diff --git a/doc/LectureNotes/exercisesweek39.ipynb b/doc/LectureNotes/exercisesweek39.ipynb new file mode 100644 index 000000000..d685e82d8 --- /dev/null +++ b/doc/LectureNotes/exercisesweek39.ipynb @@ -0,0 +1,59 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f35930ac", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "8cb567a0", + "metadata": { + "editable": true + }, + "source": [ + "# Exercises week 39\n", + "**September 25-29, 2023**\n", + "\n", + "Date: **Deadline is Sunday October 1 at midnight**" + ] + }, + { + "cell_type": "markdown", + "id": "934324b3", + "metadata": { + "editable": true + }, + "source": [ + "## Overarching aims of the exercises this week\n", + "\n", + "The aim of the exercises this week is to aid you in getting started\n", + "with writing the report. This will be discussed during the lab\n", + "sessions as well. One of the lab sessions will be recorded.\n", + "\n", + "A general guideline can be found at .\n", + "\n", + "Similarly, an example of an earlier project can be found at \n", + "\n", + "Your task this week is to\n", + "1. Write an abstract for your project\n", + "\n", + "2. Write an introduction\n", + "\n", + "3. Include references\n", + "\n", + "Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report." + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/src/week39/exercisesweek39.do.txt b/doc/src/week39/exercisesweek39.do.txt index 5134c86e1..363246a4a 100644 --- a/doc/src/week39/exercisesweek39.do.txt +++ b/doc/src/week39/exercisesweek39.do.txt @@ -1,77 +1,24 @@ -TITLE: Exercises week 38 -AUTHOR: September 18-22, 2023 -DATE: Deadline is Sunday September 24 at midnight +TITLE: Exercises week 39 +AUTHOR: September 25-29, 2023 +DATE: Deadline is Sunday October 1 at midnight ===== Overarching aims of the exercises this week ===== -The aim of the exercises this week is to derive the equations for the bias-variance tradeoff to be used in project 1 as well as testing this for a simpler function using the bootstrap method. The exercises here can be reused in project 1 as well. +The aim of the exercises this week is to aid you in getting started +with writing the report. This will be discussed during the lab +sessions as well. One of the lab sessions will be recorded. -Consider a -dataset $\mathcal{L}$ consisting of the data -$\mathbf{X}_\mathcal{L}=\{(y_j, \boldsymbol{x}_j), j=0\ldots n-1\}$. +A general guideline can be found at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md". -We assume that the true data is generated from a noisy model - -!bt -\[ -\bm{y}=f(\boldsymbol{x}) + \bm{\epsilon}. -\] -!et - -Here $\epsilon$ is normally distributed with mean zero and standard -deviation $\sigma^2$. - -In our derivation of the ordinary least squares method we defined -an approximation to the function $f$ in terms of the parameters -$\bm{\beta}$ and the design matrix $\bm{X}$ which embody our model, -that is $\bm{\tilde{y}}=\bm{X}\bm{\beta}$. - -The parameters $\bm{\beta}$ are in turn found by optimizing the mean -squared error via the so-called cost function - -!bt -\[ -C(\bm{X},\bm{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2=\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]. -\] -!et -Here the expected value $\mathbb{E}$ is the sample value. - -Show that you can rewrite this in terms of a term which contains the variance of the model itself (the so-called variance term), a -term which measures the deviation from the true data and the mean value of the model (the bias term) and finally the variance of the noise. -That is, show that -!bt -\[ -\mathbb{E}\left[(\bm{y}-\bm{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2, -\] -!et -with -!bt -\[ -\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\bm{y}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right], -\] -!et -and -!bt -\[ -\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2. -\] -!et +Similarly, an example of an earlier project can be found at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf" +Your task this week is to +o Write an abstract for your project +o Write an introduction +o Include references -Explain what the terms mean and discuss their interpretations. - -Perform then a bias-variance analysis of a simple one-dimensional (or other models of your choice) function by -studying the MSE value as function of the complexity of your model. Use ordinary least squares only. - -Discuss the bias and variance trade-off as function -of your model complexity (the degree of the polynomial) and the number -of data points, and possibly also your training and test data using the _bootstrap_ resampling method. -You can follow the code example in the jupyter-book at URL:"https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#the-bias-variance-tradeoff". - - -See also the whiteboard notes from week 37 at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" - +Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report. diff --git a/doc/src/week39/exercisesweek39.ipynb b/doc/src/week39/exercisesweek39.ipynb new file mode 100644 index 000000000..d685e82d8 --- /dev/null +++ b/doc/src/week39/exercisesweek39.ipynb @@ -0,0 +1,59 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f35930ac", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "8cb567a0", + "metadata": { + "editable": true + }, + "source": [ + "# Exercises week 39\n", + "**September 25-29, 2023**\n", + "\n", + "Date: **Deadline is Sunday October 1 at midnight**" + ] + }, + { + "cell_type": "markdown", + "id": "934324b3", + "metadata": { + "editable": true + }, + "source": [ + "## Overarching aims of the exercises this week\n", + "\n", + "The aim of the exercises this week is to aid you in getting started\n", + "with writing the report. This will be discussed during the lab\n", + "sessions as well. One of the lab sessions will be recorded.\n", + "\n", + "A general guideline can be found at .\n", + "\n", + "Similarly, an example of an earlier project can be found at \n", + "\n", + "Your task this week is to\n", + "1. Write an abstract for your project\n", + "\n", + "2. Write an introduction\n", + "\n", + "3. Include references\n", + "\n", + "Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report." + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +}