KarlHenrik
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234 KiB
JavaScript
1 line
234 KiB
JavaScript
Search.setIndex({"alltitles": {"1a)": [[60, "a"]], "3a)": [[60, "id1"]], "3b)": [[60, "b"]], "4a)": [[60, "id2"]], "4b)": [[60, "id3"]], "A Classification Tree": [[51, "a-classification-tree"]], "A Frequentist approach to data analysis": [[42, "a-frequentist-approach-to-data-analysis"], [69, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[50, "a-better-approach"]], "A first summary": [[69, "a-first-summary"]], "A quick Reminder on Lagrangian Multipliers": [[50, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[46, "a-simple-example"]], "A soft classifier": [[50, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[43, "a-top-down-perspective-on-neural-networks"]], "A11Y Dark": [[0, null]], "A11Y High Contrast Dark": [[1, null]], "A11Y High Contrast Light": [[2, null]], "A11Y Light": [[3, null]], "ADAM algorithm, taken from Goodfellow et al": [[72, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[55, "adam-optimizer"], [72, "id2"]], "API": [[27, "api"]], "About the IPython Development Team": [[20, "about-the-ipython-development-team"]], "Accuracy": [[72, "accuracy"]], "Activation functions": [[54, "activation-functions"]], "AdaGrad Properties": [[72, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[72, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[72, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[72, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[72, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[72, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[72, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[72, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[52, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[72, "adaptivity-across-dimensions"]], "Adding error analysis and training set up": [[69, "adding-error-analysis-and-training-set-up"], [70, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[43, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[72, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[51, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[52, "an-overview-of-ensemble-methods"]], "An example cell": [[23, "an-example-cell"]], "An extrapolation example": [[46, "an-extrapolation-example"]], "An optimization/minimization problem": [[69, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[70, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[72, "and-finally-adam"]], "And what about using neural networks?": [[69, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[71, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[51, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[62, null]], "Authors": [[31, null]], "Autocorrelation function": [[66, "autocorrelation-function"]], "Automatic differentiation": [[55, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[70, "back-to-ridge-and-lasso-regression"], [71, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[53, "back-to-the-cancer-data"]], "Background literature": [[64, "background-literature"]], "Bagging": [[52, "bagging"]], "Bagging Examples": [[52, "bagging-examples"]], "Basic Matrix Features": [[63, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[53, null]], "Basic math of the SVD": [[47, "basic-math-of-the-svd"], [70, "basic-math-of-the-svd"], [71, "basic-math-of-the-svd"]], "Basics": [[49, "basics"]], "Basics of a tree": [[51, "basics-of-a-tree"]], "Batch Normalization": [[43, "batch-normalization"]], "Batches and mini-batches": [[72, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[47, "bayes-theorem-and-ridge-and-lasso-regression"]], "Blinds Dark": [[4, null]], "Blinds Light": [[5, null]], "Boosting, a Bird\u2019s Eye View": [[52, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[48, "bootstrap"]], "Bringing it together, first back propagation equation": [[54, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[43, null]], "Building a tree, regression": [[51, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[43, "building-neural-networks-in-tensorflow-and-keras"]], "But none of these can compete with Newton\u2019s method": [[72, "but-none-of-these-can-compete-with-newton-s-method"]], "CDN": [[29, "cdn"]], "CHANGELOG": [[29, "changelog"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[45, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[51, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Challenge: Choosing a Fixed Learning Rate": [[72, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[43, "choose-cost-function-and-optimizer"]], "Citations": [[22, "citations"]], "Classical PCA Theorem": [[53, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[56, null]], "Code blocks and outputs": [[24, "code-blocks-and-outputs"]], "Code for SVD and Inversion of Matrices": [[47, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[72, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[56, "codes-and-approaches"]], "Codes for the SVD": [[47, "codes-for-the-svd"], [70, "codes-for-the-svd"], [71, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[57, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[43, "collect-and-pre-process-data"]], "Colors": [[0, "colors"], [1, "colors"], [2, "colors"], [3, "colors"], [4, "colors"], [5, "colors"], [6, "colors"], [7, "colors"], [8, "colors"], [9, "colors"], [10, "colors"], [11, "colors"], [12, "colors"], [13, "colors"], [14, "colors"], [15, "colors"]], "Communication