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

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"colors"], [15, "colors"]], "Communication channels": [[72, "communication-channels"]], "Compare  Bagging on Trees with Random Forests": [[54, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[46, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[74, "comparison-with-ols"]], "Compiled translation files": [[41, "compiled-translation-files"]], "Components": [[31, "components"]], "Computation of gradients": [[75, "computation-of-gradients"]], "Computing the Gini index": [[53, "computing-the-gini-index"]], "Conditions on convex functions": [[74, "conditions-on-convex-functions"]], "Confidence Intervals": [[76, "confidence-intervals"]], "Conjugate gradient method": [[57, "conjugate-gradient-method"]], "Content with notebooks": [[24, null]], "Contents": [[30, "contents"]], "Contributors": [[33, "contributors"]], "Convergence rates": [[75, "convergence-rates"]], "Convex function": [[74, "convex-function"]], "Convex functions": [[57, 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"Deriving OLS from a probability distribution": [[49, "deriving-ols-from-a-probability-distribution"], [76, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[60, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[61, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[73, "deriving-the-lasso-regression-equations"], [74, "deriving-the-lasso-regression-equations"], [74, "id6"]], "Deriving the  Ridge Regression Equations": [[73, "deriving-the-ridge-regression-equations"], [74, "deriving-the-ridge-regression-equations"], [74, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[56, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[45, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[55, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[52, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[53, "disadvantages"]], "Discriminative Modeling": [[72, "discriminative-modeling"]], "Domains and probabilities": [[69, "domains-and-probabilities"]], "Dropout": [[45, "dropout"]], "Economy-size SVD": [[73, "economy-size-svd"], [74, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[69, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[75, "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": [[54, null]], "Entropy and the ID3 algorithm": [[53, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[72, "essential-elements-of-ml"]], "Evaluate 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growth": [[46, "example-population-growth"]], "Example: The diffusion equation": [[46, "example-the-diffusion-equation"]], "Example: binary classification problem": [[45, "example-binary-classification-problem"]], "Examples": [[72, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[51, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[61, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[60, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[59, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[62, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[64, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[63, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Setting up various Python environments": [[44, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[60, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[61, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[59, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[62, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[64, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[63, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: making your own data and exploring scikit-learn": [[44, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[60, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[59, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[61, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[59, "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}": [[62, "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": [[63, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[44, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[64, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Fitting a polynomial": [[60, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[61, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[61, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[59, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[62, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[44, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[63, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[64, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[60, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[62, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[44, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[63, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[64, "exercise-5-referencing"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[50, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[50, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[50, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[50, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[50, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[50, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[44, "exercises"]], "Exercises