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

Search.setIndex({"alltitles": {"3D volumes of neurons": [[45, "d-volumes-of-neurons"], [46, "d-volumes-of-neurons"]], "A Classification Tree": [[10, "a-classification-tree"], [47, "a-classification-tree"], [48, "a-classification-tree"]], "A Frequentist approach to data analysis": [[1, "a-frequentist-approach-to-data-analysis"], [35, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[9, "a-better-approach"]], "A deep CNN model (From Raschka et al)": [[45, "a-deep-cnn-model-from-raschka-et-al"], [46, "a-deep-cnn-model-from-raschka-et-al"]], "A first summary": [[35, "a-first-summary"]], "A more advanced example": [[22, "a-more-advanced-example"], [41, "a-more-advanced-example"]], "A more compact expression": [[0, "a-more-compact-expression"], [39, "a-more-compact-expression"]], "A more efficient way of coding the above Convolution": [[45, "a-more-efficient-way-of-coding-the-above-convolution"]], "A new Cost Function": [[37, "a-new-cost-function"], [38, "a-new-cost-function"]], "A possible code using Scikit-Learn": [[47, "a-possible-code-using-scikit-learn"], [48, "a-possible-code-using-scikit-learn"]], "A possible implementation of a neural network": [[44, "a-possible-implementation-of-a-neural-network"]], "A quick Reminder on Lagrangian Multipliers": [[9, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[5, "a-simple-example"], [46, "a-simple-example"]], "A soft classifier": [[9, "a-soft-classifier"]], "A top-down approach, recursive binary splitting": [[47, "a-top-down-approach-recursive-binary-splitting"], [48, "a-top-down-approach-recursive-binary-splitting"]], "A top-down perspective on Neural networks": [[2, "a-top-down-perspective-on-neural-networks"], [42, "a-top-down-perspective-on-neural-networks"], [43, "a-top-down-perspective-on-neural-networks"]], "A typical Decision Tree with its pertinent Jargon, Classification Problem": [[47, "a-typical-decision-tree-with-its-pertinent-jargon-classification-problem"]], "A warm-up example": [[22, "a-warm-up-example"], [41, "a-warm-up-example"]], "A way to Read the Bias-Variance Tradeoff": [[38, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[22, "adam-algorithm-taken-from-goodfellow-et-al"], [41, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[14, "adam-optimizer"], [40, "adam-optimizer"], [41, "adam-optimizer"]], "Activation functions": [[13, "activation-functions"], [41, "activation-functions"], [42, "activation-functions"], [43, "activation-functions"], [43, "id3"], [44, "activation-functions"], [44, "id3"], [45, "activation-functions"], [46, "activation-functions"]], "Activation functions, Logistic and Hyperbolic ones": [[41, "activation-functions-logistic-and-hyperbolic-ones"], [42, "activation-functions-logistic-and-hyperbolic-ones"], [43, "activation-functions-logistic-and-hyperbolic-ones"]], "Activation functions, examples": [[44, "activation-functions-examples"]], "AdaBoost Examples": [[47, "adaboost-examples"], [48, "adaboost-examples"]], "AdaGrad algorithm, taken from Goodfellow et al": [[22, "adagrad-algorithm-taken-from-goodfellow-et-al"], [41, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adaptive Boosting, AdaBoost": [[47, "adaptive-boosting-adaboost"], [48, "adaptive-boosting-adaboost"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[11, "adaptive-boosting-adaboost-basic-algorithm"], [47, "adaptive-boosting-adaboost-basic-algorithm"], [48, "adaptive-boosting-adaboost-basic-algorithm"]], "Add Dense layers on top": [[45, "add-dense-layers-on-top"], [46, "add-dense-layers-on-top"]], "Adding Neural Networks": [[41, "adding-neural-networks"], [42, "adding-neural-networks"]], "Adding a hidden layer": [[42, "adding-a-hidden-layer"], [43, "adding-a-hidden-layer"]], "Adding error analysis and training set up": [[35, "adding-error-analysis-and-training-set-up"], 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polynomial fit": [[37, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[10, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[26, null]], "Artificial neurons": [[41, "artificial-neurons"], [42, "artificial-neurons"]], "Assumptions made": [[37, "assumptions-made"], [38, "assumptions-made"]], "Autocorrelation function": [[32, "autocorrelation-function"]], "Autograd with more complicated functions": [[40, "autograd-with-more-complicated-functions"], [41, "autograd-with-more-complicated-functions"]], "Automatic differentiation": [[14, "automatic-differentiation"], [40, "automatic-differentiation"], [41, "automatic-differentiation"], [42, "automatic-differentiation"]], "Automatic differentiation through examples": [[42, "automatic-differentiation-through-examples"]], "Back propagation": [[44, "back-propagation"]], "Back propagation and automatic differentiation": [[44, "back-propagation-and-automatic-differentiation"]], 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"building-a-tree-regression"]], "Building convolutional neural networks in Tensorflow and Keras": [[45, "building-convolutional-neural-networks-in-tensorflow-and-keras"], [46, "building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Building neural networks in Tensorflow and Keras": [[2, "building-neural-networks-in-tensorflow-and-keras"], [43, "building-neural-networks-in-tensorflow-and-keras"], [44, "building-neural-networks-in-tensorflow-and-keras"]], "Building our own CNN code": [[45, "building-our-own-cnn-code"], [46, "building-our-own-cnn-code"]], "Building up AdaBoost": [[47, "building-up-adaboost"], [48, "building-up-adaboost"]], "But noen of these can compete with Newton\u2019s method": [[22, "but-noen-of-these-can-compete-with-newton-s-method"]], "But none of these can compete with Newton\u2019s method": [[40, "but-none-of-these-can-compete-with-newton-s-method"], [41, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in brief": [[45, "cnns-in-brief"], [46, "cnns-in-brief"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[4, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "CNNs in more detail, simple example": [[45, "cnns-in-more-detail-simple-example"]], "Cancer Data again now with Decision Trees and other Methods": [[10, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Chain rule": [[42, "chain-rule"]], "Chain rule again": [[46, "chain-rule-again"]], "Chain rule, forward and reverse modes": [[42, "chain-rule-forward-and-reverse-modes"]], "Challenge yourself the coming weekend": [[39, "challenge-yourself-the-coming-weekend"]], "Choose cost function and optimizer": [[2, "choose-cost-function-and-optimizer"], [43, "choose-cost-function-and-optimizer"], [44, "choose-cost-function-and-optimizer"]], "Class of functions we can approximate": [[42, "class-of-functions-we-can-approximate"]], "Classical PCA Theorem": [[12, "classical-pca-theorem"]], "Classification and Regression, from linear and logistic regression to neural networks": [[29, "classification-and-regression-from-linear-and-logistic-regression-to-neural-networks"]], "Classification problems": [[39, "classification-problems"]], "Classification tree, how to split nodes": [[47, "classification-tree-how-to-split-nodes"], [48, "classification-tree-how-to-split-nodes"]], "Clustering and Unsupervised Learning": [[15, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[38, "code-example-for-cross-validation-and-k-fold-cross-validation"], [39, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example": [[42, "code-example"], [43, "code-example"]], "Code example for the Bootstrap method": [[38, "code-example-for-the-bootstrap-method"]], "Code examples from week 39 and 40": [[22, "code-examples-from-week-39-and-40"]], "Code for SVD and Inversion of Matrices": [[6, "code-for-svd-and-inversion-of-matrices"], [37, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[40, "code-with-a-number-of-minibatches-which-varies"], [41, "code-with-a-number-of-minibatches-which-varies"]], "Code with a Number of Minibatches which varies, analytical gradient": [[22, "code-with-a-number-of-minibatches-which-varies-analytical-gradient"]], "Codes and Approaches": [[15, "codes-and-approaches"]], "Codes for the SVD": [[6, "codes-for-the-svd"], [36, "codes-for-the-svd"]], "Collect and pre-process data": [[2, "collect-and-pre-process-data"], [43, "collect-and-pre-process-data"], [43, "id2"], [44, "collect-and-pre-process-data"], [44, "id2"]], "Communication channels": [[35, "communication-channels"]], "Commutative process": [[45, "commutative-process"]], "Compact expressions": [[42, "compact-expressions"], [43, "compact-expressions"]], "Compare  Bagging on Trees with Random Forests": [[11, 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"computing-the-various-gini-indices"], [48, "computing-the-various-gini-indices"]], "Computing the various Gini Indices, Hours slept": [[47, "computing-the-various-gini-indices-hours-slept"]], "Computing the various Gini Indices, Hours