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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "433db993",
+ "metadata": {},
+ "source": [
+ "# Weekly Exercises 6\n",
+ "\n",
+ "## Getting started with project 1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6b931365",
+ "metadata": {},
+ "source": [
+ "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.\n",
+ "\n",
+ "A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2a63bae1",
+ "metadata": {},
+ "source": [
+ "### Learning goals\n",
+ "\n",
+ "After completing these exercises, you will know how to\n",
+ "\n",
+ "- Create a properly formatted report in Overleaf\n",
+ "- Select and present graphs for a scientific report\n",
+ "- Write an abstract and introduction for a scientific report\n",
+ "\n",
+ "### Deliverables\n",
+ "\n",
+ "Complete the following exercises while working in an Overleaf project. Then, in canvas, include\n",
+ "\n",
+ "- An exported PDF of the report draft you have been working on.\n",
+ "- A comment linking to the github repository used in exercise 4.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e0f2d99d",
+ "metadata": {},
+ "source": [
+ "## Exercise 1: Creating the report document\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d06bfb29",
+ "metadata": {},
+ "source": [
+ "We require all projects to be formatted as proper scientific reports, and this includes using LaTeX for typesetting. We strongly recommend that you use the online LaTeX editor Overleaf, as it is much easier to start using, and has excellent support for collaboration.\n",
+ "\n",
+ "**a)** Create an account on Overleaf.com\n",
+ "\n",
+ "**b)** Download [this](https://github.com/CompPhysics/MachineLearning/blob/master/doc/LectureNotes/data/FYS_STK_Template.zip) template project.\n",
+ "\n",
+ "**c)** Create a new Overleaf project with the correct formatting by uploading the template project.\n",
+ "\n",
+ "**d)** Read the general guideline for writing a report, which can be found at .\n",
+ "\n",
+ "**e)** Look at the provided example of an earlier project, found at \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ec36f4c3",
+ "metadata": {},
+ "source": [
+ "## Exercise 2: Adding good figures\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f50723f8",
+ "metadata": {},
+ "source": [
+ "**a)** Using what you have learned so far in this course, create a plot illustrating the Bias-Variance trade-off. Make sure the lines and axes are labeled, with font size being the same as in the text.\n",
+ "\n",
+ "**b)** Add this figure to the results section of your document, with a caption that describes it. A reader should be able to understand the figure with only its contents and caption.\n",
+ "\n",
+ "**c)** Refer to the figure in your text using \\ref.\n",
+ "\n",
+ "**d)** Create a heatmap showing the MSE of a Ridge regression model for various polynomial degrees and lambda values. Make sure the axes are labeled, and that the title or colorbar describes what is plotted.\n",
+ "\n",
+ "**e)** Add this second figure to your document with a caption and reference in the text. All figures in the final report must be captioned and be referenced and used in the text.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "276c214e",
+ "metadata": {},
+ "source": [
+ "## Exercise 3: Writing an abstract and introduction\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f4134eb5",
+ "metadata": {},
+ "source": [
+ "Although much of your project 1 results are not done yet, we want you to write an abstract and introduction to get you started on writing the report. It is generally a good idea to write a lot of a report before finishing all of the results, as you get a better understanding of your methods and inquiry from doing so, along with saving a lot of time. Where you would typically describe results in the abstract, instead make something up, just this once.\n",
+ "\n",
+ "**a)** Read the guidelines on abstract and introduction before you start.\n",
+ "\n",
+ "**b)** Write an abstract for project 1 in your report.\n",
+ "\n",
+ "**c)** Write an introduction for project 1 in your report.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2f512b59",
+ "metadata": {},
+ "source": [
+ "## Exercise 4: Making the code avaliable and presentable\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "77fe1fec",
+ "metadata": {},
+ "source": [
+ "A central part of the report is the code you write to implement the methods and generate the results. To get points for the code-part of the project, you need to make your code avaliable and presentable.\n",
+ "\n",
+ "**a)** Create a github repository for project 1, or create a dedicated folder for project 1 in a github repository. Only one person in your group needs to do this.\n",
+ "\n",
+ "**b)** Add a PDF of the report to this repository, after completing exercises 1-3\n",
+ "\n",
+ "**c)** Add a folder named Code, where you can put python files for your functions and notebooks for reproducing your results.\n",
+ "\n",
+ "**d)** Add python files for functions, and a notebook to produce the figures in exercise 2, to the Code folder. Remember to use a seed for generating random data and for train-test splits.\n",
+ "\n",
+ "**e)** Create a README file in the reposotory or project folder with\n",
+ "\n",
+ "- the name of the group members\n",
+ "- a short description of the project\n",
+ "- a description of how to install the required packages to run your code from a requirements.txt file\n",
+ "- names and descriptions of the various notebooks in the Code folder and the results they produce\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f1d72c56",
+ "metadata": {},
+ "source": [
+ "## Exercise 5: Referencing\n",
+ "\n",
+ "**a)** Add a reference to Hastie et al. using your preferred referencing style. See https://www.sokogskriv.no/referansestiler/ for an overview of styles.\n",
+ "\n",
+ "**b)** Add a reference to sklearn like this: https://scikit-learn.org/stable/about.html#citing-scikit-learn\n",
+ "\n",
+ "**c)** Make a prompt to your LLM of choice, and upload the exported conversation to your GitHub repository for the project.\n",
+ "\n",
+ "**d)** At the end of the methods section of the report, write a one paragraph declaration on how and for what you have used the LLM. Link to the log on GitHub.\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/doc/LectureNotes/_build/html/chapter1.html b/doc/LectureNotes/_build/html/chapter1.html
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+++ b/doc/LectureNotes/_build/html/chapter1.html
@@ -232,6 +232,7 @@
Exercises week 37
Week 37: Gradient descent methods
Exercises week 38
+Weekly Exercises 6
Projects
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Project 1 on Machine Learning, deadline October 6 (midnight), 2025
+
Weekly Exercises 6
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+ Weekly Exercises 6 — Applied Data Analysis and Machine Learning
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Weekly Exercises 6
+
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+
+Weekly Exercises 6
+
+Getting started with project 1
+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.
+A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report.
+
+Learning goals
+After completing these exercises, you will know how to
+
+Create a properly formatted report in Overleaf
+Select and present graphs for a scientific report
+Write an abstract and introduction for a scientific report
+
+
+
+Deliverables
+Complete the following exercises while working in an Overleaf project. Then, in canvas, include
+
+
+
+
+Exercise 1: Creating the report document
+We require all projects to be formatted as proper scientific reports, and this includes using LaTeX for typesetting. We strongly recommend that you use the online LaTeX editor Overleaf, as it is much easier to start using, and has excellent support for collaboration.
+a) Create an account on Overleaf.com
+b) Download this template project.
+c) Create a new Overleaf project with the correct formatting by uploading the template project.
+d) Read the general guideline for writing a report, which can be found at CompPhysics/MachineLearning .
+e) Look at the provided example of an earlier project, found at CompPhysics/MachineLearning
+
+
+
+Exercise 3: Writing an abstract and introduction
+Although much of your project 1 results are not done yet, we want you to write an abstract and introduction to get you started on writing the report. It is generally a good idea to write a lot of a report before finishing all of the results, as you get a better understanding of your methods and inquiry from doing so, along with saving a lot of time. Where you would typically describe results in the abstract, instead make something up, just this once.
+a) Read the guidelines on abstract and introduction before you start.
+b) Write an abstract for project 1 in your report.
+c) Write an introduction for project 1 in your report.
+
+
+Exercise 4: Making the code avaliable and presentable
+A central part of the report is the code you write to implement the methods and generate the results. To get points for the code-part of the project, you need to make your code avaliable and presentable.
+a) Create a github repository for project 1, or create a dedicated folder for project 1 in a github repository. Only one person in your group needs to do this.
+b) Add a PDF of the report to this repository, after completing exercises 1-3
+c) Add a folder named Code, where you can put python files for your functions and notebooks for reproducing your results.
+d) Add python files for functions, and a notebook to produce the figures in exercise 2, to the Code folder. Remember to use a seed for generating random data and for train-test splits.
+e) Create a README file in the reposotory or project folder with
+
+the name of the group members
+a short description of the project
+a description of how to install the required packages to run your code from a requirements.txt file
+names and descriptions of the various notebooks in the Code folder and the results they produce
+
+
+
+Exercise 5: Referencing
+a) Add a reference to Hastie et al. using your preferred referencing style. See https://www.sokogskriv.no/referansestiler/ for an overview of styles.
+b) Add a reference to sklearn like this: https://scikit-learn.org/stable/about.html#citing-scikit-learn
+c) Make a prompt to your LLM of choice, and upload the exported conversation to your GitHub repository for the project.
+d) At the end of the methods section of the report, write a one paragraph declaration on how and for what you have used the LLM. Link to the log on GitHub.
+
+
+
+
+
+
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diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html
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+++ b/doc/LectureNotes/_build/html/genindex.html
@@ -229,6 +229,7 @@
Exercises week 37
Week 37: Gradient descent methods
Exercises week 38
+Weekly Exercises 6
Projects
Projects
Projects
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@@ -62,7 +62,7 @@
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@@ -231,6 +231,7 @@
Exercises week 37
Week 37: Gradient descent methods
Exercises week 38
+Weekly Exercises 6
Projects
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Projects
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
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-Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [27, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[27, "a-first-summary"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"]], "ADAM algorithm, taken from Goodfellow et al": [[30, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [30, "id2"]], "Accuracy": [[30, "accuracy"]], "Activation functions": [[12, "activation-functions"]], "AdaGrad Properties": [[30, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[30, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[30, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[30, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[30, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[30, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[30, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[30, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[30, "adaptivity-across-dimensions"]], "Adding error analysis and training set up": [[27, "adding-error-analysis-and-training-set-up"], [28, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[30, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[27, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[28, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[30, "and-finally-adam"]], "And what about using neural networks?": [[27, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[29, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[20, null]], "Autocorrelation function": [[24, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[28, "back-to-ridge-and-lasso-regression"], [29, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[22, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[21, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [28, "basic-math-of-the-svd"], [29, "basic-math-of-the-svd"]], "Basics": [[7, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Batch Normalization": [[1, "batch-normalization"]], "Batches and mini-batches": [[30, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[5, "bayes-theorem-and-ridge-and-lasso-regression"]], "Boosting, a Bird\u2019s Eye View": [[10, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[6, "bootstrap"]], "Bringing it together, first back propagation equation": [[12, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[1, null]], "Building a tree, regression": [[9, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[1, "building-neural-networks-in-tensorflow-and-keras"]], "But none of these can compete with Newton\u2019s method": [[30, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Challenge: Choosing a Fixed Learning Rate": [[30, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[14, null]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[30, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [28, "codes-for-the-svd"], [29, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"]], "Communication channels": [[27, "communication-channels"]], "Compare Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[29, "comparison-with-ols"]], "Computation of gradients": [[30, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[29, "conditions-on-convex-functions"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[30, "convergence-rates"]], "Convex function": [[29, "convex-function"]], "Convex functions": [[13, "convex-functions"], [29, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[28, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [28, "correlation-matrix"]], "Correlation Matrix with Pandas": [[28, "correlation-matrix-with-pandas"]], "Course Format": [[27, "course-format"]], "Course setting": [[23, null]], "Covariance Matrix Examples": [[28, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[28, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Deadlines for projects (tentative)": [[27, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[30, "deep-neural-networks"]], "Deep learning methods": [[27, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"]], "Defining the cost function": [[1, "defining-the-cost-function"]], "Definitions": [[19, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[30, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[28, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[28, "deriving-the-lasso-regression-equations"], [29, "deriving-the-lasso-regression-equations"], [29, "id6"]], "Deriving the Ridge Regression Equations": [[28, "deriving-the-ridge-regression-equations"], [29, "deriving-the-ridge-regression-equations"], [29, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[27, "discriminative-modeling"]], "Domains and probabilities": [[24, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[28, "economy-size-svd"], [29, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[24, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[30, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[27, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[28, "example-2"]], "Example 3": [[28, "example-3"]], "Example 4": [[28, "example-4"]], "Example Matrix": [[28, "example-matrix"], [29, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[27, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[27, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[28, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[28, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[27, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Expectation values": [[24, "expectation-values"]], "Extending to more than one variable": [[29, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[27, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[28, "fixing-the-singularity"], [29, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[22, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[28, "frequently-used-scaling-functions"], [30, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[29, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[28, "functionality-in-scikit-learn"], [30, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [28, "further-properties-important-for-our-analyses-later"], [29, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[21, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[27, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[27, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [27, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[27, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[29, "id1"], [30, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[29, "gradient-descent-and-ridge"], [30, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[30, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[29, "gradient-descent-example"], [30, "gradient-descent-example"]], "Grading": [[25, "grading"], [25, "id2"], [27, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[21, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[28, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[30, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[25, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [30, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Installing R, C++, cython or Julia": [[27, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[27, "installing-r-c-cython-numba-etc"]], "Instructor information": [[25, "instructor-information"]], "Interpretations and optimizing our parameters": [[27, "interpretations-and-optimizing-our-parameters"], [27, "id2"], [27, "id3"], [28, "interpretations-and-optimizing-our-parameters"], [28, "id1"], [28, "id2"]], "Interpreting the Ridge results": [[28, "interpreting-the-ridge-results"], [29, "interpreting-the-ridge-results"], [29, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [28, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [20, "introduction"], [21, "introduction"]], "Introduction to numerical projects": [[22, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[21, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[29, "lasso-regression"]], "Lasso case": [[29, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"]], "Learning outcomes": [[20, "learning-outcomes"], [27, "learning-outcomes"]], "Lectures and ComputerLab": [[27, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[21, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[28, "linear-regression-problems"], [29, "linear-regression-problems"]], "Linear Regression and the SVD": [[29, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [28, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[26, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[27, "machine-learning"]], "Machine learning": [[20, "machine-learning"]], "Main textbooks": [[27, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[28, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[28, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[29, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[29, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[30, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[30, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [28, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [28, "mathematics-of-the-svd-and-implications"], [29, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[27, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Meet the covariance!": [[24, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [28, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[28, "meet-the-hessian-matrix"]], "Meet the Pandas": [[27, "meet-the-pandas"]], "Memory Usage and Scalability": [[30, "memory-usage-and-scalability"]], "Memory constraints": [[30, "memory-constraints"]], "Min-Max Scaling": [[28, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"], [30, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More interpretations": [[28, "more-interpretations"], [29, "more-interpretations"], [29, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[29, "more-on-steepest-descent"]], "More on convex functions": [[29, "more-on-convex-functions"]], "More preprocessing": [[28, "more-preprocessing"], [30, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[30, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[30, "non-convex-problems"]], "Note about SVD Calculations": [[28, "note-about-svd-calculations"], [29, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[29, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[24, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[21, "numpy-and-arrays"], [27, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[27, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[29, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[27, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[27, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [27, "organizing-our-data"]], "Other Matrix and Vector Operations": [[21, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[27, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[27, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[27, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[27, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[27, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[30, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[27, "own-code-for-ordinary-least-squares"], [28, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[27, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[22, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[22, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[22, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[22, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[22, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[22, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[22, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[22, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plans for week 35": [[28, "plans-for-week-35"]], "Plans for week 36": [[29, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[30, "plans-for-week-37-lecture-monday"]], "Practical tips": [[13, "practical-tips"], [30, "practical-tips"]], "Practicalities": [[25, "practicalities"], [25, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[22, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[28, "preprocessing-our-data"]], "Prerequisites": [[27, "prerequisites"]], "Prerequisites and background": [[20, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[24, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[29, "program-example-for-gradient-descent-with-ridge-regression"], [30, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[22, null]], "Properties of PDFs": [[24, "properties-of-pdfs"]], "Pros and cons": [[30, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[20, "python-installers"], [27, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[30, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[30, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[30, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[24, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[27, "reading-material"]], "Reading