channels": [[69, "communication-channels"]], "Compare Bagging on Trees with Random Forests": [[52, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[44, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[71, "comparison-with-ols"]], "Compiled translation files": [[39, "compiled-translation-files"]], "Computation of gradients": [[72, "computation-of-gradients"]], "Computing the Gini index": [[51, "computing-the-gini-index"]], "Conditions on convex functions": [[71, "conditions-on-convex-functions"]], "Conjugate gradient method": [[55, "conjugate-gradient-method"]], "Content with notebooks": [[24, null]], "Contributors": [[31, "contributors"]], "Convergence rates": [[72, "convergence-rates"]], "Convex function": [[71, "convex-function"]], "Convex functions": [[55, "convex-functions"], [71, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[45, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[45, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[54, "convolutional-neural-network"]], "Convolutional Neural Networks": [[45, null]], "Correlation Function and Design/Feature Matrix": [[70, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[53, "correlation-matrix"], [70, "correlation-matrix"]], "Correlation Matrix with Pandas": [[70, "correlation-matrix-with-pandas"]], "Course Format": [[69, "course-format"]], "Course setting": [[65, null]], "Covariance Matrix Examples": [[70, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[70, "covariance-and-correlation-matrix"]], "Create a notebook with MyST Markdown": [[23, "create-a-notebook-with-myst-markdown"]], "Creator": [[31, "creator"]], "Cross-validation": [[48, "cross-validation"]], "Deadlines for projects (tentative)": [[69, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[51, null]], "Deep Neural Networks": [[72, "deep-neural-networks"]], "Deep learning methods": [[69, "deep-learning-methods"]], "Define model and architecture": [[43, "define-model-and-architecture"]], "Defining the cost function": [[43, "defining-the-cost-function"]], "Definitions": [[61, "definitions"]], "Deliverables": [[57, "deliverables"], [58, "deliverables"], [61, "deliverables"]], "Dependencies": [[29, "dependencies"]], "Derivation of the AdaGrad Algorithm": [[72, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[54, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[70, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[47, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[58, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[59, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[70, "deriving-the-lasso-regression-equations"], [71, "deriving-the-lasso-regression-equations"], [71, "id6"]], "Deriving the Ridge Regression Equations": [[70, "deriving-the-ridge-regression-equations"], [71, "deriving-the-ridge-regression-equations"], [71, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[54, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[43, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[53, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[50, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[51, "disadvantages"]], "Discriminative Modeling": [[69, "discriminative-modeling"]], "Domains and probabilities": [[66, "domains-and-probabilities"]], "Dropout": [[43, "dropout"]], "Economy-size SVD": [[70, "economy-size-svd"], [71, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[66, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[72, "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": [[52, null]], "Entropy and the ID3 algorithm": [[51, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[69, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[43, "evaluate-model-performance-on-test-data"]], "Example": [[27, "example"]], "Example 2": [[70, "example-2"]], "Example 3": [[70, "example-3"]], "Example 4": [[70, "example-4"]], "Example Matrix": [[70, "example-matrix"], [71, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[69, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[69, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[70, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[70, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[44, "example-exponential-decay"]], "Example: Population growth": [[44, "example-population-growth"]], "Example: The diffusion equation": [[44, "example-the-diffusion-equation"]], "Example: binary classification problem": [[43, "example-binary-classification-problem"]], "Examples": [[69, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[49, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[59, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[58, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[57, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[60, "exercise-1-scale-your-data"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[61, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[42, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[58, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[59, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[57, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[60, "exercise-2-calculate-the-gradients"]], "Exercise 2: Expectation values for Ridge