Project3/html/Project3.html
+38 -5
View File
@@ -143,6 +143,11 @@ div.toc p,a {
None,
'part-d-solving-eigenvalue-problems'),
('Part e)', 3, None, 'part-e'),
('Additonal (optional) exercise, adding 30 more points to final '
'score',
2,
None,
'additonal-optional-exercise-adding-30-more-points-to-final-score'),
('Introduction to numerical projects',
2,
None,
@@ -193,7 +198,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Nov 13, 2021</h4>
<h4>Nov 14, 2021</h4>
</center> <!-- date -->
<br>
<h1 id="paths-for-project-3">Paths for project 3 </h1>
@@ -203,10 +208,11 @@ MathJax.Hub.Config({
<ol>
<li> <a href="https://www.kaggle.com/datasets" target="_blank">Kaggle</a></li>
<li> The <a href="https://archive.ics.uci.edu/ml/index.php" target="_blank">University of California at Irvine (UCI) with its machine learning repository</a>.</li>
<li> Or other sources.</li>
</ol>
<p>The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:</p>
<ol>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests</b>, <b>Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so.</li>
<li> Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <b>linear regression (including Ridge and Lasso)</b>, <b>Logistic Regression</b>, <b>Neural Networks</b>, <b>Convolution Neural Networks</b>, <b>Recurrent Neural Networks</b>, <b>Adversarial Neural Networks</b>, <b>Support Vector Machines</b> and <b>Decision Trees, Random Forests, Bagging and Boosting</b>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <b>convolutional neural networks</b> or <b>recurrent neural networks</b>, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as <b>Principal Component Analysis</b> and <b>k-means Clustering</b>.</li>
</ol>
<p>For Boosting, feel also free to write your own codes.</p>
@@ -217,11 +223,13 @@ MathJax.Hub.Config({
<li> If possible, you should link the data sets with exisiting research and analyses thereof. Scientific articles which have used Machine Learning algorithms to analyze the data are highly welcome. Perhaps you can improve previous analyses and even publish a new article?</li>
<li> A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.</li>
</ol>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc.. </p>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..</p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.. </p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html" target="_blank">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_blank">Yadav et al</a>.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a href="https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html" target="_blank">from week 43</a> and/or the textbook by <a href="https://www.springer.com/gp/book/9789401798150" target="_blank">Yadav et al</a>.</p>
<p><b>Note</b>: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise. </p>
<h2 id="the-basic-structure-of-your-project">The basic structure of your project </h2>
<p>Here follows a set up on how to structure your report and analyze the data you have opted for.</p>
@@ -357,6 +365,31 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
<h3 id="part-e">Part e) </h3>
<p>Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods. </p>
<h2 id="additonal-optional-exercise-adding-30-more-points-to-final-score">Additonal (optional) exercise, adding 30 more points to final score </h2>
<p>This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like <b>Scikit-Learn</b>, <b>Tensorflow</b> or similar.
</p>
<p>Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
</p>
<p>Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
</p>
<h2 id="introduction-to-numerical-projects">Introduction to numerical projects </h2>
<p>Here follows a brief recipe and recommendation on how to write a report for each
doc/Projects/2021/Project3/ipynb/Project3.ipynb
+76 -41
View File
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
"id": "cf42a5c7",
"id": "92499fce",
"metadata": {
"editable": true
},
@@ -14,7 +14,7 @@
},
{
"cell_type": "markdown",
"id": "dfe8ff79",
"id": "56cf5579",
"metadata": {
"editable": true
},
@@ -22,14 +22,14 @@
"# Project 3 on Machine Learning, deadline December 17, 2021\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Nov 13, 2021**\n",
"Date: **Nov 14, 2021**\n",
"\n",
"Copyright 1999-2021, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
]
},
{
"cell_type": "markdown",
"id": "a5296ee5",
"id": "b787f690",
"metadata": {
"editable": true
},
@@ -39,7 +39,7 @@
},
{
"cell_type": "markdown",
"id": "764e1db6",
"id": "7a40125d",
"metadata": {
"editable": true
},
@@ -51,8 +51,10 @@
"\n",
"2. The [University of California at Irvine (UCI) with its machine learning repository](https://archive.ics.uci.edu/ml/index.php).\n",
"\n",
"3. Or other sources.\n",
"\n",
"The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:\n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, **Support Vector Machines** and **Decision Trees, Random Forests**, **Bagging and Boosting**. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. \n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, **Adversarial Neural Networks**, **Support Vector Machines** and **Decision Trees, Random Forests, Bagging and Boosting**. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as **Principal Component Analysis** and **k-means Clustering**.\n",
"\n",
"For Boosting, feel also free to write your own codes.\n",
"\n",
@@ -66,16 +68,18 @@
"\n",
"5. A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.\n",
"\n",
"All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc.. \n",
"All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..\n",
"\n",
"We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.. \n",
"We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.\n",
"\n",
"This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
"This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150).\n",
"\n",
"**Note**: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise."
