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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. +
+ +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), @@ -360,23 +358,8 @@ 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?
-Here follows a brief recipe and recommendation on how to write a report for each -project. -
- -Hint: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree.
Here follows a brief recipe and recommendation on how to write a report for each diff --git a/doc/Projects/2021/Project3/html/Project3-bs.html b/doc/Projects/2021/Project3/html/Project3-bs.html index c79df5535..1144eb817 100644 --- a/doc/Projects/2021/Project3/html/Project3-bs.html +++ b/doc/Projects/2021/Project3/html/Project3-bs.html @@ -74,10 +74,6 @@ doconce format html Project3.do.txt --html_style=bootstrap --pygments_html_style 2, None, 'introduction-to-numerical-projects'), - ('Introduction to numerical projects', - 2, - None, - 'introduction-to-numerical-projects'), ('Format for electronic delivery of report and programs', 2, None, @@ -136,7 +132,6 @@ MathJax.Hub.Config({
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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. +
+ +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), @@ -360,23 +358,8 @@ 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?
-Here follows a brief recipe and recommendation on how to write a report for each -project. -
- -Hint: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree.
Here follows a brief recipe and recommendation on how to write a report for each diff --git a/doc/Projects/2021/Project3/html/Project3.html b/doc/Projects/2021/Project3/html/Project3.html index 6e029085f..2e06fadd8 100644 --- a/doc/Projects/2021/Project3/html/Project3.html +++ b/doc/Projects/2021/Project3/html/Project3.html @@ -152,10 +152,6 @@ div.toc p,a { 2, None, 'introduction-to-numerical-projects'), - ('Introduction to numerical projects', - 2, - None, - 'introduction-to-numerical-projects'), ('Format for electronic delivery of report and programs', 2, None, @@ -374,8 +370,11 @@ 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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. +
+ +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), @@ -390,23 +389,8 @@ 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?
-Here follows a brief recipe and recommendation on how to write a report for each -project. -
- -Hint: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree.
Here follows a brief recipe and recommendation on how to write a report for each diff --git a/doc/Projects/2021/Project3/ipynb/Project3.ipynb b/doc/Projects/2021/Project3/ipynb/Project3.ipynb index 6be6167c4..7d98fd7d5 100644 --- a/doc/Projects/2021/Project3/ipynb/Project3.ipynb +++ b/doc/Projects/2021/Project3/ipynb/Project3.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "92499fce", + "id": "26d52fd9", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "56cf5579", + "id": "236f6cfd", "metadata": { "editable": true }, @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "b787f690", + "id": "1d3c512a", "metadata": { "editable": true }, @@ -39,7 +39,7 @@ }, { "cell_type": "markdown", - "id": "7a40125d", + "id": "4f7124c2", "metadata": { "editable": true }, @@ -79,7 +79,7 @@ }, { "cell_type": "markdown", - "id": "8c7b1223", + "id": "ae4474c6", "metadata": { "editable": true }, @@ -91,7 +91,7 @@ }, { "cell_type": "markdown", - "id": "f5f567df", + "id": "657d3638", "metadata": { "editable": true }, @@ -103,7 +103,7 @@ }, { "cell_type": "markdown", - "id": "daee2ad3", + "id": "cd7e6b5c", "metadata": { "editable": true }, @@ -115,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "07b5058f", + "id": "05c0260c", "metadata": { "editable": true }, @@ -127,7 +127,7 @@ }, { "cell_type": "markdown", - "id": "7dc2abb4", + "id": "9108ddbb", "metadata": { "editable": true }, @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "af965f2e", + "id": "4e2b05cf", "metadata": { "editable": true }, @@ -151,7 +151,7 @@ }, { "cell_type": "markdown", - "id": "adf60f4b", + "id": "e45fc3b7", "metadata": { "editable": true }, @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "4b7d456d", + "id": "f036e12d", "metadata": { "editable": true }, @@ -185,7 +185,7 @@ }, { "cell_type": "markdown", - "id": "c8eabc08", + "id": "52660f41", "metadata": { "editable": true }, @@ -197,7 +197,7 @@ }, { "cell_type": "markdown", - "id": "1c3ff570", + "id": "c1fe35cf", "metadata": { "editable": true }, @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "c98d31df", + "id": "a1395ad8", "metadata": { "editable": true }, @@ -219,7 +219,7 @@ }, { "cell_type": "markdown", - "id": "1c27b732", + "id": "aa6df14a", "metadata": { "editable": true }, @@ -229,7 +229,7 @@ }, { "cell_type": "markdown", - "id": "4f88e787", + "id": "09d87b1d", "metadata": { "editable": true }, @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "b4fa9a6c", + "id": "1dc28a4b", "metadata": { "editable": true }, @@ -252,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "0787e8d0", + "id": "9e6804ed", "metadata": { "editable": true }, @@ -264,7 +264,7 @@ }, { "cell_type": "markdown", - "id": "f1389cd4", + "id": "004eed40", "metadata": { "editable": true }, @@ -274,7 +274,7 @@ }, { "cell_type": "markdown", - "id": "08aa1c31", + "id": "877b7ed0", "metadata": { "editable": true }, @@ -286,7 +286,7 @@ }, { "cell_type": "markdown", - "id": "7b04313a", + "id": "cb45cb03", "metadata": { "editable": true }, @@ -299,7 +299,7 @@ }, { "cell_type": "markdown", - "id": "aebe353a", + "id": "fe999d48", "metadata": { "editable": true }, @@ -311,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "cd4094b4", + "id": "f6ff7ece", "metadata": { "editable": true }, @@ -321,7 +321,7 @@ }, { "cell_type": "markdown", - "id": "8f948136", + "id": "40735cb1", "metadata": { "editable": true }, @@ -333,7 +333,7 @@ }, { "cell_type": "markdown", - "id": "57d23faf", + "id": "1464be77", "metadata": { "editable": true }, @@ -343,7 +343,7 @@ }, { "cell_type": "markdown", - "id": "a62549c5", + "id": "ed9d7c03", "metadata": { "editable": true }, @@ -355,7 +355,7 @@ }, { "cell_type": "markdown", - "id": "0ee71a0b", + "id": "588fde58", "metadata": { "editable": true }, @@ -366,7 +366,7 @@ }, { "cell_type": "markdown", - "id": "1d1bf187", + "id": "4fe15315", "metadata": { "editable": true }, @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "c18bb4b3", + "id": "7fcf0aab", "metadata": { "editable": true }, @@ -399,7 +399,7 @@ }, { "cell_type": "markdown", - "id": "1855e33d", + "id": "3f519e6a", "metadata": { "editable": true }, @@ -415,7 +415,7 @@ }, { "cell_type": "markdown", - "id": "98d1de62", + "id": "f1037588", "metadata": { "editable": true }, @@ -427,7 +427,7 @@ }, { "cell_type": "markdown", - "id": "78f42475", + "id": "3a26e170", "metadata": { "editable": true }, @@ -440,8 +440,10 @@ "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", + "using at least three of the main sets of algorithms we have discussed in this\n", + "course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem.\n", + "\n", + "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", @@ -453,12 +455,14 @@ "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?" + "low variance and low bias?\n", + "\n", + "**Hint**: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree." ] }, { "cell_type": "markdown", - "id": "29edad50", + "id": "4c14d063", "metadata": { "editable": true }, @@ -489,38 +493,7 @@ }, { "cell_type": "markdown", - "id": "27d5016f", - "metadata": { - "editable": true - }, - "source": [ - "## Introduction to numerical projects\n", - "\n", - "Here follows a brief recipe and recommendation on how to write a report for each\n", - "project.\n", - "\n", - " * Give a short description of the nature of the problem and the eventual numerical methods you have used.\n", - "\n", - " * Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.\n", - "\n", - " * Include the source code of your program. Comment your program properly.\n", - "\n", - " * If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.\n", - "\n", - " * Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.\n", - "\n", - " * Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.\n", - "\n", - " * Try to give an interpretation of you results in your answers to the problems.\n", - "\n", - " * Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.\n", - "\n", - " * Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning." - ] - }, - { - "cell_type": "markdown", - "id": "441c4d7b", + "id": "f565fe9e", "metadata": { "editable": true }, @@ -542,7 +515,7 @@ }, { "cell_type": "markdown", - "id": "b3744fce", + "id": "a762ce82", "metadata": { "editable": true }, diff --git a/doc/Projects/2021/Project3/ipynb/ipynb-Project3-src.tar.gz b/doc/Projects/2021/Project3/ipynb/ipynb-Project3-src.tar.gz index 45f4f92c4..857624d16 100644 Binary files a/doc/Projects/2021/Project3/ipynb/ipynb-Project3-src.tar.gz and b/doc/Projects/2021/Project3/ipynb/ipynb-Project3-src.tar.gz differ diff --git a/doc/Projects/2021/Project3/pdf/Project3.p.tex b/doc/Projects/2021/Project3/pdf/Project3.p.tex index 3f449d195..f3d65ee30 100644 --- a/doc/Projects/2021/Project3/pdf/Project3.p.tex +++ b/doc/Projects/2021/Project3/pdf/Project3.p.tex @@ -312,8 +312,10 @@ 