regression": [[61, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[42, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[58, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[57, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[59, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[57, "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}": [[60, "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": [[61, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[42, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[58, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[59, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[59, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[57, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[60, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[42, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[61, "exercise-4-computing-the-bias-and-variance"]], "Exercise 5 - Comparing your code with sklearn": [[58, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[60, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[42, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[61, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[48, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[48, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[48, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[48, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[48, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[48, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[42, "exercises"]], "Exercises and Projects": [[48, "exercises-and-projects"]], "Exercises week 34": [[57, null]], "Exercises week 35": [[58, null]], "Exercises week 36": [[59, null]], "Exercises week 37": [[60, null]], "Exercises week 38": [[61, null]], "Expectation values": [[66, "expectation-values"]], "Extending to more than one variable": [[71, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[69, "extremely-useful-tools-strongly-recommended"]], "FAQ": [[29, "faq"]], "Features": [[29, "features"]], "Feed-forward neural networks": [[54, "feed-forward-neural-networks"]], "Feed-forward pass": [[43, "feed-forward-pass"]], "Final back propagating equation": [[54, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[43, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[42, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[70, "fixing-the-singularity"], [71, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[64, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[70, "frequently-used-scaling-functions"], [72, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[71, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[54, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[70, "functionality-in-scikit-learn"], [72, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[45, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[47, "further-properties-important-for-our-analyses-later"], [70, "further-properties-important-for-our-analyses-later"], [71, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[63, "gaussian-elimination"]], "General Features": [[51, "general-features"]], "General linear models and linear algebra": [[69, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[69, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [69, "id1"]], "Generative Adversarial Networks": [[46, "generative-adversarial-networks"]], "Generative Models": [[46, "generative-models"]], "Generative Versus Discriminative Modeling": [[69, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[53, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Github Dark": [[6, null]], "Github Dark Colorblind": [[7, null]], "Github Dark High Contrast": [[8, null]], "Github Light": [[9, null]], "Github Light Colorblind": [[10, null]], "Github Light High Contrast": [[11, null]], "Gotthard Dark": [[12, null]], "Gotthard Light": [[13, null]], "Gradient Boosting, Classification Example": [[52, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[52, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[43, "gradient-clipping"]], "Gradient Descent Example": [[71, "id1"], [72, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[52, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[44, "gradient-descent"]], "Gradient descent and Ridge": [[71, "gradient-descent-and-ridge"], [72, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[72, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[71, "gradient-descent-example"], [72, "gradient-descent-example"]], "Grading": [[67, "grading"], [67, "id2"], [69, "grading"]], "Greative": [[14, null]], "How to take derivatives of Matrix-Vector expressions": [[58, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[50, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[63, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[70, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[72, "improving-gradient-descent-with-momentum"]], "Improving performance": [[43, "improving-performance"]], "In summary": [[67, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[55, "including-stochastic-gradient-descent-with-autograd"], [72, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[53, "incremental-pca"]], "Install": [[28, "install"]], "Installation": [[27, "installation"]], "Installing R, C++, cython or Julia": [[69, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[69, "installing-r-c-cython-numba-etc"]], "Instructor information": [[67, "instructor-information"]], "Interpretations and optimizing our