]
},
{
"cell_type": "markdown",
"id": "6e4780c7",
"id": "8c7b1223",
"metadata": {
"editable": true
},
@@ -87,7 +91,7 @@
},
{
"cell_type": "markdown",
"id": "32262397",
"id": "f5f567df",
"metadata": {
"editable": true
},
@@ -99,7 +103,7 @@
},
{
"cell_type": "markdown",
"id": "e9b71dac",
"id": "daee2ad3",
"metadata": {
"editable": true
},
@@ -111,7 +115,7 @@
},
{
"cell_type": "markdown",
"id": "fbbbee47",
"id": "07b5058f",
"metadata": {
"editable": true
},
@@ -123,7 +127,7 @@
},
{
"cell_type": "markdown",
"id": "69a7f204",
"id": "7dc2abb4",
"metadata": {
"editable": true
},
@@ -135,7 +139,7 @@
},
{
"cell_type": "markdown",
"id": "887f0521",
"id": "af965f2e",
"metadata": {
"editable": true
},
@@ -147,7 +151,7 @@
},
{
"cell_type": "markdown",
"id": "f33bb254",
"id": "adf60f4b",
"metadata": {
"editable": true
},
@@ -167,7 +171,7 @@
},
{
"cell_type": "markdown",
"id": "d25629a1",
"id": "4b7d456d",
"metadata": {
"editable": true
},
@@ -181,7 +185,7 @@
},
{
"cell_type": "markdown",
"id": "4ce8d9b6",
"id": "c8eabc08",
"metadata": {
"editable": true
},
@@ -193,7 +197,7 @@
},
{
"cell_type": "markdown",
"id": "a6e88e9e",
"id": "1c3ff570",
"metadata": {
"editable": true
},
@@ -203,7 +207,7 @@
},
{
"cell_type": "markdown",
"id": "81e3dedd",
"id": "c98d31df",
"metadata": {
"editable": true
},
@@ -215,7 +219,7 @@
},
{
"cell_type": "markdown",
"id": "feb89d8f",
"id": "1c27b732",
"metadata": {
"editable": true
},
@@ -225,7 +229,7 @@
},
{
"cell_type": "markdown",
"id": "0bca56c5",
"id": "4f88e787",
"metadata": {
"editable": true
},
@@ -237,7 +241,7 @@
},
{
"cell_type": "markdown",
"id": "ab7915c8",
"id": "b4fa9a6c",
"metadata": {
"editable": true
},
@@ -248,7 +252,7 @@
},
{
"cell_type": "markdown",
"id": "c0d1ba71",
"id": "0787e8d0",
"metadata": {
"editable": true
},
@@ -260,7 +264,7 @@
},
{
"cell_type": "markdown",
"id": "d2aabdac",
"id": "f1389cd4",
"metadata": {
"editable": true
},
@@ -270,7 +274,7 @@
},
{
"cell_type": "markdown",
"id": "790e9a57",
"id": "08aa1c31",
"metadata": {
"editable": true
},
@@ -282,7 +286,7 @@
},
{
"cell_type": "markdown",
"id": "b452336c",
"id": "7b04313a",
"metadata": {
"editable": true
},
@@ -295,7 +299,7 @@
},
{
"cell_type": "markdown",
"id": "3679ddef",
"id": "aebe353a",
"metadata": {
"editable": true
},
@@ -307,7 +311,7 @@
},
{
"cell_type": "markdown",
"id": "3ed1a00e",
"id": "cd4094b4",
"metadata": {
"editable": true
},
@@ -317,7 +321,7 @@
},
{
"cell_type": "markdown",
"id": "bd6f8da3",
"id": "8f948136",
"metadata": {
"editable": true
},
@@ -329,7 +333,7 @@
},
{
"cell_type": "markdown",
"id": "dbd173d2",
"id": "57d23faf",
"metadata": {
"editable": true
},
@@ -339,7 +343,7 @@
},
{
"cell_type": "markdown",
"id": "a03aedf7",
"id": "a62549c5",
"metadata": {
"editable": true
},
@@ -351,7 +355,7 @@
},
{
"cell_type": "markdown",
"id": "ef63b2da",
"id": "0ee71a0b",
"metadata": {
"editable": true
},
@@ -362,7 +366,7 @@
},
{
"cell_type": "markdown",
"id": "744b0c7f",
"id": "1d1bf187",
"metadata": {
"editable": true
},