recommendations:": [[28, "reading-recommendations"]], "Reading suggestions week 34": [[27, "reading-suggestions-week-34"]], "Readings and Videos:": [[30, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [28, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[22, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[27, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[27, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"]], "Reminder from last week": [[28, "reminder-from-last-week"]], "Reminder on Newton-Raphson\u2019s method": [[29, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on different scaling methods": [[30, "reminder-on-different-scaling-methods"]], "Replace or not": [[13, "replace-or-not"], [30, "replace-or-not"]], "Required Technologies": [[20, "required-technologies"]], 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+Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [28, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[28, "a-first-summary"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"]], "ADAM algorithm, taken from Goodfellow et al": [[31, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [31, "id2"]], "Accuracy": [[31, "accuracy"]], "Activation functions": [[12, "activation-functions"]], "AdaGrad Properties": [[31, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[31, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[31, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[31, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[31, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[31, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[31, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[31, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[31, "adaptivity-across-dimensions"]], "Adding error analysis and training set up": [[28, "adding-error-analysis-and-training-set-up"], [29, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[31, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[28, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[29, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[31, "and-finally-adam"]], "And what about using neural networks?": [[28, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[30, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[21, null]], "Autocorrelation function": [[25, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[29, "back-to-ridge-and-lasso-regression"], [30, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[23, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[22, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [29, "basic-math-of-the-svd"], [30, "basic-math-of-the-svd"]], "Basics": [[7, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Batch Normalization": [[1, "batch-normalization"]], "Batches and mini-batches": [[31, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[5, "bayes-theorem-and-ridge-and-lasso-regression"]], "Boosting, a Bird\u2019s Eye View": [[10, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[6, "bootstrap"]], "Bringing it together, first back propagation equation": [[12, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[1, null]], "Building a tree, regression": [[9, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[1, "building-neural-networks-in-tensorflow-and-keras"]], "But none of these can compete with Newton\u2019s method": [[31, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Challenge: Choosing a Fixed Learning Rate": [[31, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[14, null]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[31, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [29, "codes-for-the-svd"], [30, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"]], "Communication channels": [[28, "communication-channels"]], "Compare Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[30, "comparison-with-ols"]], "Computation of gradients": [[31, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[30, "conditions-on-convex-functions"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[31, "convergence-rates"]], "Convex function": [[30, "convex-function"]], "Convex functions": [[13, "convex-functions"], [30, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[29, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [29, "correlation-matrix"]], "Correlation Matrix with Pandas": [[29, "correlation-matrix-with-pandas"]], "Course Format": [[28, "course-format"]], "Course setting": [[24, null]], "Covariance Matrix Examples": [[29, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[29, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Deadlines for projects (tentative)": [[28, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[31, "deep-neural-networks"]], "Deep learning methods": [[28, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"]], "Defining the cost function": [[1, "defining-the-cost-function"]], "Definitions": [[19, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[31, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[29, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[29, "deriving-the-lasso-regression-equations"], [30, "deriving-the-lasso-regression-equations"], [30, "id6"]], "Deriving the Ridge Regression Equations": [[29, "deriving-the-ridge-regression-equations"], [30, "deriving-the-ridge-regression-equations"], [30, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[28, "discriminative-modeling"]], "Domains and probabilities": [[25, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[29, "economy-size-svd"], [30, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[25, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[31, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[28, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[29, "example-2"]], "Example 3": [[29, "example-3"]], "Example 4": [[29, "example-4"]], "Example Matrix": [[29, "example-matrix"], [30, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[29, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[29, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[28, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code avaliable and presentable": [[20, "exercise-4-making-the-code-avaliable-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Expectation values": [[25, "expectation-values"]], "Extending to more than one variable": [[30, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[28, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[29, "fixing-the-singularity"], [30, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[23, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[29, "frequently-used-scaling-functions"], [31, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[30, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[29, "functionality-in-scikit-learn"], [31, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [29, "further-properties-important-for-our-analyses-later"], [30, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[22, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[28, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[28, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [28, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[28, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[30, "id1"], [31, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[30, "gradient-descent-and-ridge"], [31, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[31, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[30, "gradient-descent-example"], [31, "gradient-descent-example"]], "Grading": [[26, "grading"], [26, "id2"], [28, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[22, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[29, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[31, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[26, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [31, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Installing R, C++, cython or Julia": [[28, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[28, "installing-r-c-cython-numba-etc"]], "Instructor information": [[26, "instructor-information"]], "Interpretations and optimizing our parameters": [[28, "interpretations-and-optimizing-our-parameters"], [28, "id2"], [28, "id3"], [29, "interpretations-and-optimizing-our-parameters"], [29, "id1"], [29, "id2"]], "Interpreting the Ridge results": [[29, "interpreting-the-ridge-results"], [30, "interpreting-the-ridge-results"], [30, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [29, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [21, "introduction"], [22, "introduction"]], "Introduction