Morten Hjorth-Jensen
1 line
224 KiB
JavaScript
1 line
224 KiB
JavaScript
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"], [28, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[28, "a-first-summary"]], "A more compact expression": [[33, "a-more-compact-expression"]], "A new Cost Function": [[32, "a-new-cost-function"]], "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"]], "A way to Read the Bias-Variance Tradeoff": [[32, "a-way-to-read-the-bias-variance-tradeoff"], [33, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[31, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [31, "id2"]], "Accuracy": [[31, "accuracy"]], "Activation functions": [[12, "activation-functions"]], "AdaGrad Properties": [[31, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[31, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[31, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[31, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[31, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[31, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[31, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[31, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[31, "adaptivity-across-dimensions"]], "Adding error analysis and training set up": [[28, "adding-error-analysis-and-training-set-up"], [29, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[31, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "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": [[28, "an-optimization-minimization-problem"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[29, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[31, "and-finally-adam"]], "And what about using neural networks?": [[28, "and-what-about-using-neural-networks"]], "Another Example from Scikit-Learn\u2019s Repository": [[32, "another-example-from-scikit-learn-s-repository"], [33, "another-example-from-scikit-learn-s-repository"]], "Another Example, now with a polynomial fit": [[30, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[21, null]], "Assumptions made": [[32, "assumptions-made"]], "Autocorrelation function": [[25, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[29, "back-to-ridge-and-lasso-regression"], [30, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[23, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[22, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [29, "basic-math-of-the-svd"], [30, "basic-math-of-the-svd"]], "Basics": [[7, "basics"], [33, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Batch Normalization": [[1, "batch-normalization"]], "Batches and mini-batches": [[31, "batches-and-mini-batches"]], "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"]], "But none of these can compete with Newton\u2019s method": [[31, "but-none-of-these-can-compete-with-newton-s-method"]], "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"]], "Challenge: Choosing a Fixed Learning Rate": [[31, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Classification problems": [[33, "classification-problems"]], "Clustering and Unsupervised Learning": [[14, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[32, "code-example-for-cross-validation-and-k-fold-cross-validation"], [33, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example for the Bootstrap method": [[32, "code-example-for-the-bootstrap-method"]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[31, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [29, "codes-for-the-svd"], [30, "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": [[28, "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": [[30, "comparison-with-ols"]], "Computation of gradients": [[31, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[30, "conditions-on-convex-functions"]], "Confidence Intervals": [[32, "confidence-intervals"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[31, "convergence-rates"]], "Convex function": [[30, "convex-function"]], "Convex functions": [[13, "convex-functions"], [30, "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": [[29, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [29, "correlation-matrix"]], "Correlation Matrix with Pandas": [[29, "correlation-matrix-with-pandas"]], "Course Format": [[28, "course-format"]], "Course setting": [[24, null]], "Covariance Matrix Examples": [[29, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[29, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[32, "cross-validation-in-brief"], [33, "cross-validation-in-brief"]], "Deadlines for projects (tentative)": [[28, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[31, "deep-neural-networks"]], "Deep learning methods": [[28, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"]], "Defining the cost function": [[1, "defining-the-cost-function"]], "Definitions": [[19, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"], [23, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[31, "derivation-of-the-adagrad-algorithm"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"]], "Derivatives, example 1": [[29, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [32, "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": [[29, "deriving-the-lasso-regression-equations"], [30, "deriving-the-lasso-regression-equations"], [30, "id6"]], "Deriving the Ridge Regression Equations": [[29, "deriving-the-ridge-regression-equations"], [30, "deriving-the-ridge-regression-equations"], [30, "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": [[28, "discriminative-modeling"]], "Domains and probabilities": [[25, "domains-and-probabilities"]], "Dropout": [[1, "dropout"]], "Economy-size SVD": [[29, "economy-size-svd"], [30, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[25, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[31, "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": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[28, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"]], "Example 2": [[29, "example-2"]], "Example 3": [[29, "example-3"]], "Example 4": [[29, "example-4"]], "Example Matrix": [[29, "example-matrix"], [30, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[32, "example-code-for-bias-variance-tradeoff"]], "Example code for Logistic