@@ -378,7 +382,7 @@
},
{
"cell_type": "markdown",
"id": "00a3534d",
"id": "c18bb4b3",
"metadata": {
"editable": true
},
@@ -395,7 +399,7 @@
},
{
"cell_type": "markdown",
"id": "836da33c",
"id": "1855e33d",
"metadata": {
"editable": true
},
@@ -411,7 +415,7 @@
},
{
"cell_type": "markdown",
"id": "ff03dd04",
"id": "98d1de62",
"metadata": {
"editable": true
},
@@ -423,7 +427,38 @@
},
{
"cell_type": "markdown",
"id": "24c8d749",
"id": "78f42475",
"metadata": {
"editable": true
},
"source": [
"## Additonal (optional) exercise, adding 30 more points to final score\n",
"\n",
"This exercise can be done independently of the other tasks. Here you\n",
"can also choose the data set you want to use. Furthermore, you can use\n",
"your codes from projects 1 and 2 as well as the codes here or simply use\n",
"libraries like **Scikit-Learn**, **Tensorflow** or similar.\n",
"\n",
"Your task is to perform an analysis of the bias-variance tradeoff\n",
"using at least three of the main sets algorithms we have discussed in this\n",
"course. We will limit ourselves to a regression problem (fitting). You\n",
"are free to choose between bootstrap for resampling (recommended) or\n",
"cross-validation in order to get the best possible estimates. The\n",
"methods you could study are Linear Regression (OLS, Ridge and Lasso),\n",
"deep learning (feed forward neural networks and/or recurrent neural\n",
"networks), Ensemble methods (decision trees, bagging, random forests\n",
"and boosting) and support vector machines.\n",
"\n",
"Study the bias-variance tradeoff for at least three of these sets of\n",
"algorithms for a data set of your choice as function of the complexity\n",
"of your model. Comment and discuss the results. Discuss the pros and\n",
"cons of the various methods. Are there some methods which provide both\n",
"low variance and low bias?"
]
},
{
"cell_type": "markdown",
"id": "29edad50",
"metadata": {
"editable": true
},
@@ -454,7 +489,7 @@
},
{
"cell_type": "markdown",
"id": "af15f3f3",
"id": "27d5016f",
"metadata": {
"editable": true
},
@@ -485,7 +520,7 @@
},
{
"cell_type": "markdown",
"id": "e7455835",
"id": "441c4d7b",
"metadata": {
"editable": true
},
@@ -507,7 +542,7 @@
},
{
"cell_type": "markdown",
"id": "fa5082d0",
"id": "b3744fce",
"metadata": {
"editable": true
},
doc/Projects/2021/Project3/ipynb/ipynb-Project3-src.tar.gz
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doc/Projects/2021/Project3/pdf/Project3.p.tex
+32 -5
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@@ -149,7 +149,7 @@ Project 3 on Machine Learning, deadline December 17, 2021
% --- begin date ---
\begin{center}
Nov 13, 2021
Nov 14, 2021
\end{center}
% --- end date ---
@@ -165,12 +165,14 @@ For project 3, you can propose own data sets that relate to your research intere
\item \href{{https://www.kaggle.com/datasets}}{Kaggle}
\item The \href{{https://archive.ics.uci.edu/ml/index.php}}{University of California at Irvine (UCI) with its machine learning repository}.