studied": [[47, "computing-the-various-gini-indices-hours-studied"]], "Conditional  Probability": [[37, "conditional-probability"], [38, "conditional-probability"]], "Conditions on convex functions": [[39, "conditions-on-convex-functions"], [40, "conditions-on-convex-functions"]], "Confidence Intervals": [[38, "confidence-intervals"]], "Conjugate gradient method": [[14, "conjugate-gradient-method"], [40, "conjugate-gradient-method"], [40, "id2"], [40, "id3"], [40, "id4"], [40, "id5"], [40, "id6"], [40, "id7"]], "Conjugate gradient method and iterations": [[40, "conjugate-gradient-method-and-iterations"]], "Convex function": [[39, "convex-function"], [40, "convex-function"]], "Convex functions": [[14, "convex-functions"], [39, "convex-functions"], [40, "convex-functions"]], "Convolution": [[45, "convolution"], [46, "convolution"]], "Convolution Examples: Polynomial multiplication": [[4, "convolution-examples-polynomial-multiplication"], [45, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[4, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolution in the Fourier domain": [[45, "convolution-in-the-fourier-domain"], [46, "convolution-in-the-fourier-domain"]], "Convolution using separable kernels": [[45, "convolution-using-separable-kernels"], [46, "convolution-using-separable-kernels"]], "Convolution2DLayer: convolution in a hidden layer": [[45, "convolution2dlayer-convolution-in-a-hidden-layer"], [46, "convolution2dlayer-convolution-in-a-hidden-layer"]], "Convolutional Neural Network": [[13, "convolutional-neural-network"], [41, "convolutional-neural-network"], [42, "convolutional-neural-network"]], "Convolutional Neural Networks": [[4, null]], "Convolutional Neural Networks (recognizing images)": [[45, "convolutional-neural-networks-recognizing-images"], [46, "convolutional-neural-networks-recognizing-images"]], "Correlation Function and Design/Feature Matrix": [[36, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[12, "correlation-matrix"], [36, "correlation-matrix"]], "Correlation Matrix with Pandas": [[36, "correlation-matrix-with-pandas"]], "Correlation Matrix with Pandas and the Franke function": [[36, "correlation-matrix-with-pandas-and-the-franke-function"]], "Cost complexity pruning": [[47, "cost-complexity-pruning"], [48, "cost-complexity-pruning"]], "Cost functions": [[43, "cost-functions"], [44, "cost-functions"], [45, "cost-functions"], [46, "cost-functions"]], "Counting the number of floating point operations": [[42, "counting-the-number-of-floating-point-operations"]], "Course Format": [[35, "course-format"]], "Covariance Matrix Examples": [[36, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[36, "covariance-and-correlation-matrix"]], "Cross correlation": [[45, "cross-correlation"]], "Cross-validation": [[7, "cross-validation"]], "Cross-validation in brief": [[38, "cross-validation-in-brief"], [39, "cross-validation-in-brief"]], "Deadlines for projects (tentative)": [[35, "deadlines-for-projects-tentative"]], "Decision trees and Regression": [[47, "decision-trees-and-regression"]], "Decision trees, overarching aims": [[10, null], [47, "decision-trees-overarching-aims"]], "Deep learning methods": [[35, "deep-learning-methods"]], "Define model and architecture": [[2, "define-model-and-architecture"], [43, "define-model-and-architecture"], [44, "define-model-and-architecture"]], "Defining intermediate operations": [[42, "defining-intermediate-operations"]], "Defining the cost function": [[2, "defining-the-cost-function"], [43, "defining-the-cost-function"], [44, "defining-the-cost-function"]], "Defining the data sets to analyze yourself": [[30, "defining-the-data-sets-to-analyze-yourself"]], "Defining the problem": [[44, "defining-the-problem"]], "Definitions": [[42, "definitions"], [43, "definitions"]], "Demonstration": [[45, "demonstration"], [46, "demonstration"]], "Derivative of the cost function": [[42, "derivative-of-the-cost-function"], [43, "derivative-of-the-cost-function"]], "Derivatives and the chain rule": [[13, "derivatives-and-the-chain-rule"], [42, "derivatives-and-the-chain-rule"], [43, "derivatives-and-the-chain-rule"]], "Derivatives in terms of z_j^L": [[42, "derivatives-in-terms-of-z-j-l"], [43, "derivatives-in-terms-of-z-j-l"]], "Derivatives of the hidden layer": [[42, "derivatives-of-the-hidden-layer"], [43, "derivatives-of-the-hidden-layer"]], "Derivatives, example 1": [[36, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[6, "deriving-ols-from-a-probability-distribution"], [37, "deriving-ols-from-a-probability-distribution"], [38, "deriving-ols-from-a-probability-distribution"]], "Deriving the  Lasso Regression Equations": [[36, "deriving-the-lasso-regression-equations"], [37, "deriving-the-lasso-regression-equations"]], "Deriving the  Ridge Regression Equations": [[36, "deriving-the-ridge-regression-equations"], [37, "deriving-the-ridge-regression-equations"]], "Deriving the back propagation code for a multilayer perceptron model": [[13, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Description of two-dimensional function": [[28, "description-of-two-dimensional-function"]], "Developing a code for doing neural networks with back propagation": [[2, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [43, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [44, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[12, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[9, "different-kernels-and-mercer-s-theorem"]], "Differential equations": [[46, "differential-equations"]], "Disadvantages": [[10, "disadvantages"], [47, "disadvantages"], [48, "disadvantages"]], "Discussing the correlation data": [[0, "discussing-the-correlation-data"], [39, "discussing-the-correlation-data"]], "Does Logistic Regression do a better Job?": [[41, "does-logistic-regression-do-a-better-job"], [42, "does-logistic-regression-do-a-better-job"]], "Doing it correctly": [[37, "doing-it-correctly"], [38, "doing-it-correctly"]], "Domains and probabilities": [[32, "domains-and-probabilities"]], "Dropout": [[2, "dropout"], [42, "dropout"], [43, "dropout"]], "ELU function": [[42, "elu-function"], [43, "elu-function"], [44, "elu-function"]], "Economy-size SVD": [[36, "economy-size-svd"]], "Efficient Polynomial Multiplication": [[45, "efficient-polynomial-multiplication"]], "Elements of Probability Theory and Statistical Data Analysis": [[32, null]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[11, null], [47, "ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods"], [48, "ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods"]], "Entropy and the ID3 algorithm": [[10, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[35, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[2, "evaluate-model-performance-on-test-data"], [43, "evaluate-model-performance-on-test-data"], [44, "evaluate-model-performance-on-test-data"]], "Example 2": [[36, "example-2"]], "Example 3": [[36, "example-3"]], "Example 4": [[36, "example-4"]], "Example Matrix": [[36, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[38, "example-code-for-bias-variance-tradeoff"]], "Example of Usage of Bayes\u2019 theorem": [[37, "example-of-usage-of-bayes-theorem"], [38, "example-of-usage-of-bayes-theorem"]], "Example of own Standard scaling": [[36, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[36, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[3, "example-exponential-decay"], [44, "example-exponential-decay"]], "Example: Population growth": [[3, "example-population-growth"], [44, "example-population-growth"]], "Example: Solving the one dimensional Poisson equation": [[44, "example-solving-the-one-dimensional-poisson-equation"]], "Example: Solving the wave equation with Neural Networks": [[44, "example-solving-the-wave-equation-with-neural-networks"]], "Example: The diffusion equation": [[3, "example-the-diffusion-equation"], [44, "example-the-diffusion-equation"]], "Example: binary classification problem": [[2, "example-binary-classification-problem"], [43, "example-binary-classification-problem"], [44, "example-binary-classification-problem"]], "Examples": [[35, "examples"]], "Examples of CNN setups": [[45, "examples-of-cnn-setups"]], "Examples of XOR, OR and AND gates": [[41, "examples-of-xor-or-and-and-gates"], [42, "examples-of-xor-or-and-and-gates"]], "Examples of likelihood functions used in logistic regression and neural networks": [[8, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[0, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"], [39, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"]], "Exercise 1": [[23, "exercise-1"]], "Exercise 1 - Understand the feed forward pass": [[24, "exercise-1-understand-the-feed-forward-pass"]], "Exercise 1: Analytical exercises": [[17, "exercise-1-analytical-exercises"], [18, "exercise-1-analytical-exercises"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Including more