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

Search.setIndex({"alltitles": {"A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [24, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[24, "a-first-summary"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"]], "ADAM optimizer": [[13, "adam-optimizer"]], "Activation functions": [[12, "activation-functions"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adding error analysis and training set up": [[24, "adding-error-analysis-and-training-set-up"], [25, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[24, "an-optimization-minimization-problem"]], "And a corresponding example using scikit-learn": [[26, "and-a-corresponding-example-using-scikit-learn"]], "And finally  \\boldsymbol{X}\\boldsymbol{X}^T": [[25, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And what about using neural networks?": [[24, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[26, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[18, null]], "Autocorrelation function": [[21, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[25, "back-to-ridge-and-lasso-regression"], [26, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[19, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [25, "basic-math-of-the-svd"], [26, "basic-math-of-the-svd"]], "Basics": [[7, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Batch Normalization": [[1, "batch-normalization"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[5, "bayes-theorem-and-ridge-and-lasso-regression"]], "Boosting, a Bird\u2019s Eye View": [[10, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[6, "bootstrap"]], "Bringing it together, first back propagation equation": [[12, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[1, null]], "Building a tree, regression": [[9, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[1, "building-neural-networks-in-tensorflow-and-keras"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Clustering and Unsupervised Learning": [[14, null]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [25, "codes-for-the-svd"], [26, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"]], "Communication channels": [[24, "communication-channels"]], "Compare  Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[26, "comparison-with-ols"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[26, "conditions-on-convex-functions"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convex function": [[26, "convex-function"]], "Convex functions": [[13, "convex-functions"], [26, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[25, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [25, "correlation-matrix"]], "Correlation Matrix with Pandas": [[25, "correlation-matrix-with-pandas"]], "Course Format": [[24, "course-format"]], "Course setting": [[20, null]], "Covariance Matrix Examples": [[25, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[25, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Deadlines for projects (tentative)": [[24, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep learning methods": [[24, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"]], "Defining the cost function": [[1, "defining-the-cost-function"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[25, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[25, "deriving-the-lasso-regression-equations"], [26, "deriving-the-lasso-regression-equations"], [26, "id6"]], "Deriving the  Ridge Regression Equations": [[25, "deriving-the-ridge-regression-equations"], [26, "deriving-the-ridge-regression-equations"], [26, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[24, "discriminative-modeling"]], "Domains and probabilities": [[21, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[25, "economy-size-svd"], [26, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[21, null]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[24, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[25, "example-2"]], "Example 3": [[25, "example-3"]], "Example 4": [[25, "example-4"]], "Example Matrix": [[25, "example-matrix"], [26, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[24, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[24, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[25, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[25, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"]], "Examples": [[24, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Expectation values": [[21, "expectation-values"]], "Extending to more than one variable": [[26, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[24, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[25, "fixing-the-singularity"], [26, "fixing-the-singularity"]], "Frequently used scaling functions": [[25, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[26, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Functionality in Scikit-Learn": [[25, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [25, "further-properties-important-for-our-analyses-later"], [26, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[19, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[24, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[24, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [24, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[24, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"]], "Gradient Descent Example": [[26, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[26, "gradient-descent-and-ridge"]], "Gradient descent example": [[26, "gradient-descent-example"]], "Grading": [[22, "grading"], [22, "id2"], [24, "grading"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Important Matrix and vector handling packages": [[19, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[25, "important-technicalities-more-on-rescaling-data"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[22, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"]], "Incremental PCA": [[11, "incremental-pca"]], "Installing R, C++, cython or Julia": [[24, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[24, "installing-r-c-cython-numba-etc"]], "Instructor information": [[22, "instructor-information"]], "Interpretations and optimizing our parameters": [[24, "interpretations-and-optimizing-our-parameters"], [24, "id2"], [24, "id3"], [25, "interpretations-and-optimizing-our-parameters"], [25, "id1"], [25, "id2"]], "Interpreting the Ridge results": [[25, "interpreting-the-ridge-results"], [26, "interpreting-the-ridge-results"], [26, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [25, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [18, "introduction"], [19, "introduction"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[19, "lu-decomposition-the-inverse-of-a-matrix"]], "Lasso Regression": [[26, "lasso-regression"]], "Lasso case": [[26, "lasso-case"]], "Layers": [[1, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"]], "Learning outcomes": [[18, "learning-outcomes"], [24, "learning-outcomes"]], "Lectures and ComputerLab": [[24, "lectures-and-computerlab"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[19, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[25, "linear-regression-problems"], [26, "linear-regression-problems"]], "Linear Regression and  the SVD": [[26, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [25, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[23, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[24, "machine-learning"]], "Machine learning": [[18, "machine-learning"]], "Main textbooks": [[24, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[25, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[25, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[26, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[26, "material-for-lecture-monday-september-2"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [25, "mathematical-interpretation-of-ordinary-least-squares"], [26, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [25, "mathematics-of-the-svd-and-implications"], [26, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[24, "matrices-in-python"]], "Matrix  multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation  and activation": [[12, "matrix-vector-notation-and-activation"]], "Meet the  covariance!": [[21, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [25, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[25, "meet-the-hessian-matrix"]], "Meet the Pandas": [[24, "meet-the-pandas"]], "Min-Max Scaling": [[25, "min-max-scaling"]], "Momentum based GD": [[13, "momentum-based-gd"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More interpretations": [[25, "more-interpretations"], [26, "more-interpretations"], [26, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[26, "more-on-steepest-descent"]], "More on convex functions": [[26, "more-on-convex-functions"]], "More preprocessing": [[25, "more-preprocessing"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Note about SVD Calculations": [[25, "note-about-svd-calculations"], [26, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[26, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[21, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[19, "numpy-and-arrays"], [24, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[24, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[26, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null]], "Optimizing our parameters": [[24, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[24, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [24, "organizing-our-data"]], "Other Matrix and Vector Operations": [[19, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[24, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[24, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[24, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[24, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[24, "overview-of-first-week"]], "Own code for Ordinary Least Squares": [[24, "own-code-for-ordinary-least-squares"], [25, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[24, "pandas-ai"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plans for week 35": [[25, "plans-for-week-35"]], "Plans for week 36": [[26, "plans-for-week-36"]], "Practical tips": [[13, "practical-tips"]], "Practicalities": [[22, "practicalities"], [22, "id1"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[25, "preprocessing-our-data"]], "Prerequisites": [[24, "prerequisites"]], "Prerequisites and background": [[18, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[21, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[26, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Properties of PDFs": [[21, "properties-of-pdfs"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[18, "python-installers"], [24, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "Random Numbers": [[21, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[24, "reading-material"]], "Reading recommendations:": [[25, "reading-recommendations"]], "Reading suggestions week 34": [[24, "reading-suggestions-week-34"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [25, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis, overarching aims": [[24, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[24, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"]], "Reminder from last week": [[25, "reminder-from-last-week"]], 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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 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