parameters": [[69, "interpretations-and-optimizing-our-parameters"], [69, "id2"], [69, "id3"], [70, "interpretations-and-optimizing-our-parameters"], [70, "id1"], [70, "id2"]], "Interpreting the Ridge results": [[70, "interpreting-the-ridge-results"], [71, "interpreting-the-ridge-results"], [71, "id4"]], "Introducing JAX": [[55, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[53, "introducing-the-covariance-and-correlation-functions"], [70, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[42, "introduction"], [48, "introduction"], [62, "introduction"], [63, "introduction"]], "Introduction to numerical projects": [[64, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[52, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[52, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[53, "kernel-pca"]], "Kernels and non-linearity": [[50, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[63, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[71, "lasso-regression"]], "Lasso case": [[71, "lasso-case"]], "Layers": [[43, "layers"]], "Layers used to build CNNs": [[45, "layers-used-to-build-cnns"]], "Learn more": [[22, "learn-more"]], "Learning goals": [[57, "learning-goals"], [58, "learning-goals"], [59, "learning-goals"], [60, "learning-goals"], [61, "learning-goals"]], "Learning outcomes": [[62, "learning-outcomes"], [69, "learning-outcomes"]], "Lectures and ComputerLab": [[69, "lectures-and-computerlab"]], "License": [[27, "license"], [28, "license"], [29, "license"]], "License for Sphinx": [[35, null]], "Licenses for incorporated software": [[35, "licenses-for-incorporated-software"]], "Limitations of supervised learning with deep networks": [[43, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[63, null]], "Linear Regression": [[42, null]], "Linear Regression Problems": [[70, "linear-regression-problems"], [71, "linear-regression-problems"]], "Linear Regression and the SVD": [[71, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[42, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[47, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[47, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[47, "linking-with-the-svd"], [70, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[68, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[49, null], [49, "id1"]], "MNIST and GANs": [[46, "mnist-and-gans"]], "Machine Learning": [[69, "machine-learning"]], "Machine learning": [[62, "machine-learning"]], "Main textbooks": [[69, "main-textbooks"]], "Making a tree": [[51, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[52, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[70, "making-your-own-test-train-splitting"]], "Markdown + notebooks": [[24, "markdown-notebooks"]], "Markdown Files": [[22, null]], "Material for exercises week 35": [[70, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[71, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[71, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[72, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[72, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[47, "mathematical-interpretation-of-ordinary-least-squares"], [70, "mathematical-interpretation-of-ordinary-least-squares"], [71, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[50, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[45, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[47, "mathematics-of-the-svd-and-implications"], [70, "mathematics-of-the-svd-and-implications"], [71, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[69, "matrices-in-python"]], "Matrix multiplication": [[43, "matrix-multiplication"]], "Matrix-vector notation and activation": [[54, "matrix-vector-notation-and-activation"]], "Meet the covariance!": [[66, "meet-the-covariance"]], "Meet the Covariance Matrix": [[47, "meet-the-covariance-matrix"], [70, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[70, "meet-the-hessian-matrix"]], "Meet the Pandas": [[69, "meet-the-pandas"]], "Memory Usage and Scalability": [[72, "memory-usage-and-scalability"]], "Memory constraints": [[72, "memory-constraints"]], "Min-Max Scaling": [[70, "min-max-scaling"]], "Momentum based GD": [[55, "momentum-based-gd"], [72, "momentum-based-gd"]], "More complicated Example: The Ising model": [[48, "more-complicated-example-the-ising-model"]], "More interpretations": [[70, "more-interpretations"], [71, "more-interpretations"], [71, "id5"]], "More on Dimensionalities": [[45, "more-on-dimensionalities"]], "More on Rescaling data": [[48, "more-on-rescaling-data"]], "More on Steepest descent": [[71, "more-on-steepest-descent"]], "More on convex functions": [[71, "more-on-convex-functions"]], "More preprocessing": [[70, "more-preprocessing"], [72, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[72, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[54, "multilayer-perceptrons"]], "MyST markdown": [[24, "myst-markdown"]], "Network requirements": [[44, "network-requirements"]], "Neural Networks vs CNNs": [[45, "neural-networks-vs-cnns"]], "Neural networks": [[54, null]], "Non-Convex Problems": [[72, "non-convex-problems"]], "Note about SVD Calculations": [[70, "note-about-svd-calculations"], [71, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[71, "note-on-scikit-learn"]], "Notebooks with MyST Markdown": [[23, null]], "Numerical experiments and the covariance, central limit