to numerical projects": [[23, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[22, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[30, "lasso-regression"]], "Lasso case": [[30, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[21, "learning-outcomes"], [28, "learning-outcomes"]], "Lectures and ComputerLab": [[28, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[22, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[29, "linear-regression-problems"], [30, "linear-regression-problems"]], "Linear Regression and the SVD": [[30, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [29, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[27, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[28, "machine-learning"]], "Machine learning": [[21, "machine-learning"]], "Main textbooks": [[28, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[29, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[29, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[30, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[30, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[31, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[31, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"], [30, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [29, "mathematics-of-the-svd-and-implications"], [30, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[28, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Meet the covariance!": [[25, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [29, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[29, "meet-the-hessian-matrix"]], "Meet the Pandas": [[28, "meet-the-pandas"]], "Memory Usage and Scalability": [[31, "memory-usage-and-scalability"]], "Memory constraints": [[31, "memory-constraints"]], "Min-Max Scaling": [[29, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"], [31, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More interpretations": [[29, "more-interpretations"], [30, "more-interpretations"], [30, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[30, "more-on-steepest-descent"]], "More on convex functions": [[30, "more-on-convex-functions"]], "More preprocessing": [[29, "more-preprocessing"], [31, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[31, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[31, "non-convex-problems"]], "Note about SVD Calculations": [[29, "note-about-svd-calculations"], [30, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[30, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[25, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[22, "numpy-and-arrays"], [28, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[28, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[30, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[28, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[28, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [28, "organizing-our-data"]], "Other Matrix and Vector Operations": [[22, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[28, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[28, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[28, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[28, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[28, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[31, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[28, "own-code-for-ordinary-least-squares"], [29, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[28, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[23, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[23, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[23, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[23, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[23, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[23, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[23, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[23, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plans for week 35": [[29, "plans-for-week-35"]], "Plans for week 36": [[30, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[31, "plans-for-week-37-lecture-monday"]], "Practical tips": [[13, "practical-tips"], [31, "practical-tips"]], "Practicalities": [[26, "practicalities"], [26, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[23, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[29, "preprocessing-our-data"]], "Prerequisites": [[28, "prerequisites"]], "Prerequisites and background": [[21, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[25, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[30, "program-example-for-gradient-descent-with-ridge-regression"], [31, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[23, null]], "Properties of PDFs": [[25, "properties-of-pdfs"]], "Pros and cons": [[31, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[21, "python-installers"], [28, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[31, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[31, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[31, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[25, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[28, "reading-material"]], "Reading recommendations:": [[29, "reading-recommendations"]], "Reading suggestions week 34": [[28, "reading-suggestions-week-34"]], "Readings and Videos:": [[31, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [29, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[23, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[28, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[28, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"]], "Reminder from last week": [[29, "reminder-from-last-week"]], "Reminder on Newton-Raphson\u2019s method": [[30, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on different scaling methods": [[31, "reminder-on-different-scaling-methods"]], "Replace or not": [[13, "replace-or-not"], [31, "replace-or-not"]], "Required Technologies": [[21, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling methods": [[6, "id1"]], "Residual Error": [[29, "residual-error"], [30, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[30, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Rewriting the Covariance and/or Correlation Matrix": [[29, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the fitting procedure as a linear algebra problem": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[30, "ridge-regression"]], "Ridge and LASSO Regression": [[29, "ridge-and-lasso-regression"], [30, "ridge-and-lasso-regression"], [30, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[31, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[31, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[30, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [31, "same-code-but-now-with-momentum-gradient-descent"], [31, "id3"], [31, "id4"]], "Schedule first week": [[28, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[31, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Matrix to be inverted": [[29, "setting-up-the-matrix-to-be-inverted"], [30, "setting-up-the-matrix-to-be-inverted"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [31, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[29, "simple-case"], [30, "simple-case"]], "Simple code for solving the above problem": [[30, "simple-code-for-solving-the-above-problem"]], "Simple example code": [[31, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[30, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[30, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [28, "simple-linear-regression-model-using-scikit-learn"]], "Simple one-dimensional second-order polynomial": [[18, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[30, "simple-program"], [31, "simple-program"]], "Slightly different approach": [[31, "slightly-different-approach"]], "Sneaking in automatic differentiation using Autograd": [[31, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[23, "software-and-needed-installations"], [28, "software-and-needed-installations"]], "Solving Differential Equations with Deep Learning": [[2, null]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Some famous Matrices": [[22, "some-famous-matrices"]], "Some simple problems": [[13, "some-simple-problems"], [30, "some-simple-problems"]], "Some useful matrix and vector expressions": [[29, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [29, "splitting-our-data-in-training-and-test-data"]], "Standard steepest descent": [[13, "standard-steepest-descent"]], "Statistical analysis and optimization of