data": [[42, "exercise-1-including-more-data"]], "Exercise 1: Linear and logistic regression methods": [[25, "exercise-1-linear-and-logistic-regression-methods"]], "Exercise 1: Setting up various Python environments": [[1, "exercise-1-setting-up-various-python-environments"], [16, "exercise-1-setting-up-various-python-environments"], [35, "exercise-1-setting-up-various-python-environments"]], "Exercise 2": [[23, "exercise-2"]], "Exercise 2 - Gradient with one layer using autograd": [[24, "exercise-2-gradient-with-one-layer-using-autograd"]], "Exercise 2: Adding Ridge Regression": [[18, "exercise-2-adding-ridge-regression"]], "Exercise 2: Deep learning": [[25, "exercise-2-deep-learning"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: Extended program": [[42, "exercise-2-extended-program"]], "Exercise 2: making your own data and exploring scikit-learn": [[1, "exercise-2-making-your-own-data-and-exploring-scikit-learn"], [16, "exercise-2-making-your-own-data-and-exploring-scikit-learn"], [17, "exercise-2-making-your-own-data-and-exploring-scikit-learn"], [35, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3": [[23, "exercise-3"]], "Exercise 3 - Gradient with one layer writing backpropagation by hand": [[24, "exercise-3-gradient-with-one-layer-writing-backpropagation-by-hand"]], "Exercise 3: Decision trees and ensemble methods": [[25, "exercise-3-decision-trees-and-ensemble-methods"]], "Exercise 3: Normalizing our data": [[1, "exercise-3-normalizing-our-data"]], "Exercise 3: Split data in test and training data": [[16, "exercise-3-split-data-in-test-and-training-data"], [17, "exercise-3-split-data-in-test-and-training-data"], [35, "exercise-3-split-data-in-test-and-training-data"]], "Exercise 4 - Custom activation for each layer": [[23, "exercise-4-custom-activation-for-each-layer"]], "Exercise 4 - Gradient with two layers writing backpropagation by hand": [[24, "exercise-4-gradient-with-two-layers-writing-backpropagation-by-hand"]], "Exercise 4: Adding Ridge Regression": [[1, "exercise-4-adding-ridge-regression"]], "Exercise 4: Optimization part": [[25, "exercise-4-optimization-part"]], "Exercise 5 - Gradient with any number of layers writing backpropagation by hand": [[24, "exercise-5-gradient-with-any-number-of-layers-writing-backpropagation-by-hand"]], "Exercise 5 - Processing multiple inputs at once": [[23, "exercise-5-processing-multiple-inputs-at-once"]], "Exercise 5: Analysis of results": [[25, "exercise-5-analysis-of-results"]], "Exercise 5: Analytical exercises": [[1, "exercise-5-analytical-exercises"]], "Exercise 6 - Batched inputs": [[24, "exercise-6-batched-inputs"]], "Exercise 6 - Predicting on real data": [[23, "exercise-6-predicting-on-real-data"]], "Exercise 7 - Training": [[24, "exercise-7-training"]], "Exercise 7 - Training on real data (Optional)": [[23, "exercise-7-training-on-real-data-optional"]], "Exercise 8 (Optional) - Object orientation": [[24, "exercise-8-optional-object-orientation"]], "Exercise week 47": [[25, null]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[7, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[7, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[7, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[7, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[7, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[7, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[1, "exercises"], [16, "exercises"], [35, "exercises"]], "Exercises Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40": [[0, null]], "Exercises and Projects": [[7, "exercises-and-projects"]], "Exercises and lab session week 43": [[44, "exercises-and-lab-session-week-43"]], "Exercises week 34": [[16, null]], "Exercises week 35": [[17, null]], "Exercises week 36": [[18, null]], "Exercises week 37": [[19, null]], "Exercises week 38": [[20, null]], "Exercises week 39": [[21, null]], "Exercises week 41": [[22, null]], "Exercises week 42": [[23, null]], "Exercises week 43": [[24, null]], "Expectation value and variance": [[37, "expectation-value-and-variance"], [38, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\beta}": [[37, "expectation-value-and-variance-for-boldsymbol-beta"], [38, "expectation-value-and-variance-for-boldsymbol-beta"]], "Expectation values": [[32, "expectation-values"]], "Explicit derivatives": [[42, "explicit-derivatives"], [43, "explicit-derivatives"]], "Exploding gradients": [[42, "exploding-gradients"], [43, "exploding-gradients"]], "Extending to more predictors": [[0, "extending-to-more-predictors"], [39, "extending-to-more-predictors"]], "Extending to more than one variable": [[39, "extending-to-more-than-one-variable"], [40, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[35, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[13, "feed-forward-neural-networks"], [41, "feed-forward-neural-networks"], [42, "feed-forward-neural-networks"]], "Feed-forward pass": [[2, "feed-forward-pass"], [43, "feed-forward-pass"], [44, "feed-forward-pass"]], "Feedback connections": [[46, "feedback-connections"]], "Final back propagating equation": [[13, "final-back-propagating-equation"], [42, "final-back-propagating-equation"], [43, "final-back-propagating-equation"]], "Final derivatives": [[42, "final-derivatives"]], "Final expression": [[42, "final-expression"], [43, "final-expression"]], "Final expressions": [[40, "final-expressions"]], "Final expressions for the biases of the hidden layer": [[42, "final-expressions-for-the-biases-of-the-hidden-layer"], [43, "final-expressions-for-the-biases-of-the-hidden-layer"]], "Final part": [[45, "final-part"], [46, "final-part"]], "Final regressor code": [[47, "final-regressor-code"], [48, "final-regressor-code"]], "Final technicalities I": [[44, "final-technicalities-i"]], "Final technicalities II": [[44, "final-technicalities-ii"]], "Final technicalities III": [[44, "final-technicalities-iii"]], "Final technicalities IV": [[44, "final-technicalities-iv"]], "Final visualization": [[45, "final-visualization"], [46, "final-visualization"]], "Finally, evaluate the model": [[45, "finally-evaluate-the-model"], [46, "finally-evaluate-the-model"]], "Finding the Limit": [[38, "finding-the-limit"]], "Finding the number of parameters": [[45, "finding-the-number-of-parameters"]], "Fine-tuning neural network hyperparameters": [[2, "fine-tuning-neural-network-hyperparameters"], [42, "fine-tuning-neural-network-hyperparameters"], [43, "fine-tuning-neural-network-hyperparameters"]], "First network example, simple percepetron with one input": [[42, "first-network-example-simple-percepetron-with-one-input"], [43, "first-network-example-simple-percepetron-with-one-input"]], "Fitting an Equation of State for Dense Nuclear Matter": [[1, "fitting-an-equation-of-state-for-dense-nuclear-matter"], [35, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[36, "fixing-the-singularity"]], "Flattening Layer": [[45, "flattening-layer"], [46, "flattening-layer"]], "For exercise sessions: Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week": [[36, "for-exercise-sessions-why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week"]], "Forget and input": [[46, "forget-and-input"]], "Format for electronic delivery of report and programs": [[28, "format-for-electronic-delivery-of-report-and-programs"], [29, "format-for-electronic-delivery-of-report-and-programs"], [30, "format-for-electronic-delivery-of-report-and-programs"]], "Forward and reverse modes": [[42, "forward-and-reverse-modes"]], "Four effective ways to learn an RNN and preparing for next week": [[46, "four-effective-ways-to-learn-an-rnn-and-preparing-for-next-week"]], "Fourier series and Toeplitz matrices": [[45, "fourier-series-and-toeplitz-matrices"]], "Frequently used scaling functions": [[36, "frequently-used-scaling-functions"]], "From FFNNs and CNNs to recurrent neural networks (RNNs)": [[46, "from-ffnns-and-cnns-to-recurrent-neural-networks-rnns"]], "From OLS to Ridge and Lasso": [[37, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[13, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Full object-oriented implementation": [[43, "full-object-oriented-implementation"], [44, "full-object-oriented-implementation"]], "Fully Connected Layers": [[45, "fully-connected-layers"], [46, "fully-connected-layers"]], "Functionality in Scikit-Learn": [[36, "functionality-in-scikit-learn"]], "Functions using mathematical functions from Numpy": [[40, "functions-using-mathematical-functions-from-numpy"], [41, "functions-using-mathematical-functions-from-numpy"]], "Further Dimensionality Remarks": [[4, "further-dimensionality-remarks"]], "Further Manipulations": [[36, "further-manipulations"]], "Further example: Computing the Gini index": [[47, "further-example-computing-the-gini-index"], [48, "further-example-computing-the-gini-index"]], "Further properties (important for our analyses