Regression": [[33, "example-code-for-logistic-regression"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[28, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[29, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[29, "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": [[28, "examples"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[33, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-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: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "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: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "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, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "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": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "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 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "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 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "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]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Expectation value and variance": [[32, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[32, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[25, "expectation-values"]], "Extending to more predictors": [[33, "extending-to-more-predictors"]], "Extending to more than one variable": [[30, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[28, "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"]], "Finding the Limit": [[32, "finding-the-limit"]], "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": [[29, "fixing-the-singularity"], [30, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[23, "format-for-electronic-delivery-of-report-and-programs"]], "Frequently used scaling functions": [[29, "frequently-used-scaling-functions"], [31, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[30, "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": [[29, "functionality-in-scikit-learn"], [31, "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"], [29, "further-properties-important-for-our-analyses-later"], [30, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[22, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[28, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[28, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [28, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[28, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "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": [[30, "id1"], [31, "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": [[30, "gradient-descent-and-ridge"], [31, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[31, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[30, "gradient-descent-example"], [31, "gradient-descent-example"]], "Grading": [[26, "grading"], [26, "id2"], [28, "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"]], "Identifying Terms": [[32, "identifying-terms"]], "Important Matrix and vector handling packages": [[22, "important-matrix-and-vector-handling-packages"]], "Important technicalities: More on Rescaling data": [[29, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[31, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"]], "In summary": [[26, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [31, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[33, "including-more-classes"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[32, "independent-and-identically-distributed-iid"]], "Installing R, C++, cython or Julia": [[28, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[28, "installing-r-c-cython-numba-etc"]], "Instructor information": [[26, "instructor-information"]], "Interpretations and optimizing our parameters": [[28, "interpretations-and-optimizing-our-parameters"], [28, "id2"], [28, "id3"], [29, "interpretations-and-optimizing-our-parameters"], [29, "id1"], [29, "id2"]], "Interpreting the Ridge results": [[29, "interpreting-the-ridge-results"], [30, "interpreting-the-ridge-results"], [30, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [29, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [21, "introduction"], [22, "introduction"]], "Introduction to numerical projects": [[23, "introduction-to-numerical-projects"]], "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": [[22, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab sessions week 39": [[33, "lab-sessions-week-39"]], "Lasso Regression": [[30, "lasso-regression"]], "Lasso case": [[30, "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"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[21, "learning-outcomes"], [28, "learning-outcomes"]], "Lecture material": [[33, "lecture-material"]], "Lectures and ComputerLab": [[28, "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": [[22, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[29, "linear-regression-problems"], [30, "linear-regression-problems"]], "Linear Regression and the SVD": [[30, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linear classifier": [[33, "linear-classifier"]], "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"], [32, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [29, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[27, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"], [33, "logistic-regression"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[28, "machine-learning"]], "Machine learning": [[21, "machine-learning"]], "Main textbooks": [[28, "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": [[29, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[29, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[30, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[30, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[31, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[31, "material-for-the-lab-sessions"], [32, "material-for-the-lab-sessions"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [29, "mathematical-interpretation-of-ordinary-least-squares"], [30, "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"], [29, "mathematics-of-the-svd-and-implications"], [30, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[28, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[32, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[33, "maximum-likelihood"]], "Meet the covariance!": [[25, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [29, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[29, "meet-the-hessian-matrix"]], "Meet the Pandas": [[28, "meet-the-pandas"]], "Memory Usage and Scalability": [[31, "memory-usage-and-scalability"]], "Memory