data": [[21, "statistical-analysis-and-optimization-of-data"], [28, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[13, "steepest-descent"], [30, "steepest-descent"]], "Stochastic Gradient Descent": [[31, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[13, "stochastic-gradient-descent-sgd"], [31, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[25, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[31, "strongly-convex-case"]], "Support Vector Machines, overarching aims": [[8, null]], "Systematic reduction": [[3, "systematic-reduction"]], "Teachers": [[28, "teachers"]], "Teachers and Grading": [[26, null]], "Teaching Assistants Fall semester 2023": [[26, "teaching-assistants-fall-semester-2023"]], "Tentative deadllines for projects": [[26, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[0, "testing-the-means-squared-error-as-function-of-complexity"], [29, "testing-the-means-squared-error-as-function-of-complexity"]], "Textbooks": [[27, null]], "The Algorithm before theorem": [[11, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[1, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[9, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[9, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[3, "the-cifar01-data-set"]], "The Hessian matrix": [[30, "the-hessian-matrix"], [31, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[30, "the-hessian-matrix-for-ridge-regression"], [31, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[29, "the-jacobian"]], "The MNIST dataset again": [[3, "the-mnist-dataset-again"]], "The OLS case": [[30, "the-ols-case"]], "The RELU function family": [[1, "the-relu-function-family"]], "The Ridge case": [[30, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[29, "the-svd-a-fantastic-algorithm"], [30, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[1, "the-softmax-function"]], "The \\chi^2 function": [[0, "the-chi-2-function"], [28, "the-chi-2-function"], [28, "id4"], [28, "id5"], [28, "id6"], [28, "id7"], [28, "id8"]], "The bias-variance tradeoff": [[6, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[2, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[29, "the-complete-code-with-a-simple-data-set"]], "The cost/loss function": [[29, "the-cost-loss-function"]], "The course has two central parts": [[21, "the-course-has-two-central-parts"]], "The derivative of the cost/loss function": [[30, "the-derivative-of-the-cost-loss-function"], [31, "the-derivative-of-the-cost-loss-function"]], "The equations": [[30, "the-equations"]], "The equations for ordinary least squares": [[29, "the-equations-for-ordinary-least-squares"]], "The first Case": [[30, "the-first-case"]], "The gradient step": [[31, "the-gradient-step"]], "The ideal": [[30, "the-ideal"]], "The logistic function": [[7, "the-logistic-function"]], "The mean squared error and its derivative": [[29, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[8, "the-moons-example"]], "The multilayer perceptron (MLP)": [[12, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[2, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The plethora of machine learning algorithms/methods": [[28, "the-plethora-of-machine-learning-algorithms-methods"]], "The sensitiveness of the gradient descent": [[30, "the-sensitiveness-of-the-gradient-descent"]], "The singular value decomposition": [[5, "the-singular-value-decomposition"], [29, "the-singular-value-decomposition"], [30, "the-singular-value-decomposition"]], "The two-dimensional case": [[8, "the-two-dimensional-case"]], "Theoretical Convergence Speed and convex optimization": [[31, "theoretical-convergence-speed-and-convex-optimization"]], "Time decay rate": [[31, "time-decay-rate"]], "To our real data: nuclear binding energies. 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Linear Regression", "14. Building a Feed Forward Neural Network", "15. Solving Differential Equations with Deep Learning", "16. Convolutional Neural Networks", "17. Recurrent neural networks: Overarching view", "4. Ridge and Lasso Regression", "5. Resampling Methods", "6. Logistic Regression", "8. Support Vector Machines, overarching aims", "9. Decision trees, overarching aims", "10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods", "11. Basic ideas of the Principal Component Analysis (PCA)", "13. Neural networks", "7. Optimization, the central part of any Machine Learning algortithm", "12. Clustering and Unsupervised Learning", "Exercises week 34", "Exercises week 35", "Exercises week 36", "Exercises week 37", "Exercises week 38", "Weekly Exercises 6", "Applied Data Analysis and Machine Learning", "2. 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"xgboost": 10, "yaml": [], "yet": 30, "your": [0, 10, 16, 18, 23, 29]}})
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/statistics.html b/doc/LectureNotes/_build/html/statistics.html
index cd2f12154..4bc6c26b2 100644
--- a/doc/LectureNotes/_build/html/statistics.html
+++ b/doc/LectureNotes/_build/html/statistics.html
@@ -232,6 +232,7 @@
Exercises week 37
Week 37: Gradient descent methods
Exercises week 38
+Weekly Exercises 6
Projects
Projects
Projects
Projects
Projects
Projects
Projects
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb
new file mode 100644
index 000000000..2c928c85c
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb
@@ -0,0 +1,171 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "433db993",
+ "metadata": {},
+ "source": [
+ "# Weekly Exercises 6\n",
+ "\n",
+ "## Getting started with project 1\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6b931365",
+ "metadata": {},
+ "source": [
+ "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.\n",
+ "\n",
+ "A short feedback to the this exercise will be available before the project deadline. And you can reuse these elements in your final report.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2a63bae1",
+ "metadata": {},
+ "source": [
+ "### Learning goals\n",
+ "\n",
+ "After completing these exercises, you will know how to\n",
+ "\n",
+ "- Create a properly formatted report in Overleaf\n",
+ "- Select and present graphs for a scientific report\n",
+ "- Write an abstract and introduction for a scientific report\n",
+ "\n",
+ "### Deliverables\n",
+ "\n",
+ "Complete the following exercises while working in an Overleaf project. Then, in canvas, include\n",
+ "\n",
+ "- An exported PDF of the report draft you have been working on.\n",
+ "- A comment linking to the github repository used in exercise 4.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e0f2d99d",
+ "metadata": {},
+ "source": [
+ "## Exercise 1: Creating the report document\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d06bfb29",
+ "metadata": {},
+ "source": [
+ "We require all projects to be formatted as proper scientific reports, and this includes using LaTeX for typesetting. We strongly recommend that you use the online LaTeX editor Overleaf, as it is much easier to start using, and has excellent support for collaboration.\n",
+ "\n",
+ "**a)** Create an account on Overleaf.com\n",
+ "\n",
+ "**b)** Download [this](https://github.com/CompPhysics/MachineLearning/blob/master/doc/LectureNotes/data/FYS_STK_Template.zip) template project.\n",
+ "\n",
+ "**c)** Create a new Overleaf project with the correct formatting by uploading the template project.\n",
+ "\n",
+ "**d)** Read the general guideline for writing a report, which can be found at .\n",
+ "\n",
+ "**e)** Look at the provided example of an earlier project, found at \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ec36f4c3",
+ "metadata": {},
+ "source": [
+ "## Exercise 2: Adding good figures\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f50723f8",
+ "metadata": {},
+ "source": [
+ "**a)** Using what you have learned so far in this course, create a plot illustrating the Bias-Variance trade-off. Make sure the lines and axes are labeled, with font size being the same as in the text.\n",
+ "\n",
+ "**b)** Add this figure to the results section of your document, with a caption that describes it. A reader should be able to understand the figure with only its contents and caption.\n",
+ "\n",
+ "**c)** Refer to the figure in your text using \\ref.\n",
+ "\n",
+ "**d)** Create a heatmap showing the MSE of a Ridge regression model for various polynomial degrees and lambda values. Make sure the axes are labeled, and that the title or colorbar describes what is plotted.\n",
+ "\n",
+ "**e)** Add this second figure to your document with a caption and reference in the text. All figures in the final report must be captioned and be referenced and used in the text.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "276c214e",
