FYS-STK4155/doc/LectureNotes/_build/html/searchindex.js

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"adam-optimizer"], [73, "id2"]], "API": [[27, "api"]], "About the IPython Development Team": [[20, "about-the-ipython-development-team"]], "Accuracy": [[73, "accuracy"]], "Activation functions": [[54, "activation-functions"]], "AdaGrad Properties": [[73, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[73, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[73, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[73, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[73, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[73, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[73, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[73, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[52, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[73, "adaptivity-across-dimensions"]], "Adding error analysis 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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": [[73, "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": [[73, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[56, "codes-and-approaches"]], "Codes for the SVD": [[47, "codes-for-the-svd"], [71, "codes-for-the-svd"], [72, "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": [[70, "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": [[72, "comparison-with-ols"]], "Compiled translation files": [[39, "compiled-translation-files"]], "Computation of gradients": [[73, "computation-of-gradients"]], "Computing the Gini index": [[51, "computing-the-gini-index"]], "Conditions on convex functions": [[72, "conditions-on-convex-functions"]], "Conjugate gradient 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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": [[70, "discriminative-modeling"]], "Domains and probabilities": [[67, "domains-and-probabilities"]], "Dropout": [[43, "dropout"]], "Economy-size SVD": [[71, "economy-size-svd"], [72, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[67, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[73, "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": [[70, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[43, "evaluate-model-performance-on-test-data"]], "Example": [[27, "example"]], "Example 2": [[71, "example-2"]], "Example 3": [[71, "example-3"]], "Example 4": [[71, "example-4"]], "Example Matrix": [[71, "example-matrix"], [72, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[70, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[70, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[71, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[71, "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": [[70, "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: Creating the report document": [[62, "exercise-1-creating-the-report-document"]], "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: Adding good figures": [[62, "exercise-2-adding-good-figures"]], "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 3: Writing an abstract and introduction": [[62, "exercise-3-writing-an-abstract-and-introduction"]], "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 4: Making the code available and presentable": [[62, "exercise-4-making-the-code-available-and-presentable"]], "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 5: Referencing": [[62, "exercise-5-referencing"]], "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"]], 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"gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[72, "gradient-descent-example"], [73, "gradient-descent-example"]], "Grading": [[68, "grading"], [68, "id2"], [70, "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": [[64, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[71, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[73, "improving-gradient-descent-with-momentum"]], "Improving performance": [[43, "improving-performance"]], "In summary": [[68, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[55, "including-stochastic-gradient-descent-with-autograd"], [73, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[53, "incremental-pca"]], "Install": [[28, "install"]], "Installation": [[27, "installation"]], "Installing R, C++, cython or Julia": [[70, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[70, "installing-r-c-cython-numba-etc"]], "Instructor information": [[68, "instructor-information"]], "Interpretations and optimizing our parameters": [[70, "interpretations-and-optimizing-our-parameters"], [70, "id2"], [70, "id3"], [71, "interpretations-and-optimizing-our-parameters"], [71, "id1"], [71, "id2"]], "Interpreting the Ridge results": [[71, "interpreting-the-ridge-results"], [72, "interpreting-the-ridge-results"], [72, "id4"]], "Introducing JAX": [[55, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[53, "introducing-the-covariance-and-correlation-functions"], [71, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[42, "introduction"], [48, "introduction"], [63, "introduction"], [64, "introduction"]], "Introduction to numerical projects": [[65, "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": [[64, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[72, "lasso-regression"]], "Lasso case": [[72, "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"], [62, "learning-goals"]], "Learning 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"matrices-in-python"]], "Matrix  multiplication": [[43, "matrix-multiplication"]], "Matrix-vector notation  and activation": [[54, "matrix-vector-notation-and-activation"]], "Meet the  covariance!": [[67, "meet-the-covariance"]], "Meet the Covariance Matrix": [[47, "meet-the-covariance-matrix"], [71, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[71, "meet-the-hessian-matrix"]], "Meet the Pandas": [[70, "meet-the-pandas"]], "Memory Usage and Scalability": [[73, "memory-usage-and-scalability"]], "Memory constraints": [[73, "memory-constraints"]], "Min-Max Scaling": [[71, "min-max-scaling"]], "Momentum based GD": [[55, "momentum-based-gd"], [73, "momentum-based-gd"]], "More complicated Example: The Ising model": [[48, "more-complicated-example-the-ising-model"]], "More interpretations": [[71, "more-interpretations"], [72, "more-interpretations"], [72, "id5"]], "More on Dimensionalities": [[45, "more-on-dimensionalities"]], "More on Rescaling data": [[48, "more-on-rescaling-data"]], "More on Steepest descent": [[72, "more-on-steepest-descent"]], "More on convex functions": [[72, "more-on-convex-functions"]], "More preprocessing": [[71, "more-preprocessing"], [73, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[73, "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": [[73, "non-convex-problems"]], "Note about SVD Calculations": [[71, "note-about-svd-calculations"], [72, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[72, "note-on-scikit-learn"]], "Notebooks with MyST Markdown": [[23, null]], "Numerical experiments and the covariance, central limit theorem": [[67, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[64, "numpy-and-arrays"], [70, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[70, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[72, "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": [[70, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[70, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[43, "optimizing-the-cost-function"]], "Organizing our data": [[42, "organizing-our-data"], [70, "organizing-our-data"]], "Other Matrix and Vector Operations": [[64, "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": [[70, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[70, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[70, "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": [[70, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[70, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[73, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[70, "own-code-for-ordinary-least-squares"], [71, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[53, "pca-and-scikit-learn"]], "Pandas AI": [[70, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[65, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for  the Runge  function": [[65, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[65, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[65, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[65, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[65, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[65, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h):  Cross-validation as resampling techniques, adding more 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"some-simple-problems"], [72, "some-simple-problems"]], "Some useful matrix and vector expressions": [[71, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[42, "splitting-our-data-in-training-and-test-data"], [71, "splitting-our-data-in-training-and-test-data"]], "Standard steepest descent": [[55, "standard-steepest-descent"]], "Statistical analysis and optimization of data": [[63, "statistical-analysis-and-optimization-of-data"], [70, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[55, "steepest-descent"], [72, "steepest-descent"]], "Stochastic Gradient Descent": [[73, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[55, "stochastic-gradient-descent-sgd"], [73, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[67, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[73, "strongly-convex-case"]], 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49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 64, 65, 67, 70, 71, 72, 73], "zeros_lik": 46, "zeroth": 71, "zfill": 46, "zip": [46, 48], "zm_h": [42, 70], "zn": [], "zone": [], "zoom": 70, "zscout": 20, "zx": [64, 70], "zy": [64, 70], "zz": [64, 70], "\u00f8yvind": [48, 71, 73]}, "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", "&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "The MIT License (MIT)", "The IPython licensing terms", "Welcome to your Jupyter Book", "Markdown Files", "Notebooks with MyST Markdown", "Content with notebooks", "&lt;no title&gt;", "&lt;no title&gt;", "markdown-it-container", "markdown-it-deflist", "markdown-it-texmath", "&lt;no title&gt;", "Authors", "&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "License for Sphinx", "&lt;no title&gt;", "&lt;no title&gt;", "&lt;no title&gt;", "Translation workflow", "&lt;no title&gt;", "&lt;no title&gt;", "<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", "Exercises week 39", "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 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