later)": [[6, "further-properties-important-for-our-analyses-later"], [36, "further-properties-important-for-our-analyses-later"]], "Further remarks": [[45, "further-remarks"]], "Further simplification": [[45, "further-simplification"]], "Gating mechanism: Long Short Term Memory (LSTM)": [[46, "gating-mechanism-long-short-term-memory-lstm"]], "Gaussian Elimination": [[27, "gaussian-elimination"]], "General Features": [[10, "general-features"], [47, "general-features"]], "General linear models and linear algebra": [[35, "general-linear-models-and-linear-algebra"]], "Generalizing the above one-dimensional case": [[45, "generalizing-the-above-one-dimensional-case"]], "Generalizing the fitting procedure as a linear algebra problem": [[35, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [35, "id1"]], "Generative Adversarial Networks": [[5, "generative-adversarial-networks"]], "Generative Models": [[5, "generative-models"]], "Geometric Interpretation and link with Singular Value Decomposition": [[12, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting serious, the  back propagation equations for a neural network": [[42, "getting-serious-the-back-propagation-equations-for-a-neural-network"]], "Getting started with Jax, note the way we import numpy": [[22, "getting-started-with-jax-note-the-way-we-import-numpy"], [41, "getting-started-with-jax-note-the-way-we-import-numpy"]], "Gradient Boosting, Classification Example": [[11, "gradient-boosting-classification-example"], [48, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[11, "gradient-boosting-examples-of-regression"], [48, "gradient-boosting-examples-of-regression"]], "Gradient Boosting, algorithm": [[48, "gradient-boosting-algorithm"]], "Gradient Clipping": [[2, "gradient-clipping"], [42, "gradient-clipping"], [43, "gradient-clipping"]], "Gradient Descent Example": [[39, "id1"], [40, "id8"]], "Gradient boosting, making our own code for a regression case": [[48, "gradient-boosting-making-our-own-code-for-a-regression-case"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[11, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"], [48, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[3, "gradient-descent"], [44, "gradient-descent"]], "Gradient descent and Logistic regression": [[0, "gradient-descent-and-logistic-regression"], [41, "gradient-descent-and-logistic-regression"]], "Gradient descent and Ridge": [[39, "gradient-descent-and-ridge"], [40, "gradient-descent-and-ridge"]], "Gradient descent example": [[39, "gradient-descent-example"], [40, "gradient-descent-example"]], "Gradient expressions": [[42, "gradient-expressions"], [43, "gradient-expressions"]], "Gradient method": [[40, "gradient-method"]], "Gradients of loss functions": [[46, "gradients-of-loss-functions"]], "Grading": [[33, "grading"], [35, "grading"]], "Grid Search": [[39, "grid-search"]], "Growing a classification tree": [[47, "growing-a-classification-tree"], [48, "growing-a-classification-tree"]], "Hidden layers": [[42, "hidden-layers"], [43, "hidden-layers"]], "Homogeneous data": [[42, "homogeneous-data"], [43, "homogeneous-data"]], "Housing data, the code": [[1, "housing-data-the-code"]], "How do we set it up?": [[47, "how-do-we-set-it-up"]], "How to do image compression before the era of deep learning": [[45, "how-to-do-image-compression-before-the-era-of-deep-learning"]], "How to set up the cross-validation for Ridge and/or Lasso": [[39, "how-to-set-up-the-cross-validation-for-ridge-and-or-lasso"]], "Hyperplanes and all that": [[9, "hyperplanes-and-all-that"]], "Identifying Terms": [[38, "identifying-terms"]], "Illustration of a single perceptron model and a multi-perceptron model": [[41, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"], [42, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"]], "Implementing a memory cell in a neural network": [[46, "implementing-a-memory-cell-in-a-neural-network"]], "Important Matrix and vector handling packages": [[27, "important-matrix-and-vector-handling-packages"]], "Important observations": [[42, "important-observations"], [43, "important-observations"]], "Important technicalities: More on Rescaling data": [[37, "important-technicalities-more-on-rescaling-data"]], "Importing Keras and Tensorflow": [[45, "importing-keras-and-tensorflow"], [46, "importing-keras-and-tensorflow"]], "Improving gradient descent with momentum": [[40, "improving-gradient-descent-with-momentum"]], "Improving performance": [[2, "improving-performance"], [43, "improving-performance"], [44, "improving-performance"]], "In general not this simple": [[42, "in-general-not-this-simple"]], "In summary": [[33, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[14, "including-stochastic-gradient-descent-with-autograd"], [22, "including-stochastic-gradient-descent-with-autograd"], [40, "including-stochastic-gradient-descent-with-autograd"], [41, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[0, "including-more-classes"], [39, "including-more-classes"]], "Incremental PCA": [[12, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[37, "independent-and-identically-distributed-iid"]], "Independent and Identically Distrubuted (iid)": [[38, "independent-and-identically-distrubuted-iid"]], "Input gate": [[46, "input-gate"]], "Inputs to the activation function": [[42, "inputs-to-the-activation-function"], [43, "inputs-to-the-activation-function"]], "Insights from the paper by Glorot and Bengio": [[42, "insights-from-the-paper-by-glorot-and-bengio"], [43, "insights-from-the-paper-by-glorot-and-bengio"]], "Installing R, C++, cython or Julia": [[35, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[35, "installing-r-c-cython-numba-etc"]], "Instructor information": [[33, "instructor-information"]], "Interpretations and optimizing our parameters": [[35, "interpretations-and-optimizing-our-parameters"], [35, "id2"], [35, "id3"], [36, "interpretations-and-optimizing-our-parameters"], [36, "id1"], [36, "id2"]], "Interpretations of Bayes\u2019 Theorem": [[37, "interpretations-of-bayes-theorem"], [38, "interpretations-of-bayes-theorem"]], "Interpreting the Ridge results": [[36, "interpreting-the-ridge-results"], [37, "interpreting-the-ridge-results"]], "Introducing JAX": [[14, "introducing-jax"], [22, "introducing-jax"], [40, "introducing-jax"], [41, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[12, "introducing-the-covariance-and-correlation-functions"], [36, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[1, "introduction"], [7, "introduction"], [26, "introduction"], [27, "introduction"]], "Introduction to Neural networks": [[41, "introduction-to-neural-networks"], [42, "introduction-to-neural-networks"]], "Introduction to numerical projects": [[28, "introduction-to-numerical-projects"], [29, "introduction-to-numerical-projects"], [30, "introduction-to-numerical-projects"]], "Inverse of Rectangular Matrix": [[37, "inverse-of-rectangular-matrix"]], "Is the Logistic activation function (Sigmoid)  our choice?": [[42, "is-the-logistic-activation-function-sigmoid-our-choice"], [43, "is-the-logistic-activation-function-sigmoid-our-choice"]], "Iterative Fitting, Classification and AdaBoost": [[11, "iterative-fitting-classification-and-adaboost"], [47, "iterative-fitting-classification-and-adaboost"], [48, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[11, "iterative-fitting-regression-and-squared-error-cost-function"], [47, "iterative-fitting-regression-and-squared-error-cost-function"], [48, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[12, "kernel-pca"]], "Kernels and non-linearity": [[9, "kernels-and-non-linearity"]], "Key Idea": [[45, "key-idea"], [46, "key-idea"]], "LSTM details": [[46, "lstm-details"]], "LU Decomposition, the inverse of a matrix": [[27, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab  sessions on Tuesday and Wednesday": [[45, "lab-sessions-on-tuesday-and-wednesday"]], "Lab session: Material from last week and relevant for the first project": [[39, "lab-session-material-from-last-week-and-relevant-for-the-first-project"]], "Lab sessions Tuesday and Wednesday": [[41, "lab-sessions-tuesday-and-wednesday"]], "Lab sessions week 39": [[40, "lab-sessions-week-39"]], "Lasso Regression": [[37, "lasso-regression"]], "Lasso and Bayes": [[37, "lasso-and-bayes"], [38, "lasso-and-bayes"]], "Lasso case": [[37, "lasso-case"]], "Layers": [[2, "layers"], [43, "layers"], [44, "layers"], [45, "layers"], [46, "layers"]], "Layers of a CNN": [[45, "layers-of-a-cnn"], [46, "layers-of-a-cnn"]], "Layers used to build CNNs": [[4, "layers-used-to-build-cnns"], [45, "layers-used-to-build-cnns"], [46, "layers-used-to-build-cnns"]], "Layout of a neural network with three hidden layers": [[42, "layout-of-a-neural-network-with-three-hidden-layers"]], "Layout of a neural network with three hidden layers (last later = l=L=4, first layer l=0)": [[43, "layout-of-a-neural-network-with-three-hidden-layers-last-later-l-l-4-first-layer-l-0"]], "Layout of a simple