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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. + +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), @@ -327,32 +329,8 @@ 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} +\textbf{Hint}: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree. -Here follows a brief recipe and recommendation on how to write a report for each -project. - -\begin{itemize} - \item Give a short description of the nature of the problem and the eventual numerical methods you have used. - - \item Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself. - - \item Include the source code of your program. Comment your program properly. - - \item If possible, try to find analytic solutions, or known limits in order to test your program when developing the code. - - \item Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes. - - \item Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc. - - \item Try to give an interpretation of you results in your answers to the problems. - - \item Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it. - - \item Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning. -\end{itemize} - -\noindent \subsection{Introduction to numerical projects} Here follows a brief recipe and recommendation on how to write a report for each diff --git a/doc/Projects/2021/Project3/pdf/Project3.pdf b/doc/Projects/2021/Project3/pdf/Project3.pdf index d396699d1..0c940663d 100644 Binary files a/doc/Projects/2021/Project3/pdf/Project3.pdf and b/doc/Projects/2021/Project3/pdf/Project3.pdf differ diff --git a/doc/Projects/2021/Project3/pdf/Project3.tex b/doc/Projects/2021/Project3/pdf/Project3.tex index 76f4a7b73..b9caeb691 100644 --- a/doc/Projects/2021/Project3/pdf/Project3.tex +++ b/doc/Projects/2021/Project3/pdf/Project3.tex @@ -286,8 +286,10 @@ 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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. + +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), @@ -301,32 +303,8 @@ 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} +\textbf{Hint}: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree. -Here follows a brief recipe and recommendation on how to write a report for each -project. - -\begin{itemize} - \item Give a short description of the nature of the problem and the eventual numerical methods you have used. - - \item Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself. - - \item Include the source code of your program. Comment your program properly. - - \item If possible, try to find analytic solutions, or known limits in order to test your program when developing the code. - - \item Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes. - - \item Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc. - - \item Try to give an interpretation of you results in your answers to the problems. - - \item Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it. - - \item Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning. -\end{itemize} - -\noindent \subsection*{Introduction to numerical projects} Here follows a brief recipe and recommendation on how to write a report for each diff --git a/doc/src/Projects/2021/Project3/Project3.do.txt b/doc/src/Projects/2021/Project3/Project3.do.txt index c3c1b8811..86512bdd8 100644 --- a/doc/src/Projects/2021/Project3/Project3.do.txt +++ b/doc/src/Projects/2021/Project3/Project3.do.txt @@ -179,8 +179,10 @@ 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 +using at least three of the main sets of algorithms we have discussed in this +course. We will limit ourselves to a regression problem (fitting). However, feel free to venture into a classification problem. + +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), @@ -194,34 +196,7 @@ 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 -project. - - * Give a short description of the nature of the problem and the eventual numerical methods you have used. - - * Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself. - - * Include the source code of your program. Comment your program properly. - - * If possible, try to find analytic solutions, or known limits in order to test your program when developing the code. - - * Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes. - - * Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc. - - * Try to give an interpretation of you results in your answers to the problems. - - * Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it. - - * Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning. - - - +_Hint_: when you use different methods, pay attention to how you represent (and understand) the complexity of the model. For for example decision trees, this is represented by the depth of the tree.