theorem": [[66, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[63, "numpy-and-arrays"], [69, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[69, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[71, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[55, null]], "Optimizing our parameters": [[69, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[69, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[43, "optimizing-the-cost-function"]], "Organizing our data": [[42, "organizing-our-data"], [69, "organizing-our-data"]], "Other Matrix and Vector Operations": [[63, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[46, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[69, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[69, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[69, "other-popular-texts"]], "Other techniques": [[53, "other-techniques"]], "Other types of networks": [[54, "other-types-of-networks"]], "Other ways of visualizing the trees": [[51, "other-ways-of-visualizing-the-trees"]], "Our Copyright Policy": [[20, "our-copyright-policy"]], "Our model for the nuclear binding energies": [[69, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[69, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[72, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[69, "own-code-for-ordinary-least-squares"], [70, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[53, "pca-and-scikit-learn"]], "Pandas AI": [[69, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[64, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[64, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[64, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[64, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[64, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[64, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[64, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[64, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[44, "partial-differential-equations"]], "Pitaya Smoothie": [[15, null]], "Plans for week 35": [[70, "plans-for-week-35"]], "Plans for week 36": [[71, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[72, "plans-for-week-37-lecture-monday"]], "Practical tips": [[55, "practical-tips"], [72, "practical-tips"]], "Practicalities": [[67, "practicalities"], [67, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[64, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[46, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[70, "preprocessing-our-data"]], "Prerequisites": [[69, "prerequisites"]], "Prerequisites and background": [[62, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[45, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[66, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[71, "program-example-for-gradient-descent-with-ridge-regression"], [72, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[55, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[64, null]], "Properties of PDFs": [[66, "properties-of-pdfs"]], "Pros and cons": [[72, "pros-and-cons"]], "Pros and cons of trees, pros": [[51, "pros-and-cons-of-trees-pros"]], "Python installers": [[62, "python-installers"], [69, "python-installers"]], "Quickly add YAML metadata for MyST Notebooks": [[23, "quickly-add-yaml-metadata-for-myst-notebooks"]], "RMS prop": [[55, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[72, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[72, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[72, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[66, "random-numbers"]], "Random forests": [[52, "random-forests"]], "Randomized PCA": [[53, "randomized-pca"]], "Reading material": [[69, "reading-material"]], "Reading recommendations:": [[70, "reading-recommendations"]], "Reading suggestions 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"reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[48, "reminder-on-statistics"]], "Reminder on different scaling methods": [[72, "reminder-on-different-scaling-methods"]], "Replace or not": [[55, "replace-or-not"], [72, "replace-or-not"]], "Required Technologies": [[62, "required-technologies"]], "Resampling Methods": [[48, null]], "Resampling and the Bias-Variance Trade-off": [[61, "resampling-and-the-bias-variance-trade-off"]], "Resampling methods": [[48, "id1"]], "Residual Error": [[70, "residual-error"], [71, "residual-error"]], "Resources on differential equations and deep learning": [[44, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[71, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[55, "revisiting-our-linear-regression-solvers"]], "Rewriting the Covariance and/or Correlation Matrix": [[70, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the fitting 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"simple-case"], [71, "simple-case"]], "Simple code for solving the above problem": [[71, "simple-code-for-solving-the-above-problem"]], "Simple example code": [[72, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[71, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[71, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[42, "simple-linear-regression-model-using-scikit-learn"], [69, "simple-linear-regression-model-using-scikit-learn"]], "Simple one-dimensional second-order polynomial": [[60, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[71, "simple-program"], [72, "simple-program"]], "Slightly different approach": [[72, "slightly-different-approach"]], "Sneaking in automatic differentiation using