neural network with no hidden layer": [[42, "layout-of-a-simple-neural-network-with-no-hidden-layer"], [43, "layout-of-a-simple-neural-network-with-no-hidden-layer"]], "Layout of a simple neural network with one hidden layer": [[42, "layout-of-a-simple-neural-network-with-one-hidden-layer"], [43, "layout-of-a-simple-neural-network-with-one-hidden-layer"]], "Layout of a simple neural network with two input nodes, one  hidden layer and one output node": [[42, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-and-one-output-node"]], "Layout of a simple neural network with two input nodes, one  hidden layer with two hidden noeds and one output node": [[43, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-with-two-hidden-noeds-and-one-output-node"]], "Layout of input to first hidden layer l=1 from input layer l=0": [[43, "layout-of-input-to-first-hidden-layer-l-1-from-input-layer-l-0"]], "Learning outcomes": [[26, "learning-outcomes"], [35, "learning-outcomes"]], "Learning rate methods": [[43, "learning-rate-methods"], [44, "learning-rate-methods"]], "Lecture Monday  October 21": [[44, "lecture-monday-october-21"]], "Lecture Monday  October 7": [[42, "lecture-monday-october-7"]], "Lecture Monday September 23": [[40, "lecture-monday-september-23"]], "Lecture Monday September 23, Optimization, the central part of any Machine Learning algortithm": [[40, "lecture-monday-september-23-optimization-the-central-part-of-any-machine-learning-algortithm"]], "Lecture Monday September 30, 2024": [[41, "lecture-monday-september-30-2024"]], "Lecture October 14, 2024": [[43, "lecture-october-14-2024"]], "Lectures and ComputerLab": [[35, "lectures-and-computerlab"]], "Limitations of NNs": [[42, "limitations-of-nns"], [43, "limitations-of-nns"]], "Limitations of supervised learning with deep networks": [[2, "limitations-of-supervised-learning-with-deep-networks"], [42, "limitations-of-supervised-learning-with-deep-networks"], [43, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[27, null]], "Linear Regression": [[1, null]], "Linear Regression Problems": [[36, "linear-regression-problems"]], "Linear Regression and  the SVD": [[37, "linear-regression-and-the-svd"]], "Linear Regression code, Intercept handling first": [[36, "linear-regression-code-intercept-handling-first"]], "Linear Regression, basic elements": [[1, "linear-regression-basic-elements"]], "Linear classifier": [[39, "linear-classifier"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[6, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[6, "linking-the-regression-analysis-with-a-statistical-interpretation"], [37, "linking-the-regression-analysis-with-a-statistical-interpretation"], [38, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with RNNs": [[46, "linking-with-rnns"]], "Linking with the SVD": [[6, "linking-with-the-svd"], [36, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[34, "links-to-relevant-courses-at-the-university-of-oslo"]], "List of contents:": [[45, "list-of-contents"], [46, "list-of-contents"]], "Logistic Regression": [[8, null], [8, "id1"], [39, "logistic-regression"]], "Logistic function as the root of problems": [[42, "logistic-function-as-the-root-of-problems"], [43, "logistic-function-as-the-root-of-problems"]], "MNIST and GANs": [[5, "mnist-and-gans"]], "Machine Learning": [[35, "machine-learning"]], "Machine learning": [[26, "machine-learning"]], "Main textbooks": [[35, "main-textbooks"]], "Making a tree": [[10, "making-a-tree"], [47, "making-a-tree"], [48, "making-a-tree"]], "Making an  ADAboost code yourself": [[48, "making-an-adaboost-code-yourself"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[11, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"], [47, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"], [48, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[36, "making-your-own-test-train-splitting"]], "Marginal Probability": [[37, "marginal-probability"], [38, "marginal-probability"]], "Material for Lecture Monday November 4": [[46, "material-for-lecture-monday-november-4"]], "Material for Lecture Monday October 28": [[45, "material-for-lecture-monday-october-28"]], "Material for lecture Monday September 16": [[39, "material-for-lecture-monday-september-16"]], "Material for lecture Monday September 2": [[37, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 9": [[38, "material-for-lecture-monday-september-9"]], "Material for lecture Monday, August 26": [[36, "material-for-lecture-monday-august-26"]], "Material for the active learning sessions Tuesday and Wednesday": [[37, "material-for-the-active-learning-sessions-tuesday-and-wednesday"]], "Material for the active learning sessions on Tuesday and Wednesday": [[42, "material-for-the-active-learning-sessions-on-tuesday-and-wednesday"], [43, "material-for-the-active-learning-sessions-on-tuesday-and-wednesday"]], "Material for the lab sessions": [[38, "material-for-the-lab-sessions"]], "Material for the lab sessions, additional ways to present classification results and other practicalities": [[46, "material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities"]], "Material for the lecture on Monday October 7, 2024": [[42, "material-for-the-lecture-on-monday-october-7-2024"]], "Mathematical Interpretation of Ordinary Least Squares": [[6, "mathematical-interpretation-of-ordinary-least-squares"], [36, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical model": [[41, "mathematical-model"], [41, "id2"], [41, "id3"], [41, "id4"], [41, "id5"]], "Mathematical optimization of convex functions": [[9, "mathematical-optimization-of-convex-functions"]], "Mathematical setup": [[46, "mathematical-setup"]], "Mathematics of CNNs": [[4, "mathematics-of-cnns"], [45, "mathematics-of-cnns"]], "Mathematics of deep learning": [[42, "mathematics-of-deep-learning"], [43, "mathematics-of-deep-learning"], [44, "mathematics-of-deep-learning"]], "Mathematics of deep learning and neural networks": [[42, "mathematics-of-deep-learning-and-neural-networks"]], "Mathematics of the SVD and implications": [[6, "mathematics-of-the-svd-and-implications"], [36, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[35, "matrices-in-python"]], "Matrix  multiplication": [[2, "matrix-multiplication"], [43, "matrix-multiplication"], [44, "matrix-multiplication"]], "Matrix multiplications": [[43, "matrix-multiplications"], [44, "matrix-multiplications"]], "Matrix-vector notation": [[41, "matrix-vector-notation"]], "Matrix-vector notation  and activation": [[13, "matrix-vector-notation-and-activation"], [41, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[37, "maximum-likelihood-estimation-mle"], [38, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[39, "maximum-likelihood"]], "Meet the  covariance!": [[32, "meet-the-covariance"]], "Meet the Covariance Matrix": [[6, "meet-the-covariance-matrix"], [36, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[36, "meet-the-hessian-matrix"]], "Meet the Pandas": [[35, "meet-the-pandas"]], "Memory considerations": [[45, "memory-considerations"]], "Min-Max Scaling": [[36, "min-max-scaling"]], "Minimization process": [[44, "minimization-process"]], "Minimizing the cost function using gradient descent and automatic differentiation": [[44, "minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation"]], "Minimizing the cross entropy": [[0, "minimizing-the-cross-entropy"], [39, "minimizing-the-cross-entropy"]], "Minor rewrite": [[46, "minor-rewrite"]], "Momentum based GD": [[14, "momentum-based-gd"], [22, "momentum-based-gd"], [40, "momentum-based-gd"], [41, "momentum-based-gd"]], "Momentum parameter": [[40, "momentum-parameter"], [41, "momentum-parameter"]], "More LSTM details": [[46, "more-lstm-details"]], "More autograd": [[40, "more-autograd"], [41, "more-autograd"]], "More bagging": [[47, "more-bagging"], [48, "more-bagging"]], "More basic Statistics and Bayes\u2019 theorem": [[37, "more-basic-statistics-and-bayes-theorem"], [38, "more-basic-statistics-and-bayes-theorem"]], "More classes": [[0, "more-classes"], [39, "more-classes"]], "More complicated Example: The Ising model": [[7, "more-complicated-example-the-ising-model"]], "More complicated function": [[42, "more-complicated-function"]], "More complicated functions using the elements of their arguments directly": [[40, "more-complicated-functions-using-the-elements-of-their-arguments-directly"], [41, "more-complicated-functions-using-the-elements-of-their-arguments-directly"]], "More considerations": [[42, "more-considerations"], [43, "more-considerations"]], "More details": [[44, "more-details"], [44, "id6"]], "More examples on bootstrap and cross-validation and errors": [[38, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[36, "more-interpretations"], [37, "more-interpretations"]], "More limitations": [[42, "more-limitations"], [43, "more-limitations"]], "More on