and Projects": [[50, "exercises-and-projects"]], "Exercises week 34": [[59, null]], "Exercises week 35": [[60, null]], "Exercises week 36": [[61, null]], "Exercises week 37": [[62, null]], "Exercises week 38": [[63, null]], "Exercises week 39": [[64, null]], "Expectation value and variance": [[76, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[76, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[69, "expectation-values"]], "Extending to more than one variable": [[74, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[72, "extremely-useful-tools-strongly-recommended"]], "FAQ": [[29, "faq"]], "Features": [[29, "features"]], "Feed-forward neural networks": [[56, "feed-forward-neural-networks"]], "Feed-forward 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link with Singular Value Decomposition": [[55, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting started with project 1": [[64, "getting-started-with-project-1"]], "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": [[54, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[54, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[45, "gradient-clipping"]], "Gradient Descent Example": [[74, "id1"], [75, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[54, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[46, "gradient-descent"]], "Gradient descent and Ridge": [[74, "gradient-descent-and-ridge"], [75, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[75, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[74, "gradient-descent-example"], [75, "gradient-descent-example"]], "Grading": [[70, "grading"], [70, "id2"], [72, "grading"]], "Greative": [[14, null]], "History": [[30, "history"]], "How to take derivatives of Matrix-Vector expressions": [[60, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[52, "hyperplanes-and-all-that"]], "Identifying Terms": [[76, "identifying-terms"]], "Important Matrix and vector handling packages": [[66, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[73, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[75, "improving-gradient-descent-with-momentum"]], "Improving performance": [[45, "improving-performance"]], "In summary": [[70, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[57, "including-stochastic-gradient-descent-with-autograd"], [75, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[55, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[76, "independent-and-identically-distributed-iid"]], "Install": [[28, "install"]], "Installation": [[27, "installation"]], "Installing R, C++, cython or Julia": [[72, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[72, "installing-r-c-cython-numba-etc"]], "Instructor information": [[70, "instructor-information"]], "Interpretations and optimizing our parameters": [[72, "interpretations-and-optimizing-our-parameters"], [72, "id2"], [72, "id3"], [73, "interpretations-and-optimizing-our-parameters"], [73, "id1"], [73, "id2"]], "Interpreting the Ridge results": [[73, "interpreting-the-ridge-results"], [74, "interpreting-the-ridge-results"], [74, "id4"]], "Introducing JAX": [[57, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[55, "introducing-the-covariance-and-correlation-functions"], [73, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[44, "introduction"], [50, "introduction"], [65, "introduction"], [66, "introduction"]], "Introduction to numerical projects": [[67, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[54, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[54, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[55, "kernel-pca"]], "Kernels and non-linearity": [[52, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[66, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[74, "lasso-regression"]], "Lasso case": [[74, "lasso-case"]], "Layers": [[45, "layers"]], "Layers used to build CNNs": [[47, "layers-used-to-build-cnns"]], "Learn more": [[22, "learn-more"]], "Learning goals": [[59, "learning-goals"], [60, "learning-goals"], [61, "learning-goals"], [62, "learning-goals"], [63, "learning-goals"], [64, "learning-goals"]], "Learning outcomes": [[65, "learning-outcomes"], [72, "learning-outcomes"]], "Lectures and ComputerLab": [[72, "lectures-and-computerlab"]], "License": [[27, "license"], [28, "license"], [29, "license"]], "License for Sphinx": [[37, null]], "Licenses for incorporated software": [[37, "licenses-for-incorporated-software"]], "Limitations of supervised learning with deep networks": [[45, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[66, null]], "Linear Regression": [[44, null]], "Linear Regression Problems": [[73, "linear-regression-problems"], [74, "linear-regression-problems"]], "Linear Regression and  the SVD": [[74, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[44, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[49, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[49, "linking-the-regression-analysis-with-a-statistical-interpretation"], [76, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[49, "linking-with-the-svd"], [73, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[71, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[51, null], [51, "id1"]], "MNIST and GANs": [[48, "mnist-and-gans"]], "Machine Learning": [[72, "machine-learning"]], "Machine learning": [[65, "machine-learning"]], "Main