constraints": [[31, "memory-constraints"]], "Min-Max Scaling": [[29, "min-max-scaling"]], "Minimizing the cross entropy": [[33, "minimizing-the-cross-entropy"]], "Momentum based GD": [[13, "momentum-based-gd"], [31, "momentum-based-gd"]], "More classes": [[33, "more-classes"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More examples on bootstrap and cross-validation and errors": [[32, "more-examples-on-bootstrap-and-cross-validation-and-errors"], [33, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[29, "more-interpretations"], [30, "more-interpretations"], [30, "id5"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[30, "more-on-steepest-descent"]], "More on convex functions": [[30, "more-on-convex-functions"]], "More preprocessing": [[29, "more-preprocessing"], [31, "more-preprocessing"]], "Motivation for Adaptive Step Sizes": [[31, "motivation-for-adaptive-step-sizes"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural networks": [[12, null]], "Non-Convex Problems": [[31, "non-convex-problems"]], "Note about SVD Calculations": [[29, "note-about-svd-calculations"], [30, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[30, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[25, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[22, "numpy-and-arrays"], [28, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[28, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[33, "optimization-and-deep-learning"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[30, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null], [33, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimizing our parameters": [[28, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[28, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"]], "Organizing our data": [[0, "organizing-our-data"], [28, "organizing-our-data"]], "Other Matrix and Vector Operations": [[22, "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": [[28, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[28, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other popular texts": [[28, "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": [[28, "our-model-for-the-nuclear-binding-energies"]], "Overview of first week": [[28, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[31, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[28, "own-code-for-ordinary-least-squares"], [29, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[28, "pandas-ai"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[23, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part b: Adding Ridge regression for the Runge function": [[23, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c: Writing your own gradient descent code": [[23, "part-c-writing-your-own-gradient-descent-code"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[23, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e: Writing our own code for Lasso regression": [[23, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f: Stochastic gradient descent": [[23, "part-f-stochastic-gradient-descent"]], "Part g: Bias-variance trade-off and resampling techniques": [[23, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[23, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plan for week 39, September 22-26, 2025": [[33, "plan-for-week-39-september-22-26-2025"]], "Plans for week 35": [[29, "plans-for-week-35"]], "Plans for week 36": [[30, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[31, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[32, "plans-for-week-38-lecture-monday-september-15"]], "Plotting the Histogram": [[32, "plotting-the-histogram"]], "Plotting the mean value for each group": [[33, "plotting-the-mean-value-for-each-group"]], "Practical tips": [[13, "practical-tips"], [31, "practical-tips"]], "Practicalities": [[26, "practicalities"], [26, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[23, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[29, "preprocessing-our-data"]], "Prerequisites": [[28, "prerequisites"]], "Prerequisites and background": [[21, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[25, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[30, "program-example-for-gradient-descent-with-ridge-regression"], [31, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[23, null]], "Properties of PDFs": [[25, "properties-of-pdfs"]], "Pros and cons": [[31, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[21, "python-installers"], [28, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[31, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[31, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[31, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[25, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[28, "reading-material"]], "Reading recommendations:": [[29, "reading-recommendations"]], "Reading suggestions week 34": [[28, "reading-suggestions-week-34"]], "Readings and Videos": [[32, "readings-and-videos"]], "Readings and Videos, logistic regression": [[33, "readings-and-videos-logistic-regression"]], "Readings and Videos, resampling methods": [[33, "readings-and-videos-resampling-methods"]], "Readings and Videos:": [[31, "readings-and-videos"]], "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"], [29, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[23, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[28, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[28, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"]], "Reminder from last week": [[29, "reminder-from-last-week"]], "Reminder on Newton-Raphson\u2019s method": [[30, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on different scaling methods": [[31, "reminder-on-different-scaling-methods"]], "Replace or not": [[13, "replace-or-not"], [31, "replace-or-not"]], "Required Technologies": [[21, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[32, "resampling-approaches-can-be-computationally-expensive"], [33, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [32, "resampling-methods"], [32, "id2"], [33, "resampling-methods"], [33, "id1"]], "Resampling methods: Bootstrap": [[32, "resampling-methods-bootstrap"], [33, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[32, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[32, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[32, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[32, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[29, "residual-error"], [30, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[30, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[33, "revisiting-our-logistic-regression-case"]], "Rewriting