Dimensionalities": [[4, "more-on-dimensionalities"], [45, "more-on-dimensionalities"]], "More on Rescaling data": [[7, "more-on-rescaling-data"]], "More on Steepest descent": [[39, "more-on-steepest-descent"], [40, "more-on-steepest-descent"]], "More on activation functions, output layers": [[42, "more-on-activation-functions-output-layers"], [43, "more-on-activation-functions-output-layers"], [44, "more-on-activation-functions-output-layers"]], "More on convex functions": [[39, "more-on-convex-functions"], [40, "more-on-convex-functions"]], "More on momentum based approaches": [[40, "more-on-momentum-based-approaches"], [41, "more-on-momentum-based-approaches"]], "More on the general approximation theorem": [[42, "more-on-the-general-approximation-theorem"]], "More preprocessing": [[36, "more-preprocessing"]], "More preprocessing examples, two-dimensional example, the Franke function": [[36, "more-preprocessing-examples-two-dimensional-example-the-franke-function"]], "More technicalities": [[44, "more-technicalities"]], "More thinking": [[36, "more-thinking"]], "More top-down perspectives": [[42, "more-top-down-perspectives"], [43, "more-top-down-perspectives"]], "Multiclass classification": [[43, "multiclass-classification"], [44, "multiclass-classification"]], "Multilayer perceptrons": [[13, "multilayer-perceptrons"], [41, "multilayer-perceptrons"], [42, "multilayer-perceptrons"]], "Multivariable functions": [[42, "multivariable-functions"]], "Network requirements": [[3, "network-requirements"], [44, "network-requirements"]], "Neural Networks vs CNNs": [[4, "neural-networks-vs-cnns"], [45, "neural-networks-vs-cnns"], [46, "neural-networks-vs-cnns"]], "Neural network types": [[41, "neural-network-types"], [42, "neural-network-types"]], "Neural networks": [[13, null]], "New expression for the derivative": [[42, "new-expression-for-the-derivative"]], "New image (or volume)": [[45, "new-image-or-volume"]], "New vector": [[45, "new-vector"]], "Note about SVD Calculations": [[36, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[37, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[32, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[27, "numpy-and-arrays"], [35, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[35, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[39, "optimization-and-deep-learning"]], "Optimization, the central part of any Machine Learning algortithm": [[14, null], [39, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimized Convolution2DLayer": [[45, "optimized-convolution2dlayer"], [46, "optimized-convolution2dlayer"]], "Optimizing our parameters": [[35, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[35, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[2, "optimizing-the-cost-function"], [43, "optimizing-the-cost-function"], [44, "optimizing-the-cost-function"]], "Optimizing the parameters": [[42, "optimizing-the-parameters"], [43, "optimizing-the-parameters"]], "Ordinary Differential Equations first": [[44, "ordinary-differential-equations-first"]], "Organizing our data": [[1, "organizing-our-data"], [35, "organizing-our-data"]], "Other Matrix and Vector Operations": [[27, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[5, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[35, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[35, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other ingredients of a neural network": [[42, "other-ingredients-of-a-neural-network"]], "Other measures in classification studies: Cancer Data  again": [[0, "other-measures-in-classification-studies-cancer-data-again"], [39, "other-measures-in-classification-studies-cancer-data-again"]], "Other parameters": [[42, "other-parameters"]], "Other popular texts": [[35, "other-popular-texts"]], "Other techniques": [[12, "other-techniques"]], "Other types of networks": [[13, "other-types-of-networks"], [41, "other-types-of-networks"], [42, "other-types-of-networks"]], "Other useful relations": [[36, "other-useful-relations"]], "Other ways of visualizing the trees": [[10, "other-ways-of-visualizing-the-trees"], [47, "other-ways-of-visualizing-the-trees"], [48, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[35, "our-model-for-the-nuclear-binding-energies"]], "Output gate": [[46, "output-gate"]], "Output layer": [[42, "output-layer"], [43, "output-layer"]], "Overarching aims of the exercises this week": [[18, "overarching-aims-of-the-exercises-this-week"], [19, "overarching-aims-of-the-exercises-this-week"], [20, "overarching-aims-of-the-exercises-this-week"], [21, "overarching-aims-of-the-exercises-this-week"], [22, "overarching-aims-of-the-exercises-this-week"], [23, "overarching-aims-of-the-exercises-this-week"], [24, "overarching-aims-of-the-exercises-this-week"], [25, "overarching-aims-of-the-exercises-this-week"]], "Overarching view of a neural network": [[42, "overarching-view-of-a-neural-network"]], "Overview of first week": [[35, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent": [[40, "overview-video-on-stochastic-gradient-descent"], [41, "overview-video-on-stochastic-gradient-descent"]], "Own code for Ordinary Least Squares": [[35, "own-code-for-ordinary-least-squares"], [36, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[12, "pca-and-scikit-learn"]], "Padding": [[45, "padding"]], "Pandas AI": [[35, "pandas-ai"]], "Parameters of neural networks": [[42, "parameters-of-neural-networks"]], "Parameters to train, common settings": [[45, "parameters-to-train-common-settings"]], "Part a)": [[30, "part-a"]], "Part a) : Ordinary Least Square (OLS) on the Franke function": [[28, "part-a-ordinary-least-square-ols-on-the-franke-function"]], "Part a), setting up the problem": [[30, "part-a-setting-up-the-problem"]], "Part a): Write your own Stochastic Gradient Descent  code, first step": [[29, "part-a-write-your-own-stochastic-gradient-descent-code-first-step"]], "Part b)": [[30, "part-b"], [30, "id1"]], "Part b): Adding Ridge regression for  the Franke function": [[28, "part-b-adding-ridge-regression-for-the-franke-function"]], "Part b): Writing your own Neural Network code": [[29, "part-b-writing-your-own-neural-network-code"]], "Part c)": [[30, "part-c"]], "Part c) Neural networks": [[30, "part-c-neural-networks"]], "Part c): Adding Lasso for the Franke function": [[28, "part-c-adding-lasso-for-the-franke-function"]], "Part c): Testing different activation functions": [[29, "part-c-testing-different-activation-functions"]], "Part d)": [[30, "part-d"]], "Part d) Neural network complexity": [[30, "part-d-neural-network-complexity"]], "Part d): Classification  analysis using neural networks": [[29, "part-d-classification-analysis-using-neural-networks"]], "Part d): Paper and pencil part": [[28, "part-d-paper-and-pencil-part"]], "Part e)": [[30, "part-e"], [30, "id2"]], "Part e): Bias-variance trade-off and resampling techniques": [[28, "part-e-bias-variance-trade-off-and-resampling-techniques"]], "Part e): Write your Logistic Regression code, final step": [[29, "part-e-write-your-logistic-regression-code-final-step"]], "Part f) Critical evaluation of the various algorithms": [[29, "part-f-critical-evaluation-of-the-various-algorithms"]], "Part f):  Cross-validation as resampling techniques, adding more complexity": [[28, "part-f-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Part g): Analysis of real data": [[28, "part-g-analysis-of-real-data"]], "Partial Differential Equations": [[3, "partial-differential-equations"], [44, "partial-differential-equations"]], "Paths for project 3": [[30, "paths-for-project-3"]], "Plan for week 39, September 23-27, 2024": [[40, "plan-for-week-39-september-23-27-2024"]], "Plan for week 41, October 7-11": [[42, "plan-for-week-41-october-7-11"]], "Plan for week 44": [[45, "plan-for-week-44"]], "Plan for week 46": [[47, "plan-for-week-46"]], "Plan for week 47": [[48, "plan-for-week-47"]], "Plans for the lab sessions": [[39, "plans-for-the-lab-sessions"]], "Plans for week 35": [[36, "plans-for-week-35"]], "Plans for week 36": [[37, "plans-for-week-36"]], "Plans for week 37, lab sessions": [[38, "plans-for-week-37-lab-sessions"]], "Plans for week 37, lecture Monday": [[38, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 16": [[39, "plans-for-week-38-lecture-monday-september-16"]], "Plans for week 40": [[41, "plans-for-week-40"]], "Plans for week 43": [[44, "plans-for-week-43"]], "Plans for week 45": [[46, "plans-for-week-45"]], "Plotting the Histogram": [[38, "plotting-the-histogram"]], "Plotting the mean value for each group": [[39, "plotting-the-mean-value-for-each-group"]], "Pooling": [[45, "pooling"]], "Pooling Layer": [[45, "pooling-layer"], [46, "pooling-layer"]], "Pooling arithmetic": [[45, "pooling-arithmetic"]], "Pooling types (From Raschka et al)": [[45, "pooling-types-from-raschka-et-al"]], "Practical