differences": [[30, "main-differences"]], "Main textbooks": [[72, "main-textbooks"]], "Making a tree": [[53, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[54, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[73, "making-your-own-test-train-splitting"]], "Markdown + notebooks": [[24, "markdown-notebooks"]], "Markdown Files": [[22, null]], "Masked records": [[30, "masked-records"]], "Material for exercises week 35": [[73, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[74, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[74, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[75, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[75, "material-for-the-lab-sessions"], [76, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[49, "mathematical-interpretation-of-ordinary-least-squares"], [73, "mathematical-interpretation-of-ordinary-least-squares"], [74, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[52, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[47, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[49, "mathematics-of-the-svd-and-implications"], [73, "mathematics-of-the-svd-and-implications"], [74, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[72, "matrices-in-python"]], "Matrix  multiplication": [[45, "matrix-multiplication"]], "Matrix-vector notation  and activation": [[56, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[76, "maximum-likelihood-estimation-mle"]], "Meet the  covariance!": [[69, "meet-the-covariance"]], "Meet the Covariance Matrix": [[49, "meet-the-covariance-matrix"], [73, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[73, "meet-the-hessian-matrix"]], "Meet the Pandas": [[72, "meet-the-pandas"]], "Memory Usage and Scalability": [[75, "memory-usage-and-scalability"]], "Memory constraints": [[75, "memory-constraints"]], "Min-Max Scaling": [[73, "min-max-scaling"]], "Momentum based GD": [[57, "momentum-based-gd"], [75, "momentum-based-gd"]], "More complicated Example: The Ising model": [[50, "more-complicated-example-the-ising-model"]], "More examples on bootstrap and cross-validation and errors": [[76, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[73, "more-interpretations"], [74, "more-interpretations"], [74, "id5"]], "More on Dimensionalities": [[47, "more-on-dimensionalities"]], "More on Rescaling data": [[50, "more-on-rescaling-data"]], "More on Steepest descent": [[74, "more-on-steepest-descent"]], "More on convex functions": [[74, "more-on-convex-functions"]], "More preprocessing": [[73, "more-preprocessing"], [75, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[75, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[56, "multilayer-perceptrons"]], "MyST markdown": [[24, "myst-markdown"]], "NCSA Open Source License": [[31, null]], "Network requirements": [[46, "network-requirements"]], "Neural Networks vs CNNs": [[47, "neural-networks-vs-cnns"]], "Neural networks": [[56, null]], "New features": [[30, "new-features"]], "Non-Convex Problems": [[75, "non-convex-problems"]], "Note about SVD Calculations": [[73, "note-about-svd-calculations"], [74, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[74, "note-on-scikit-learn"]], "Notebooks with MyST Markdown": [[23, null]], "Numerical experiments and the covariance, central limit theorem": [[69, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[66, "numpy-and-arrays"], [72, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[72, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[74, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[57, null]], "Optimizing maskedarray": [[30, "optimizing-maskedarray"]], "Optimizing our parameters": [[72, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[72, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[45, "optimizing-the-cost-function"]], "Organizing our data": [[44, "organizing-our-data"], [72, "organizing-our-data"]], "Other Matrix and Vector Operations": [[66, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[48, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[72, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[72, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[72, "other-popular-texts"]], "Other techniques": [[55, "other-techniques"]], "Other types of networks": [[56, "other-types-of-networks"]], "Other ways of visualizing the trees": [[53, "other-ways-of-visualizing-the-trees"]], "Our Copyright Policy": [[20, "our-copyright-policy"]], "Our model for the nuclear binding energies": [[72, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[72, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[75, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[72, "own-code-for-ordinary-least-squares"], [73, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[55, "pca-and-scikit-learn"]], "Pandas AI": [[72, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[67, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[67, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[67, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[67, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[67, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[67, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[67, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[67, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[46, "partial-differential-equations"]], "Pitaya Smoothie": [[15, null]], "Plans for week 35": [[73, "plans-for-week-35"]], "Plans for week 36": [[74, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[75, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[76, "plans-for-week-38-lecture-monday-september-15"]], "Plotting the Histogram": [[76, "plotting-the-histogram"]], "Practical tips": [[57, "practical-tips"], [75, "practical-tips"]], "Practicalities": [[70, "practicalities"], [70, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[67, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[48, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[73, "preprocessing-our-data"]], "Prerequisites": [[72, "prerequisites"]], "Prerequisites and background": [[65, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[47, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[69, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[74, "program-example-for-gradient-descent-with-ridge-regression"], [75, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[57, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[67, null]], "Properties of PDFs": [[69, "properties-of-pdfs"]], "Pros and cons": [[75, "pros-and-cons"]], "Pros and cons of trees, pros": [[53, "pros-and-cons-of-trees-pros"]], "Python installers": [[65, "python-installers"], [72, "python-installers"]], "Quickly add YAML metadata for MyST Notebooks": [[23, "quickly-add-yaml-metadata-for-myst-notebooks"]], "RMS prop": [[57, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[75, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[75, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[75, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[69, "random-numbers"]], "Random forests": [[54, "random-forests"]], "Randomized PCA": [[55, "randomized-pca"]], "Reading material": [[72, "reading-material"]], "Reading recommendations:": [[73, "reading-recommendations"]], "Reading suggestions week 34": [[72, "reading-suggestions-week-34"]], "Readings and Videos": [[76, "readings-and-videos"]], "Readings and Videos:": [[75, "readings-and-videos"]], "Recurrent neural networks": [[56, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[48, null]], "Reducing the number of degrees of freedom, overarching view": [[44, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [73, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[46, "reformulating-the-problem"]], "Regression Case": [[54, "regression-case"]], "Regression analysis and resampling methods": [[67, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[72, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[72, "regression-analysis-overarching-aims-ii"]], "Regularization": [[45, "regularization"]], "Reminder from last week": [[73, "reminder-from-last-week"]], "Reminder on Newton-Raphson\u2019s method": [[74, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[50, "reminder-on-statistics"]], "Reminder on different scaling methods": [[75, "reminder-on-different-scaling-methods"]], "Replace or not": [[57, "replace-or-not"], [75, "replace-or-not"]], "Required Technologies": [[65, "required-technologies"]], "Resampling Methods": [[50, null]], "Resampling and the Bias-Variance Trade-off": [[63, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[76, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[50, "id1"], [76, "resampling-methods"], [76, "id2"]], "Resampling methods: Bootstrap": [[76, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[76, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[76, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[76, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[76, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[73, "residual-error"], [74, "residual-error"]], "Resources on differential equations and deep learning": [[46, "resources-on-differential-equations-and-deep-learning"]], "Revision notes": [[30, "revision-notes"]], "Revisiting Ordinary Least Squares": [[74, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[57, "revisiting-our-linear-regression-solvers"]], "Rewriting the Covariance and/or Correlation Matrix": [[73, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[76, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[72, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[72, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[74, "ridge-regression"]], "Ridge and LASSO Regression": [[73, "ridge-and-lasso-regression"], [74, "ridge-and-lasso-regression"], [74, "id2"]], "Ridge and Lasso Regression": [[49, null], [49, "id1"]], "SGD example": [[75, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[75, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[74, "svd-analysis"]], "Same code but now with momentum gradient descent": [[57, "same-code-but-now-with-momentum-gradient-descent"], [75, "same-code-but-now-with-momentum-gradient-descent"], [75, "id3"], [75, "id4"]], "Sample Roles and Directives": [[22, "sample-roles-and-directives"]], "Schedule first week": [[72, "schedule-first-week"]], "Schematic Regression Procedure": [[53, "schematic-regression-procedure"]], "Second moment of the gradient": [[75, "second-moment-of-the-gradient"]], "September 15-19": [[63, "september-15-19"]], "Setting up the Back propagation algorithm": [[56, "setting-up-the-back-propagation-algorithm"]], "Setting up the Matrix to be inverted": [[73, "setting-up-the-matrix-to-be-inverted"], [74, "setting-up-the-matrix-to-be-inverted"]], "Setting