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zX-j?&QVt})&#(VRuSG?+I}O6{yP)6B#Oyu{4e>+{lM1+|q8Zl$HRA$Aal0>y4)Ay$ z`*@^Ni{cNH=Rw%#(Ufe|>B3+VdKyAu* z^zpi`V_mYC9YVwDW3eO2*~l%~L@#skf>X9;yq!+Yr`OUltwqjCte4fJJE$J$sv zBA`db$;WaIkky~eXZkT&NoTQm8N^B>xg1%Se4h_uMm>@|mp)(Uwo{c8)pV*;rMX;u zD8}oEWMV3Qx-^|g1KC^xm8me)2PJbbo5Ro7l;$Y~P%soGH^_}*7NAJpM0m`>x1NUBX2kp>If$1#Mh;my+&UMU;j+5u`YEFL3DY5w;Z|o_?SCegS yJY~s9ElS;Nd~-G\n", "contain more information. There you can find examples of previous\n", - "reports, the projects themselves, how we rade reports etc. How to\n", + "reports, the projects themselves, how we grade reports etc. How to\n", "write reports will also be discussed during the various lab\n", "sessions. Please do ask us if you are in doubt.\n", "\n", @@ -532,7 +532,7 @@ "\n", "1. For a discussion and derivation of the variances and mean squared errors using linear regression, see the [Lecture notes on ridge regression by Wessel N. van Wieringen](https://arxiv.org/abs/1509.09169)\n", "\n", - "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis here." + "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis of parts g) and h)." ] }, { @@ -635,7 +635,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/project1.html b/doc/LectureNotes/_build/html/project1.html index a58f39dd7..44d08f6bb 100644 --- a/doc/LectureNotes/_build/html/project1.html +++ b/doc/LectureNotes/_build/html/project1.html @@ -421,7 +421,7 @@ reports written like a standard scientific/technical report. The links at CompPhysics/MachineLearning contain more information. There you can find examples of previous -reports, the projects themselves, how we rade reports etc. How to +reports, the projects themselves, how we grade reports etc. How to write reports will also be discussed during the various lab sessions. Please do ask us if you are in doubt.

When using codes and material from other sources, you should refer to @@ -651,7 +651,7 @@ include both Ridge and Lasso regression in the final analysis.

Background literature#

  1. For a discussion and derivation of the variances and mean squared errors using linear regression, see the Lecture notes on ridge regression by Wessel N. van Wieringen

    2. -

  2. The textbook of Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer, chapters 3 and 7 are the most relevant ones for the analysis here.

    3. +

  3. The textbook of Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer, chapters 3 and 7 are the most relevant ones for the analysis of parts g) and h).

diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js index 1fe533d3d..1ad914449 100644 --- a/doc/LectureNotes/_build/html/searchindex.js +++ b/doc/LectureNotes/_build/html/searchindex.js @@ -1 +1 @@ -Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [26, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[26, "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": [[26, "adding-error-analysis-and-training-set-up"], [27, "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": [[26, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[27, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And what about using neural networks?": [[26, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[28, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[19, null]], "Autocorrelation function": [[23, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[27, "back-to-ridge-and-lasso-regression"], [28, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[21, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[20, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [27, "basic-math-of-the-svd"], [28, "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 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"Cross-validation": [[6, "cross-validation"]], "Deadlines for projects (tentative)": [[26, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep learning methods": [[26, "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": [[27, "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": [[27, "deriving-the-lasso-regression-equations"], [28, 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"economy-size-svd"], [28, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[23, 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": [[26, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[27, "example-2"]], "Example 3": [[27, "example-3"]], "Example 4": [[27, "example-4"]], "Example Matrix": [[27, "example-matrix"], [28, "example-matrix"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[26, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[26, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[27, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[27, "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": [[26, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: 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, use the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-use-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Expectation values": [[23, "expectation-values"]], "Extending to more than one variable": [[28, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[26, "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": [[27, "fixing-the-singularity"], [28, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[21, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[27, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[28, "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": [[27, "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"], [27, "further-properties-important-for-our-analyses-later"], [28, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[20, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[26, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[26, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [26, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[26, "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": [[28, "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": [[28, "gradient-descent-and-ridge"]], "Gradient descent example": [[28, "gradient-descent-example"]], "Grading": [[24, "grading"], [24, "id2"], [26, "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": [[20, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[27, "important-technicalities-more-on-rescaling-data"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[24, "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": [[26, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[26, "installing-r-c-cython-numba-etc"]], "Instructor information": [[24, "instructor-information"]], "Interpretations and optimizing our parameters": [[26, "interpretations-and-optimizing-our-parameters"], [26, "id2"], [26, "id3"], [27, "interpretations-and-optimizing-our-parameters"], [27, "id1"], [27, "id2"]], "Interpreting the Ridge results": [[27, "interpreting-the-ridge-results"], [28, "interpreting-the-ridge-results"], [28, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, 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[27, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[25, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[26, "machine-learning"]], "Machine learning": [[19, "machine-learning"]], "Main textbooks": [[26, "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": [[27, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[27, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[28, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[28, "material-for-lecture-monday-september-2"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [27, "mathematical-interpretation-of-ordinary-least-squares"], [28, "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"], [27, "mathematics-of-the-svd-and-implications"], [28, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[26, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Meet the covariance!": [[23, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [27, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[27, "meet-the-hessian-matrix"]], "Meet the Pandas": [[26, "meet-the-pandas"]], "Min-Max Scaling": [[27, "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": [[27, "more-interpretations"], [28, "more-interpretations"], [28, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[28, "more-on-steepest-descent"]], "More on convex functions": [[28, "more-on-convex-functions"]], "More preprocessing": [[27, "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": [[27, "note-about-svd-calculations"], [28, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[28, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[23, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[20, "numpy-and-arrays"], [26, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[26, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[28, "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": [[26, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[26, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [26, "organizing-our-data"]], "Other Matrix and Vector Operations": [[20, "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": [[26, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[26, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[26, "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": [[26, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[26, "overview-of-first-week"]], "Own code for Ordinary Least Squares": [[26, "own-code-for-ordinary-least-squares"], [27, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, 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"a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[26, "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": [[26, "adding-error-analysis-and-training-set-up"], [27, "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": [[26, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[27, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And what about using neural networks?": [[26, "and-what-about-using-neural-networks"]], "Another Example, now with a polynomial fit": [[28, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[19, null]], "Autocorrelation function": [[23, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[27, "back-to-ridge-and-lasso-regression"], [28, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[21, "background-literature"]], 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"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"], [27, "codes-for-the-svd"], [28, "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": [[26, "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": [[28, "comparison-with-ols"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[28, "conditions-on-convex-functions"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convex function": [[28, "convex-function"]], "Convex functions": [[13, "convex-functions"], [28, "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, 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"derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[27, "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": [[27, "deriving-the-lasso-regression-equations"], [28, "deriving-the-lasso-regression-equations"], [28, "id6"]], "Deriving the Ridge Regression Equations": [[27, "deriving-the-ridge-regression-equations"], [28, "deriving-the-ridge-regression-equations"], [28, "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": [[26, "discriminative-modeling"]], "Domains and probabilities": [[23, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[27, "economy-size-svd"], [28, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[23, 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": [[26, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, 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[[1, "example-binary-classification-problem"]], "Examples": [[26, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: 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, use the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-use-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Expectation values": [[23, "expectation-values"]], "Extending to more than one variable": [[28, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[26, "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": [[27, "fixing-the-singularity"], [28, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[21, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[27, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[28, "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": [[27, "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"], [27, "further-properties-important-for-our-analyses-later"], [28, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[20, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[26, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": 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information": [[24, "instructor-information"]], "Interpretations and optimizing our parameters": [[26, "interpretations-and-optimizing-our-parameters"], [26, "id2"], [26, "id3"], [27, "interpretations-and-optimizing-our-parameters"], [27, "id1"], [27, "id2"]], "Interpreting the Ridge results": [[27, "interpreting-the-ridge-results"], [28, "interpreting-the-ridge-results"], [28, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [27, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [19, "introduction"], [20, "introduction"]], "Introduction to numerical projects": [[21, "introduction-to-numerical-projects"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, 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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": [[26, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[26, "overview-of-first-week"]], "Own code for Ordinary Least Squares": [[26, "own-code-for-ordinary-least-squares"], [27, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[26, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[21, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[21, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[21, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the 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26], "uio": 26, "univers": [12, 25], "unsupervis": 14, "up": [0, 2, 9, 12, 15, 26, 27, 28], "updat": 21, "us": [0, 1, 2, 3, 7, 13, 16, 18, 19, 21, 26, 27, 28], "v": 3, "valid": [6, 21], "valu": [5, 11, 23, 27, 28], "variabl": [23, 28], "varianc": [6, 21], "variou": 0, "vector": [8, 12, 16, 20, 26, 27], "versu": 26, "view": [0, 4, 10, 27], "virtual": 15, "visual": [1, 9], "wai": [9, 21], "wave": 2, "we": 26, "wednesdai": 28, "week": [15, 16, 17, 18, 26, 27, 28], "weekli": [], "what": [0, 26, 27, 28], "which": 1, "why": 26, "wisconsin": 7, "write": [4, 11, 21, 28], "x": 27, "xgboost": 10, "yet": 28, "your": [0, 10, 16, 18, 21, 27]}}) \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb index 5b6eea634..85723ce73 100644 --- a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb @@ -39,7 +39,7 @@ "links at\n", "\n", "contain more information. There you can find examples of previous\n", - "reports, the projects themselves, how we rade reports etc. How to\n", + "reports, the projects themselves, how we grade reports etc. How to\n", "write reports will also be discussed during the various lab\n", "sessions. Please do ask us if you are in doubt.\n", "\n", @@ -532,7 +532,7 @@ "\n", "1. For a discussion and derivation of the variances and mean squared errors using linear regression, see the [Lecture notes on ridge regression by Wessel N. van Wieringen](https://arxiv.org/abs/1509.09169)\n", "\n", - "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis here." + "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis of parts g) and h)." ] }, { @@ -635,7 +635,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, "nbformat": 4, "nbformat_minor": 5 } \ No newline at end of file diff --git a/doc/LectureNotes/project1.ipynb b/doc/LectureNotes/project1.ipynb index 1dd18f760..aba42cd41 100644 --- a/doc/LectureNotes/project1.ipynb +++ b/doc/LectureNotes/project1.ipynb @@ -39,7 +39,7 @@ "links at\n", "\n", "contain more information. There you can find examples of previous\n", - "reports, the projects themselves, how we rade reports etc. How to\n", + "reports, the projects themselves, how we grade reports etc. How to\n", "write reports will also be discussed during the various lab\n", "sessions. Please do ask us if you are in doubt.\n", "\n", @@ -532,7 +532,7 @@ "\n", "1. For a discussion and derivation of the variances and mean squared errors using linear regression, see the [Lecture notes on ridge regression by Wessel N. van Wieringen](https://arxiv.org/abs/1509.09169)\n", "\n", - "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis here." + "2. The textbook of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570), chapters 3 and 7 are the most relevant ones for the analysis of parts g) and h)." ] }, { @@ -635,7 +635,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, "nbformat": 4, "nbformat_minor": 5 }