\item Or other sources.
\end{enumerate}
\noindent
The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:
\begin{enumerate}
\item Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among \textbf{linear regression (including Ridge and Lasso)}, \textbf{Logistic Regression}, \textbf{Neural Networks}, \textbf{Convolution Neural Networks}, \textbf{Recurrent Neural Networks}, \textbf{Support Vector Machines} and \textbf{Decision Trees, Random Forests}, \textbf{Bagging and Boosting}. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into \textbf{convolutional neural networks} or \textbf{recurrent neural networks}, or extensions of neural networkds, feel free to do so.
\item Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among \textbf{linear regression (including Ridge and Lasso)}, \textbf{Logistic Regression}, \textbf{Neural Networks}, \textbf{Convolution Neural Networks}, \textbf{Recurrent Neural Networks}, \textbf{Adversarial Neural Networks}, \textbf{Support Vector Machines} and \textbf{Decision Trees, Random Forests, Bagging and Boosting}. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into \textbf{convolutional neural networks} or \textbf{recurrent neural networks}, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as \textbf{Principal Component Analysis} and \textbf{k-means Clustering}.
\end{enumerate}
\noindent
@@ -189,11 +191,13 @@ For Boosting, feel also free to write your own codes.
\end{enumerate}
\noindent
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides \href{{https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html}}{from week 43} and/or the textbook by \href{{https://www.springer.com/gp/book/9789401798150}}{Yadav et al}.
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides \href{{https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html}}{from week 43} and/or the textbook by \href{{https://www.springer.com/gp/book/9789401798150}}{Yadav et al}.
\textbf{Note}: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise.
\subsection{The basic structure of your project}
@@ -300,6 +304,29 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
\paragraph{Part e).}
Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods.
\subsection{Additonal (optional) exercise, adding 30 more points to final score}
This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like \textbf{Scikit-Learn}, \textbf{Tensorflow} or similar.
Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
\subsection{Introduction to numerical projects}
Here follows a brief recipe and recommendation on how to write a report for each
doc/Projects/2021/Project3/pdf/Project3.pdf
BIN
View File
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doc/Projects/2021/Project3/pdf/Project3.tex
+32 -5
View File
@@ -123,7 +123,7 @@ Project 3 on Machine Learning, deadline December 17, 2021
% --- begin date ---
\begin{center}
Nov 13, 2021
Nov 14, 2021
\end{center}
% --- end date ---
@@ -139,12 +139,14 @@ For project 3, you can propose own data sets that relate to your research intere
\item \href{{https://www.kaggle.com/datasets}}{Kaggle}
\item The \href{{https://archive.ics.uci.edu/ml/index.php}}{University of California at Irvine (UCI) with its machine learning repository}.
\item Or other sources.
\end{enumerate}
\noindent
The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:
\begin{enumerate}
\item Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among \textbf{linear regression (including Ridge and Lasso)}, \textbf{Logistic Regression}, \textbf{Neural Networks}, \textbf{Convolution Neural Networks}, \textbf{Recurrent Neural Networks}, \textbf{Support Vector Machines} and \textbf{Decision Trees, Random Forests}, \textbf{Bagging and Boosting}. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into \textbf{convolutional neural networks} or \textbf{recurrent neural networks}, or extensions of neural networkds, feel free to do so.