up the network using Autograd; The full program": [[46, "setting-up-the-network-using-autograd-the-full-program"]], "Should masked arrays be filled before processing or not?": [[30, "should-masked-arrays-be-filled-before-processing-or-not"]], "Show me": [[29, "show-me"]], "Similar (second order function now) problem but now with AdaGrad": [[57, "similar-second-order-function-now-problem-but-now-with-adagrad"], [75, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[53, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[73, "simple-case"], [74, "simple-case"]], "Simple code for solving the above problem": [[74, "simple-code-for-solving-the-above-problem"]], "Simple example code": [[75, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[74, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric 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"solving-the-wave-equation-with-neural-networks"]], "Some famous Matrices": [[66, "some-famous-matrices"]], "Some simple problems": [[57, "some-simple-problems"], [74, "some-simple-problems"]], "Some useful matrix and vector expressions": [[73, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[44, "splitting-our-data-in-training-and-test-data"], [73, "splitting-our-data-in-training-and-test-data"]], "Standard Approach based on the Normal Distribution": [[76, "standard-approach-based-on-the-normal-distribution"]], "Standard steepest descent": [[57, "standard-steepest-descent"]], "Statistical analysis": [[76, "statistical-analysis"]], "Statistical analysis and optimization of data": [[65, "statistical-analysis-and-optimization-of-data"], [72, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[57, "steepest-descent"], [74, "steepest-descent"]], "Stochastic Gradient Descent": [[75, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[57, "stochastic-gradient-descent-sgd"], [75, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[69, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[75, "strongly-convex-case"]], "Structure of translation files": [[41, "structure-of-translation-files"]], "Summing up": [[76, "summing-up"]], "Support Vector Machines, overarching aims": [[52, null]], "Systematic reduction": [[47, "systematic-reduction"]], "Teachers": [[72, "teachers"]], "Teachers and Grading": [[70, null]], "Teaching Assistants Fall semester 2023": [[70, "teaching-assistants-fall-semester-2023"]], "Tentative deadllines for projects": [[70, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[44, "testing-the-means-squared-error-as-function-of-complexity"], [73, "testing-the-means-squared-error-as-function-of-complexity"]], "Textbooks": [[71, null]], "Thanks": [[30, "thanks"]], "The Algorithm before theorem": [[55, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[45, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[53, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[53, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[47, "the-cifar01-data-set"]], "The Central Limit Theorem": [[76, "the-central-limit-theorem"]], "The Hessian matrix": [[74, "the-hessian-matrix"], [75, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[74, "the-hessian-matrix-for-ridge-regression"], [75, "the-hessian-matrix-for-ridge-regression"]], "The IPython licensing terms": [[20, null]], "The Jacobian": [[73, "the-jacobian"]], "The MIT License (MIT)": [[19, null]], "The MNIST dataset again": [[47, "the-mnist-dataset-again"]], "The OLS case": [[74, "the-ols-case"]], "The RELU function family": [[45, "the-relu-function-family"]], "The Ridge case": [[74, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[73, "the-svd-a-fantastic-algorithm"], [74, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[45, "the-softmax-function"]], "The \\chi^2 function": [[44, "the-chi-2-function"], [72, "the-chi-2-function"], [72, "id4"], [72, "id5"], [72, "id6"], [72, "id7"], [72, "id8"]], "The bias-variance tradeoff": [[50, "the-bias-variance-tradeoff"], [76, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[46, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[73, "the-complete-code-with-a-simple-data-set"]], "The cost/loss function": [[73, "the-cost-loss-function"]], "The course has two central parts": [[65, "the-course-has-two-central-parts"]], "The derivative of the cost/loss function": [[74, "the-derivative-of-the-cost-loss-function"], [75, "the-derivative-of-the-cost-loss-function"]], "The equations": [[74, "the-equations"]], "The equations for ordinary least squares": [[73, "the-equations-for-ordinary-least-squares"]], "The first Case": [[74, "the-first-case"]], "The gradient step": [[75, "the-gradient-step"]], "The ideal": [[74, "the-ideal"]], "The logistic function": [[51, "the-logistic-function"]], "The mean squared error and its derivative": [[73, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[52, "the-moons-example"]], "The multilayer  perceptron (MLP)": [[56, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[46, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The plethora  of machine learning algorithms/methods": [[72, "the-plethora-of-machine-learning-algorithms-methods"]], "The same example but now with cross-validation": [[76, "the-same-example-but-now-with-cross-validation"]], "The sensitiveness of the gradient descent": [[74, 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