Autograd": [[72, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[64, "software-and-needed-installations"], [69, "software-and-needed-installations"]], "Solving Differential Equations with Deep Learning": [[44, null]], "Solving the one dimensional Poisson equation": [[44, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[44, "solving-the-wave-equation-with-neural-networks"]], "Some famous Matrices": [[63, "some-famous-matrices"]], "Some simple problems": [[55, "some-simple-problems"], [71, "some-simple-problems"]], "Some useful matrix and vector expressions": [[70, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[42, "splitting-our-data-in-training-and-test-data"], [70, "splitting-our-data-in-training-and-test-data"]], "Standard steepest descent": [[55, "standard-steepest-descent"]], "Statistical analysis and optimization of data": [[62, "statistical-analysis-and-optimization-of-data"], [69, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[55, "steepest-descent"], [71, "steepest-descent"]], "Stochastic Gradient Descent": [[72, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[55, "stochastic-gradient-descent-sgd"], [72, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[66, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[72, "strongly-convex-case"]], "Structure of translation files": [[39, "structure-of-translation-files"]], "Support Vector Machines, overarching aims": [[50, null]], "Systematic reduction": [[45, "systematic-reduction"]], "Teachers": [[69, "teachers"]], "Teachers and Grading": [[67, null]], "Teaching Assistants Fall semester 2023": [[67, "teaching-assistants-fall-semester-2023"]], "Tentative deadllines for projects": [[67, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of 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"the-ols-case"]], "The RELU function family": [[43, "the-relu-function-family"]], "The Ridge case": [[71, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[70, "the-svd-a-fantastic-algorithm"], [71, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[43, "the-softmax-function"]], "The \\chi^2 function": [[42, "the-chi-2-function"], [69, "the-chi-2-function"], [69, "id4"], [69, "id5"], [69, "id6"], [69, "id7"], [69, "id8"]], "The bias-variance tradeoff": [[48, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[44, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[70, "the-complete-code-with-a-simple-data-set"]], "The cost/loss function": [[70, "the-cost-loss-function"]], "The course has two central parts": [[62, "the-course-has-two-central-parts"]], "The derivative of the cost/loss function": [[71, "the-derivative-of-the-cost-loss-function"], [72, "the-derivative-of-the-cost-loss-function"]], "The equations": [[71, 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"zz": [63, 69], "\u00f8yvind": [48, 70, 72]}, "titles": ["A11Y Dark", "A11Y High Contrast Dark", "A11Y High Contrast Light", "A11Y Light", "Blinds Dark", "Blinds Light", "Github Dark", "Github Dark Colorblind", "Github Dark High Contrast", "Github Light", "Github Light Colorblind", "Github Light High Contrast", "Gotthard Dark", "Gotthard Light", "Greative", "Pitaya Smoothie", "<no title>", "<no title>", "<no title>", "The MIT License (MIT)", "The IPython licensing terms", "Welcome to your Jupyter Book", "Markdown Files", "Notebooks with MyST Markdown", "Content with notebooks", "<no title>", "<no title>", "markdown-it-container", "markdown-it-deflist", "markdown-it-texmath", "<no title>", "Authors", "<no title>", "<no title>", "<no title>", "License for Sphinx", "<no title>", "<no title>", "<no title>", "Translation workflow", "<no title>", "<no title>", "<span class=\"section-number\">3. </span>Linear Regression", "<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network", "<span class=\"section-number\">15. </span>Solving Differential Equations with Deep Learning", "<span class=\"section-number\">16. </span>Convolutional Neural Networks", "<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view", "<span class=\"section-number\">4. </span>Ridge and Lasso Regression", "<span class=\"section-number\">5. </span>Resampling Methods", "<span class=\"section-number\">6. </span>Logistic Regression", "<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims", "<span class=\"section-number\">9. </span>Decision trees, overarching aims", "<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods", "<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)", "<span class=\"section-number\">13. </span>Neural networks", "<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm", "<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning", "Exercises week 34", "Exercises week 35", "Exercises week 36", "Exercises week 37", "Exercises week 38", "Applied Data Analysis and Machine Learning", "<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features", "Project 1 on Machine Learning, deadline October 6 (midnight), 2025", "Course setting", "<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis", "Teachers and Grading", "Textbooks", "Week 34: Introduction to the course, Logistics and Practicalities", "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression", "Week 36: Linear Regression and Gradient descent", "Week 37: Gradient descent methods"], "titleterms": {"": [50, 52, 71, 72], "0": 29, "04": 29, "05": 29, "06": 29, "07": 29, "1": [42, 57, 58, 59, 60, 61, 64, 70], "11": 29, "15": [29, 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