+ "metadata": {},
+ "source": [
+ "## Exercise 3: Writing an abstract and introduction\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f4134eb5",
+ "metadata": {},
+ "source": [
+ "Although much of your project 1 results are not done yet, we want you to write an abstract and introduction to get you started on writing the report. It is generally a good idea to write a lot of a report before finishing all of the results, as you get a better understanding of your methods and inquiry from doing so, along with saving a lot of time. Where you would typically describe results in the abstract, instead make something up, just this once.\n",
+ "\n",
+ "**a)** Read the guidelines on abstract and introduction before you start.\n",
+ "\n",
+ "**b)** Write an abstract for project 1 in your report.\n",
+ "\n",
+ "**c)** Write an introduction for project 1 in your report.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2f512b59",
+ "metadata": {},
+ "source": [
+ "## Exercise 4: Making the code avaliable and presentable\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "77fe1fec",
+ "metadata": {},
+ "source": [
+ "A central part of the report is the code you write to implement the methods and generate the results. To get points for the code-part of the project, you need to make your code avaliable and presentable.\n",
+ "\n",
+ "**a)** Create a github repository for project 1, or create a dedicated folder for project 1 in a github repository. Only one person in your group needs to do this.\n",
+ "\n",
+ "**b)** Add a PDF of the report to this repository, after completing exercises 1-3\n",
+ "\n",
+ "**c)** Add a folder named Code, where you can put python files for your functions and notebooks for reproducing your results.\n",
+ "\n",
+ "**d)** Add python files for functions, and a notebook to produce the figures in exercise 2, to the Code folder. Remember to use a seed for generating random data and for train-test splits.\n",
+ "\n",
+ "**e)** Create a README file in the reposotory or project folder with\n",
+ "\n",
+ "- the name of the group members\n",
+ "- a short description of the project\n",
+ "- a description of how to install the required packages to run your code from a requirements.txt file\n",
+ "- names and descriptions of the various notebooks in the Code folder and the results they produce\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f1d72c56",
+ "metadata": {},
+ "source": [
+ "## Exercise 5: Referencing\n",
+ "\n",
+ "**a)** Add a reference to Hastie et al. using your preferred referencing style. See https://www.sokogskriv.no/referansestiler/ for an overview of styles.\n",
+ "\n",
+ "**b)** Add a reference to sklearn like this: https://scikit-learn.org/stable/about.html#citing-scikit-learn\n",
+ "\n",
+ "**c)** Make a prompt to your LLM of choice, and upload the exported conversation to your GitHub repository for the project.\n",
+ "\n",
+ "**d)** At the end of the methods section of the report, write a one paragraph declaration on how and for what you have used the LLM. Link to the log on GitHub.\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_toc.yml b/doc/LectureNotes/_toc.yml
index 81c5448ff..844fa7df0 100644
--- a/doc/LectureNotes/_toc.yml
+++ b/doc/LectureNotes/_toc.yml
@@ -50,6 +50,7 @@ parts:
- file: exercisesweek37.ipynb
- file: week37.ipynb
- file: exercisesweek38.ipynb
+ - file: exercisesweek39.ipynb
- caption: Projects
numbered: false
chapters:
diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb
index fe89adb05..93dd115a2 100644
--- a/doc/pub/week37/ipynb/week37.ipynb
+++ b/doc/pub/week37/ipynb/week37.ipynb
@@ -108,7 +108,10 @@
"id": "947b67ee",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -353,7 +356,10 @@
"id": "a48d43f0",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -533,7 +539,10 @@
"id": "81740e7b",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -642,7 +651,10 @@
"id": "494e82a7",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -719,7 +731,10 @@
"id": "6a917123",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -1080,7 +1095,10 @@
"id": "602bda4c",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -1181,7 +1199,10 @@
"id": "77a60fcd",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -1229,7 +1250,10 @@
"id": "9bdf875b",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2295,7 +2319,10 @@
"id": "c721352d",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2366,7 +2393,10 @@
"id": "fc5df7eb",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2445,7 +2475,10 @@
"id": "adef9763",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2540,7 +2573,10 @@
"id": "bcf65acf",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2631,7 +2667,10 @@
"id": "300a02a4",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2686,7 +2725,10 @@
"id": "030efc5d",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2766,7 +2808,10 @@
"id": "0ba7d8f7",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2842,7 +2887,10 @@
"id": "c2a2732a",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -2957,7 +3005,10 @@
"id": "46375144",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -3080,7 +3131,10 @@
"id": "469ca11e",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
"outputs": [],
"source": [
@@ -3464,13 +3518,48 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 8,
"id": "2ed0cafc",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "True theta: [2, 0.5, 3.7]\n",
+ "Fitted theta: [2.08376632 0.19569961 3.97898392]\n",
+ "Sklearn fitted theta: [2.08376632 0.19569961 3.97898392]\n",
+ "MSE with intercept column\n",
+ "0.004113634617443139\n",
+ "MSE with intercept column from SKL\n",
+ "0.004113634617443147\n",
+ "Manual intercept: 2.083766322923907\n",
+ "Fitted theta (without intercept): [0.19569961 3.97898392]\n",
+ "Sklearn intercept: 2.0837663229239043\n",
+ "Sklearn fitted theta (without intercept): [0.19569961 3.97898392]\n",
+ "MSE with Manual intercept\n",
+ "4.346195723169266\n",
+ "MSE with Sklearn intercept\n",
+ "0.004113634617443131\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
@@ -3538,7 +3627,7 @@
"y_offset = np.average(y, axis=0)\n",
"X_offset = np.average(X, axis=0)\n",
"\n",
- "theta = fit_theta(X - X_offset, y - y_offset)\n",
+ "theta = fit_theta(X - X_offset, y)# - y_offset)\n",
"intercept = np.mean(y_offset - X_offset @ theta)\n",
"\n",
"print(f\"Manual intercept: {intercept}\")\n",
@@ -3548,7 +3637,7 @@
"ypredictOwn = X @ theta\n",
"ypredictSKL = skl.predict(X)\n",
"print(f\"MSE with Manual intercept\")\n",
- "print(MSE(y,ypredictOwn+intercept))\n",
+ "print(MSE(y,ypredictOwn))#+intercept))\n",
"print(f\"MSE with Sklearn intercept\")\n",
"print(MSE(y,ypredictSKL))\n",
"\n",
@@ -3656,13 +3745,121 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 2,
"id": "4f9b1fa0",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Theta values for own Ridge implementation\n",
+ "[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
+ " 2.80847477e-01 2.12552073e-01 8.13220608e-02 -1.69634577e-02\n",
+ " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
+ " -9.80609616e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
+ " 2.64742912e-02 1.63249532e-02 -5.01831251e-05 -2.15098090e-02]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n",
+ " 2.80847477e-01 2.12552073e-01 8.13220608e-02 -1.69634577e-02\n",
+ " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
+ " -9.80609615e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n",
+ " 2.64742912e-02 1.63249532e-02 -5.01831207e-05 -2.15098090e-02]\n",
+ "MSE values for own Ridge implementation\n",
+ "4.3632959215700067e-07\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "4.363295916323784e-07\n",
+ "Theta values for own Ridge implementation\n",
+ "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
+ " 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
+ " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
+ " 0.02976145 0.04543942]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n",
+ " 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
+ " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n",
+ " 0.02976145 0.04543942]\n",
+ "MSE values for own Ridge implementation\n",
+ "5.194042827197027e-06\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "5.1940428268204826e-06\n",
+ "Theta values for own Ridge implementation\n",
+ "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
+ " 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
+ " 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