\item Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among \textbf{linear regression (including Ridge and Lasso)}, \textbf{Logistic Regression}, \textbf{Neural Networks}, \textbf{Convolution Neural Networks}, \textbf{Recurrent Neural Networks}, \textbf{Adversarial Neural Networks}, \textbf{Support Vector Machines} and \textbf{Decision Trees, Random Forests, Bagging and Boosting}. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into \textbf{convolutional neural networks} or \textbf{recurrent neural networks}, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as \textbf{Principal Component Analysis} and \textbf{k-means Clustering}.
\end{enumerate}
\noindent
@@ -163,11 +165,13 @@ For Boosting, feel also free to write your own codes.
\end{enumerate}
\noindent
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides \href{{https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html}}{from week 43} and/or the textbook by \href{{https://www.springer.com/gp/book/9789401798150}}{Yadav et al}.
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides \href{{https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html}}{from week 43} and/or the textbook by \href{{https://www.springer.com/gp/book/9789401798150}}{Yadav et al}.
\textbf{Note}: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise.
\subsection*{The basic structure of your project}
@@ -274,6 +278,29 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
\paragraph{Part e).}
Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods.
\subsection*{Additonal (optional) exercise, adding 30 more points to final score}
This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like \textbf{Scikit-Learn}, \textbf{Tensorflow} or similar.
Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
\subsection*{Introduction to numerical projects}
Here follows a brief recipe and recommendation on how to write a report for each
doc/src/Projects/2021/Project3/Project3.do.txt
+34 -5
View File
@@ -10,10 +10,10 @@ DATE: today
For project 3, you can propose own data sets that relate to your research interests or just use existing data sets from say
o "Kaggle":"https://www.kaggle.com/datasets"
o The "University of California at Irvine (UCI) with its machine learning repository":"https://archive.ics.uci.edu/ml/index.php".
o Or other sources.
The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:
o Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among _linear regression (including Ridge and Lasso)_, _Logistic Regression_, _Neural Networks_, _Convolution Neural Networks_, _Recurrent Neural Networks_, _Support Vector Machines_ and _Decision Trees, Random Forests_, _Bagging and Boosting_. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so.
o Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among _linear regression (including Ridge and Lasso)_, _Logistic Regression_, _Neural Networks_, _Convolution Neural Networks_, _Recurrent Neural Networks_, _Adversarial Neural Networks_, _Support Vector Machines_ and _Decision Trees, Random Forests, Bagging and Boosting_. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as _Principal Component Analysis_ and _k-means Clustering_.
For Boosting, feel also free to write your own codes.
@@ -27,11 +27,14 @@ o If possible, you should link the data sets with exisiting research and analyse
o A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides "from week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html" and/or the textbook by "Yadav et al":"https://www.springer.com/gp/book/9789401798150".
This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides "from week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html" and/or the textbook by "Yadav et al":"https://www.springer.com/gp/book/9789401798150".
_Note_: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise.
===== The basic structure of your project =====
@@ -168,6 +171,32 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods.
===== Additonal (optional) exercise, adding 30 more points to final score =====
This exercise can be done independently of the other tasks. Here you
can also choose the data set you want to use. Furthermore, you can use
your codes from projects 1 and 2 as well as the codes here or simply use
libraries like _Scikit-Learn_, _Tensorflow_ or similar.
Your task is to perform an analysis of the bias-variance tradeoff
using at least three of the main sets algorithms we have discussed in this
course. We will limit ourselves to a regression problem (fitting). You
are free to choose between bootstrap for resampling (recommended) or
cross-validation in order to get the best possible estimates. The
methods you could study are Linear Regression (OLS, Ridge and Lasso),
deep learning (feed forward neural networks and/or recurrent neural
networks), Ensemble methods (decision trees, bagging, random forests
and boosting) and support vector machines.
Study the bias-variance tradeoff for at least three of these sets of
algorithms for a data set of your choice as function of the complexity
of your model. Comment and discuss the results. Discuss the pros and
cons of the various methods. Are there some methods which provide both
low variance and low bias?
===== Introduction to numerical projects =====
Here follows a brief recipe and recommendation on how to write a report for each