tips": [[14, "practical-tips"], [22, "practical-tips"], [40, "practical-tips"], [41, "practical-tips"]], "Practicalities": [[33, "practicalities"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[28, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[5, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[36, "preprocessing-our-data"]], "Prerequisites": [[35, "prerequisites"]], "Prerequisites and background": [[26, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[4, "prerequisites-collect-and-pre-process-data"], [45, "prerequisites-collect-and-pre-process-data"], [46, "prerequisites-collect-and-pre-process-data"]], "Printing out as text": [[47, "printing-out-as-text"], [48, "printing-out-as-text"]], "Probability Distribution Functions": [[32, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[39, "program-example-for-gradient-descent-with-ridge-regression"], [40, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[14, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 7 (midnight), 2024": [[28, null]], "Project 2 on Machine Learning, deadline November 4 (Midnight)": [[29, null]], "Project 3 on Machine Learning, deadline December 9 (midnight), 2024": [[30, null]], "Properties of PDFs": [[32, "properties-of-pdfs"]], "Pros and cons of trees, pros": [[10, "pros-and-cons-of-trees-pros"], [47, "pros-and-cons-of-trees-pros"], [48, "pros-and-cons-of-trees-pros"]], "Pruning the tree": [[47, "pruning-the-tree"], [48, "pruning-the-tree"]], "Python installers": [[26, "python-installers"], [35, "python-installers"]], "RMS prop": [[14, "rms-prop"], [40, "rms-prop"], [41, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[22, "rmsprop-algorithm-taken-from-goodfellow-et-al"], [41, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[22, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"], [40, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"], [41, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "RNNs": [[46, "rnns"]], "RNNs in more detail": [[46, "rnns-in-more-detail"]], "RNNs in more detail, part 2": [[46, "rnns-in-more-detail-part-2"]], "RNNs in more detail, part 3": [[46, "rnns-in-more-detail-part-3"]], "RNNs in more detail, part 4": [[46, "rnns-in-more-detail-part-4"]], "RNNs in more detail, part 5": [[46, "rnns-in-more-detail-part-5"]], "RNNs in more detail, part 6": [[46, "rnns-in-more-detail-part-6"]], "RNNs in more detail, part 7": [[46, "rnns-in-more-detail-part-7"]], "Random Forest Algorithm": [[47, "random-forest-algorithm"], [48, "random-forest-algorithm"]], "Random Forests Compared with other Methods on the Cancer Data": [[47, "random-forests-compared-with-other-methods-on-the-cancer-data"], [48, "random-forests-compared-with-other-methods-on-the-cancer-data"]], "Random Numbers": [[32, "random-numbers"]], "Random forests": [[11, "random-forests"], [47, "random-forests"], [48, "random-forests"]], "Randomized Grid Search": [[39, "randomized-grid-search"]], "Randomized PCA": [[12, "randomized-pca"]], "Reading material": [[35, "reading-material"]], "Reading recommendations": [[42, "reading-recommendations"], [43, "reading-recommendations"], [44, "reading-recommendations"]], "Reading recommendations:": [[36, "reading-recommendations"]], "Reading suggestions week 34": [[35, "reading-suggestions-week-34"]], "Recurrent neural networks": [[13, "recurrent-neural-networks"], [41, "recurrent-neural-networks"], [42, "recurrent-neural-networks"]], "Recurrent neural networks (RNNs): Overarching view": [[46, "recurrent-neural-networks-rnns-overarching-view"]], "Recurrent neural networks: Overarching view": [[5, null]], "Reducing the number of degrees of freedom, overarching view": [[1, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [36, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reducing the number of operations": [[42, "reducing-the-number-of-operations"]], "Reformulating the problem": [[3, "reformulating-the-problem"], [44, "reformulating-the-problem"]], "Regression Case": [[11, "regression-case"], [48, "regression-case"]], "Regression analysis and resampling methods": [[28, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[35, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[35, "regression-analysis-overarching-aims-ii"]], "Regression trees": [[47, "regression-trees"], [48, "regression-trees"]], "Regular NNs don\u2019t scale well to full images": [[45, "regular-nns-dont-scale-well-to-full-images"], [46, "regular-nns-dont-scale-well-to-full-images"]], "Regularization": [[2, "regularization"], [43, "regularization"], [44, "regularization"]], "Relevance": [[41, "relevance"], [42, "relevance"], [43, "relevance"]], "Remarks on the speed": [[45, "remarks-on-the-speed"], [46, "remarks-on-the-speed"]], "Reminder on Statistics": [[7, "reminder-on-statistics"]], "Reminder on books with hands-on material and codes": [[42, "reminder-on-books-with-hands-on-material-and-codes"], [43, "reminder-on-books-with-hands-on-material-and-codes"], [44, "reminder-on-books-with-hands-on-material-and-codes"]], "Reminder on the chain rule and gradients": [[42, "reminder-on-the-chain-rule-and-gradients"]], "Replace or not": [[14, "replace-or-not"], [40, "replace-or-not"], [41, "replace-or-not"]], "Required Technologies": [[26, "required-technologies"]], "Resampling Methods": [[7, null]], "Resampling approaches can be computationally expensive": [[38, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[7, "id1"], [38, "resampling-methods"], [38, "id2"]], "Resampling methods: Bootstrap": [[38, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[38, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[38, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[38, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[38, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[36, "residual-error"]], "Resources on differential equations and deep learning": [[3, "resources-on-differential-equations-and-deep-learning"], [44, "resources-on-differential-equations-and-deep-learning"]], "Revisiting our Linear Regression Solvers": [[14, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[39, "revisiting-our-logistic-regression-case"], [40, "revisiting-our-logistic-regression-case"]], "Revisiting our first homework": [[39, "revisiting-our-first-homework"], [40, "revisiting-our-first-homework"]], "Rewriting as dot products": [[45, "rewriting-as-dot-products"]], "Rewriting the Covariance and/or Correlation Matrix": [[36, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[38, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[35, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[35, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[37, "ridge-regression"]], "Ridge and Bayes": [[37, "ridge-and-bayes"], [38, "ridge-and-bayes"]], "Ridge and LASSO Regression": [[36, "ridge-and-lasso-regression"], [37, "ridge-and-lasso-regression"]], "Ridge and Lasso Regression": [[6, null], [6, "id1"]], "Running with Keras": [[45, "running-with-keras"], [46, "running-with-keras"]], "SGD example": [[40, "sgd-example"], [41, "sgd-example"]], "SVD analysis": [[37, "svd-analysis"]], "Same code but now with momentum gradient descent": [[14, "same-code-but-now-with-momentum-gradient-descent"], [22, "same-code-but-now-with-momentum-gradient-descent"], [22, "id1"], [40, "same-code-but-now-with-momentum-gradient-descent"], [40, "id9"], [40, "id10"], [41, "same-code-but-now-with-momentum-gradient-descent"], [41, "id1"]], "Schedule first week": [[35, "schedule-first-week"]], "Schedulers": [[45, "schedulers"], [46, "schedulers"]], "Schematic Regression Procedure": [[10, "schematic-regression-procedure"], [47, "schematic-regression-procedure"], [48, "schematic-regression-procedure"]], "Searching for Optimal Regularization Parameters \\lambda": [[39, "searching-for-optimal-regularization-parameters-lambda"]], "Second moment of the gradient": [[40, "second-moment-of-the-gradient"], [41, "second-moment-of-the-gradient"]], "Sequential data only?": [[46, "sequential-data-only"]], "Set up  the model": [[45, "set-up-the-model"], [46, "set-up-the-model"]], "Setting it up": [[45, "setting-it-up"], [46, "setting-it-up"]], "Setting up a Multi-layer perceptron model for classification": [[43, "setting-up-a-multi-layer-perceptron-model-for-classification"], [44, "setting-up-a-multi-layer-perceptron-model-for-classification"]], "Setting up the Back propagation algorithm": [[13, "setting-up-the-back-propagation-algorithm"]], "Setting up the Back propagation algorithm, part 3": [[42, "setting-up-the-back-propagation-algorithm-part-3"], [43, "setting-up-the-back-propagation-algorithm-part-3"], [44, "setting-up-the-back-propagation-algorithm-part-3"]], "Setting up the Matrix to be inverted": [[36, "setting-up-the-matrix-to-be-inverted"]], "Setting up the back propagation algorithm": [[42, "setting-up-the-back-propagation-algorithm"]], "Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations": [[43, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"], [44, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"]], "Setting