+ " -0.01708852 -0.01708781]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n",
+ " 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n",
+ " 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
+ " -0.01708852 -0.01708781]\n",
+ "MSE values for own Ridge implementation\n",
+ "2.0940821989643363e-05\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "2.094082198961999e-05\n",
+ "Theta values for own Ridge implementation\n",
+ "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
+ " 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
+ " 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
+ " 0.00249435 0.00105081]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n",
+ " 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n",
+ " 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n",
+ " 0.00249435 0.00105081]\n",
+ "MSE values for own Ridge implementation\n",
+ "0.0003153514830957865\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "0.00031535148309580783\n",
+ "Theta values for own Ridge implementation\n",
+ "[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
+ " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
+ " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
+ " -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
+ " 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n",
+ " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
+ " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
+ " -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n",
+ " 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n",
+ "MSE values for own Ridge implementation\n",
+ "0.015072388895177157\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "0.0150723888951771\n",
+ "Theta values for own Ridge implementation\n",
+ "[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
+ " 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
+ " 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
+ " 0.0036237 0.003301 ]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n",
+ " 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n",
+ " 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n",
+ " 0.0036237 0.003301 ]\n",
+ "MSE values for own Ridge implementation\n",
+ "0.26409315307910036\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "0.26409315307910025\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
@@ -3746,13 +3943,143 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 4,
"id": "a731e32c",
"metadata": {
"collapsed": false,
- "editable": true
+ "editable": true,
+ "jupyter": {
+ "outputs_hidden": false
+ }
},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Theta values for own Ridge implementation\n",
+ "[ 6.21437387e-02 -6.21799480e-01 4.97375876e-02 2.80186212e-01\n",
+ " 2.13204296e-01 8.21806408e-02 -1.64261842e-02 -6.49525927e-02\n",
+ " -7.40621002e-02 -5.97380172e-02 -3.53631498e-02 -1.00892602e-02\n",
+ " 1.06457090e-02 2.41129954e-02 2.93712126e-02 2.65682547e-02\n",
+ " 1.64586608e-02 8.86820363e-05 -2.13996549e-02]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[ 6.21437387e-02 -6.21799480e-01 4.97375876e-02 2.80186212e-01\n",
+ " 2.13204296e-01 8.21806408e-02 -1.64261842e-02 -6.49525927e-02\n",
+ " -7.40621002e-02 -5.97380172e-02 -3.53631498e-02 -1.00892602e-02\n",
+ " 1.06457090e-02 2.41129954e-02 2.93712126e-02 2.65682547e-02\n",
+ " 1.64586608e-02 8.86820368e-05 -2.13996549e-02]\n",
+ "Intercept from own implementation:\n",
+ "1.0303792191716266\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "1.030379219171611\n",
+ "MSE values for own Ridge implementation\n",
+ "4.5384372495623863e-07\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "4.538437249513786e-07\n",
+ "Theta values for own Ridge implementation\n",
+ "[-0.02347793 -0.37069922 -0.07332612 0.11841713 0.16193346 0.1301137\n",
+ " 0.07578485 0.02473008 -0.01354652 -0.03746205 -0.048708 -0.04998023\n",
+ " -0.04397732 -0.03302123 -0.01896364 -0.00321213 0.01320154 0.02954601\n",
+ " 0.04532178]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[-0.02347793 -0.37069922 -0.07332612 0.11841713 0.16193346 0.1301137\n",
+ " 0.07578485 0.02473008 -0.01354652 -0.03746205 -0.048708 -0.04998023\n",
+ " -0.04397732 -0.03302123 -0.01896364 -0.00321213 0.01320154 0.02954601\n",
+ " 0.04532178]\n",
+ "Intercept from own implementation:\n",
+ "1.0367447638630856\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "1.0367447638630596\n",
+ "MSE values for own Ridge implementation\n",
+ "5.753660262133006e-06\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "5.753660262105462e-06\n",
+ "Theta values for own Ridge implementation\n",
+ "[-0.12806426 -0.15525674 -0.05487426 0.0191961 0.05293494 0.0605132\n",
+ " 0.05479386 0.04368354 0.03139359 0.01993241 0.01011079 0.00212882\n",
+ " -0.00410226 -0.00879058 -0.01217801 -0.0144992 -0.01596432 -0.01675341\n",
+ " -0.01701673]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[-0.12806426 -0.15525674 -0.05487426 0.0191961 0.05293494 0.0605132\n",
+ " 0.05479386 0.04368354 0.03139359 0.01993241 0.01011079 0.00212882\n",
+ " -0.00410226 -0.00879058 -0.01217801 -0.0144992 -0.01596432 -0.01675341\n",
+ " -0.01701673]\n",
+ "Intercept from own implementation:\n",
+ "1.0457044830369082\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "1.0457044830369118\n",
+ "MSE values for own Ridge implementation\n",
+ "2.891180548496047e-05\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "2.891180548496749e-05\n",
+ "Theta values for own Ridge implementation\n",
+ "[-0.13729887 -0.08409267 -0.03383964 -0.00374257 0.01182892 0.01878432\n",
+ " 0.02095086 0.02056419 0.01888753 0.01662493 0.01416442 0.01171602\n",
+ " 0.00938921 0.00723663 0.0052788 0.00351837 0.00194828 0.00055647\n",
+ " -0.00067131]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[-0.13729887 -0.08409267 -0.03383964 -0.00374257 0.01182892 0.01878432\n",
+ " 0.02095086 0.02056419 0.01888753 0.01662493 0.01416442 0.01171602\n",
+ " 0.00938921 0.00723663 0.0052788 0.00351837 0.00194828 0.00055647\n",
+ " -0.00067131]\n",
+ "Intercept from own implementation:\n",
+ "1.0395764153518305\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "1.0395764153518303\n",
+ "MSE values for own Ridge implementation\n",
+ "6.344515538040167e-05\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "6.344515538040063e-05\n",
+ "Theta values for own Ridge implementation\n",
+ "[-0.05814585 -0.04390414 -0.02861232 -0.01777492 -0.01046009 -0.00550644\n",
+ " -0.00210846 0.00024979 0.00189794 0.00305065 0.00385122 0.00439783\n",
+ " 0.00475926 0.00498468 0.00510982 0.00516093 0.00515753 0.00511424\n",
+ " 0.00504205]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[-0.05814585 -0.04390414 -0.02861232 -0.01777492 -0.01046009 -0.00550644\n",
+ " -0.00210846 0.00024979 0.00189794 0.00305065 0.00385122 0.00439783\n",
+ " 0.00475926 0.00498468 0.00510982 0.00516093 0.00515753 0.00511424\n",
+ " 0.00504205]\n",
+ "Intercept from own implementation:\n",
+ "1.0036921863049417\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "1.0036921863049417\n",
+ "MSE values for own Ridge implementation\n",
+ "0.0008213907109028527\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "0.000821390710902852\n",
+ "Theta values for own Ridge implementation\n",
+ "[-0.00952707 -0.00855426 -0.00684557 -0.00542639 -0.00433676 -0.00350466\n",
+ " -0.00286296 -0.00236187 -0.0019659 -0.00164965 -0.0013947 -0.00118745\n",
+ " -0.0010177 -0.0008777 -0.00076148 -0.00066442 -0.00058287 -0.00051397\n",
+ " -0.00045544]\n",
+ "Theta values for Scikit-Learn Ridge implementation\n",
+ "[-0.00952707 -0.00855426 -0.00684557 -0.00542639 -0.00433676 -0.00350466\n",
+ " -0.00286296 -0.00236187 -0.0019659 -0.00164965 -0.0013947 -0.00118745\n",
+ " -0.0010177 -0.0008777 -0.00076148 -0.00066442 -0.00058287 -0.00051397\n",
+ " -0.00045544]\n",
+ "Intercept from own implementation:\n",
+ "0.9661173541241802\n",
+ "Intercept from Scikit-Learn Ridge implementation\n",
+ "0.9661173541241802\n",
+ "MSE values for own Ridge implementation\n",
+ "0.0031252083411001533\n",
+ "MSE values for Scikit-Learn Ridge implementation\n",
+ "0.0031252083411001533\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
@@ -3766,7 +4093,7 @@
" return np.sum((y_data-y_model)**2)/n\n",
"# A seed just to ensure that the random numbers are the same for every run.\n",
"# Useful for eventual debugging.\n",
- "np.random.seed(315)\n",
+ "np.random.seed(3155)\n",
"\n",
"n = 100\n",
"x = np.random.rand(n)\n",
@@ -3850,7 +4177,25 @@
]
}
],
- "metadata": {},
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.15"
+ }
+ },
"nbformat": 4,
"nbformat_minor": 5
}