the Covariance and/or Correlation Matrix": [[29, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[32, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[28, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[30, "ridge-regression"]], "Ridge and LASSO Regression": [[29, "ridge-and-lasso-regression"], [30, "ridge-and-lasso-regression"], [30, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[31, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[31, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[30, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [31, "same-code-but-now-with-momentum-gradient-descent"], [31, "id3"], [31, "id4"]], "Schedule first week": [[28, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[31, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Matrix to be inverted": [[29, "setting-up-the-matrix-to-be-inverted"], [30, "setting-up-the-matrix-to-be-inverted"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [31, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[29, "simple-case"], [30, "simple-case"]], "Simple code for solving the above problem": [[30, "simple-code-for-solving-the-above-problem"]], "Simple example": [[33, "simple-example"]], "Simple example code": [[31, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[30, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[30, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [28, "simple-linear-regression-model-using-scikit-learn"]], "Simple one-dimensional second-order polynomial": [[18, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[30, "simple-program"], [31, "simple-program"]], "Slightly different approach": [[31, "slightly-different-approach"]], "Sneaking in automatic differentiation using Autograd": [[31, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[23, "software-and-needed-installations"], [28, "software-and-needed-installations"]], "Solving Differential Equations with Deep Learning": [[2, null]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Solving using Newton-Raphson\u2019s method": [[33, "solving-using-newton-raphson-s-method"]], "Some famous Matrices": [[22, "some-famous-matrices"]], "Some selected properties": [[33, "some-selected-properties"]], "Some simple problems": [[13, "some-simple-problems"], [30, "some-simple-problems"]], "Some useful matrix and vector expressions": [[29, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [29, "splitting-our-data-in-training-and-test-data"]], "Standard Approach based on the Normal Distribution": [[32, "standard-approach-based-on-the-normal-distribution"]], "Standard steepest descent": [[13, "standard-steepest-descent"]], "Statistical analysis": [[32, "statistical-analysis"], [33, "statistical-analysis"]], "Statistical analysis and optimization of data": [[21, "statistical-analysis-and-optimization-of-data"], [28, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[13, "steepest-descent"], [30, "steepest-descent"]], "Stochastic Gradient Descent": [[31, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[13, "stochastic-gradient-descent-sgd"], [31, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[25, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[31, "strongly-convex-case"]], "Summing up": [[32, "summing-up"], [33, "summing-up"]], "Support Vector Machines, overarching aims": [[8, null]], "Synthetic data generation": [[33, "synthetic-data-generation"]], "Systematic reduction": [[3, "systematic-reduction"]], "Teachers": [[28, "teachers"]], "Teachers and Grading": [[26, null]], "Teaching Assistants Fall semester 2023": [[26, "teaching-assistants-fall-semester-2023"]], "Tentative deadllines for projects": [[26, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[0, "testing-the-means-squared-error-as-function-of-complexity"], [29, "testing-the-means-squared-error-as-function-of-complexity"]], "Textbooks": [[27, null]], "The Algorithm before theorem": [[11, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[1, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[9, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[9, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[3, "the-cifar01-data-set"]], "The Central Limit Theorem": [[32, "the-central-limit-theorem"]], "The Hessian matrix": [[30, "the-hessian-matrix"], [31, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[30, "the-hessian-matrix-for-ridge-regression"], [31, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[29, "the-jacobian"]], "The MNIST dataset again": [[3, "the-mnist-dataset-again"]], "The OLS case": [[30, "the-ols-case"]], "The RELU function family": [[1, "the-relu-function-family"]], "The Ridge case": [[30, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[29, "the-svd-a-fantastic-algorithm"], [30, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[1, "the-softmax-function"]], "The \\chi^2 function": [[0, "the-chi-2-function"], [28, "the-chi-2-function"], [28, "id4"], [28, "id5"], [28, "id6"], [28, "id7"], [28, "id8"]], "The bias-variance tradeoff": [[6, "the-bias-variance-tradeoff"], [32, "the-bias-variance-tradeoff"], [33, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[2, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[29, "the-complete-code-with-a-simple-data-set"]], "The cost function rewritten": [[33, "the-cost-function-rewritten"]], "The cost/loss function": [[29, "the-cost-loss-function"]], "The course has two central parts": [[21, "the-course-has-two-central-parts"]], "The derivative of the cost/loss function": [[30, "the-derivative-of-the-cost-loss-function"], [31, "the-derivative-of-the-cost-loss-function"]], "The equations": [[30, "the-equations"]], "The equations for ordinary least squares": [[29, "the-equations-for-ordinary-least-squares"]], "The equations to solve": [[33, "the-equations-to-solve"]], "The first Case": [[30, "the-first-case"]], "The gradient step": [[31, "the-gradient-step"]], "The ideal": [[30, "the-ideal"]], "The logistic function": [[7, "the-logistic-function"], [33, "the-logistic-function"]], "The mean squared error and its derivative": [[29, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[8, "the-moons-example"]], "The multilayer perceptron (MLP)": [[12, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": 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