up the back propagation algorithm, part 1": [[43, "setting-up-the-back-propagation-algorithm-part-1"], [44, "setting-up-the-back-propagation-algorithm-part-1"]], "Setting up the back propagation algorithm, part 2": [[42, "setting-up-the-back-propagation-algorithm-part-2"], [43, "setting-up-the-back-propagation-algorithm-part-2"], [44, "setting-up-the-back-propagation-algorithm-part-2"]], "Setting up the code": [[44, "setting-up-the-code"]], "Setting up the equations for a neural network": [[42, "setting-up-the-equations-for-a-neural-network"], [43, "setting-up-the-equations-for-a-neural-network"]], "Setting up the network using Autograd": [[44, "setting-up-the-network-using-autograd"]], "Setting up the network using Autograd; The full program": [[3, "setting-up-the-network-using-autograd-the-full-program"], [44, "setting-up-the-network-using-autograd-the-full-program"]], "Setting up the network using Autograd; The trial solution": [[44, "setting-up-the-network-using-autograd-the-trial-solution"]], "Setting up the problem": [[44, "setting-up-the-problem"]], "Setup of Network": [[44, "setup-of-network"]], "Similar (second order function now) problem but now with AdaGrad": [[14, "similar-second-order-function-now-problem-but-now-with-adagrad"], [22, "similar-second-order-function-now-problem-but-now-with-adagrad"], [40, "similar-second-order-function-now-problem-but-now-with-adagrad"], [41, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[10, "simple-python-code-to-read-in-data-and-perform-classification"], [47, "simple-python-code-to-read-in-data-and-perform-classification"], [48, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple Voting Example, head or tail": [[47, "simple-voting-example-head-or-tail"], [48, "simple-voting-example-head-or-tail"]], "Simple case": [[36, "simple-case"]], "Simple code for solving the above problem": [[37, "simple-code-for-solving-the-above-problem"]], "Simple example": [[39, "simple-example"], [42, "simple-example"]], "Simple example code": [[40, "simple-example-code"], [41, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[37, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[39, "simple-geometric-interpretation"], [40, "simple-geometric-interpretation"]], "Simple implementation of GD for OLS, Ridge and Lasso": [[41, "simple-implementation-of-gd-for-ols-ridge-and-lasso"]], "Simple linear regression model using scikit-learn": [[1, "simple-linear-regression-model-using-scikit-learn"], [35, "simple-linear-regression-model-using-scikit-learn"]], "Simple neural network and the  back propagation equations": [[42, "simple-neural-network-and-the-back-propagation-equations"], [43, "simple-neural-network-and-the-back-propagation-equations"]], "Simple program": [[39, "simple-program"], [40, "simple-program"]], "Simpler examples first, and automatic differentiation": [[42, "simpler-examples-first-and-automatic-differentiation"]], "Slightly different approach": [[40, "slightly-different-approach"], [41, "slightly-different-approach"]], "Smarter way of evaluating the above function": [[42, "smarter-way-of-evaluating-the-above-function"]], "Software and needed installations": [[28, "software-and-needed-installations"], [30, "software-and-needed-installations"], [35, "software-and-needed-installations"]], "Solving Differential Equations  with Deep Learning": [[3, null]], "Solving differential equations  with Deep Learning": [[44, "solving-differential-equations-with-deep-learning"]], "Solving differential equations with RNNs": [[46, "solving-differential-equations-with-rnns"]], "Solving partial differential equations with neural networks": [[30, "solving-partial-differential-equations-with-neural-networks"]], "Solving the equation using Autograd": [[44, "solving-the-equation-using-autograd"]], "Solving the one dimensional Poisson equation": [[3, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation - the full program using Autograd": [[44, "solving-the-wave-equation-the-full-program-using-autograd"]], "Solving the wave equation with Neural Networks": [[3, "solving-the-wave-equation-with-neural-networks"]], "Solving using Newton-Raphson\u2019s method": [[39, "solving-using-newton-raphson-s-method"], [40, "solving-using-newton-raphson-s-method"]], "Some famous Matrices": [[27, "some-famous-matrices"]], "Some parallels from real analysis": [[42, "some-parallels-from-real-analysis"]], "Some selected properties": [[39, "some-selected-properties"]], "Some simple problems": [[14, "some-simple-problems"], [39, "some-simple-problems"], [40, "some-simple-problems"]], "Some useful matrix and vector expressions": [[36, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[1, "splitting-our-data-in-training-and-test-data"], [35, "splitting-our-data-in-training-and-test-data"], [36, "splitting-our-data-in-training-and-test-data"]], "Squared-Error Example and Iterative Fitting": [[47, "squared-error-example-and-iterative-fitting"], [48, "squared-error-example-and-iterative-fitting"]], "Standard Approach based on the Normal Distribution": [[38, "standard-approach-based-on-the-normal-distribution"]], "Standard imports first": [[47, "standard-imports-first"], [48, "standard-imports-first"]], "Standard steepest descent": [[14, "standard-steepest-descent"], [40, "standard-steepest-descent"]], "Statistical analysis": [[38, "statistical-analysis"]], "Statistical analysis and optimization of data": [[26, "statistical-analysis-and-optimization-of-data"], [35, "statistical-analysis-and-optimization-of-data"]], "Steepest Descent Example": [[48, "steepest-descent-example"]], "Steepest descent": [[14, "steepest-descent"], [39, "steepest-descent"], [40, "steepest-descent"]], "Steepest descent  method": [[40, "steepest-descent-method"], [40, "id1"]], "Steepest descent example": [[40, "steepest-descent-example"]], "Still thinking": [[36, "still-thinking"]], "Stochastic Gradient Descent": [[40, "stochastic-gradient-descent"], [41, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[14, "stochastic-gradient-descent-sgd"], [40, "stochastic-gradient-descent-sgd"], [41, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[32, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strong correlations": [[45, "strong-correlations"], [46, "strong-correlations"]], "Suggested reading and videos": [[39, "suggested-reading-and-videos"]], "Suggested readings and videos": [[41, "suggested-readings-and-videos"]], "Summarizing: Performing a general discrete convolution (From Raschka et al)": [[45, "summarizing-performing-a-general-discrete-convolution-from-raschka-et-al"]], "Summary from last week, using gradient descent methods, limitations": [[41, "summary-from-last-week-using-gradient-descent-methods-limitations"]], "Summary of RNNs": [[46, "summary-of-rnns"]], "Summary of a  typical RNN": [[46, "summary-of-a-typical-rnn"]], "Summing up": [[38, "summing-up"]], "Support Vector Machines, overarching aims": [[9, null]], "Systematic reduction": [[4, "systematic-reduction"], [45, "systematic-reduction"], [46, "systematic-reduction"]], "Teachers": [[35, "teachers"]], "Teachers and Grading": [[33, null]], "Teaching Assistants Fall semester 2023": [[33, "teaching-assistants-fall-semester-2023"]], "Teaching schedule with links to material": [[31, null]], "Technicalities": [[44, "technicalities"]], "Tensorflow": [[43, "tensorflow"], [44, "tensorflow"]], "Test Function for what happens with OLS, Ridge and Lasso": [[37, "test-function-for-what-happens-with-ols-ridge-and-lasso"]], "Testing the Means Squared Error as function of Complexity": [[1, "testing-the-means-squared-error-as-function-of-complexity"], [36, "testing-the-means-squared-error-as-function-of-complexity"]], "Testing the XOR gate and other gates": [[43, "testing-the-xor-gate-and-other-gates"], [44, "testing-the-xor-gate-and-other-gates"]], "Textbooks": [[34, null]], "The  back propagation equations for a neural network": [[43, "the-back-propagation-equations-for-a-neural-network"]], "The Algorithm before theorem": [[12, "the-algorithm-before-theorem"]], "The Boston housing data example": [[1, "the-boston-housing-data-example"]], "The Breast Cancer Data, now with Keras": [[2, "the-breast-cancer-data-now-with-keras"], [43, "the-breast-cancer-data-now-with-keras"], [44, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[10, "the-cart-algorithm-for-classification"], [47, "the-cart-algorithm-for-classification"], [48, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[10, "the-cart-algorithm-for-regression"], [47, "the-cart-algorithm-for-regression"], [48, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[4, "the-cifar01-data-set"], [45, "the-cifar01-data-set"], [46, "the-cifar01-data-set"]], "The Central Limit Theorem": [[38, "the-central-limit-theorem"]], "The Convolutional Neural Network (CNN)": [[45, "the-convolutional-neural-network-cnn"], [46, "the-convolutional-neural-network-cnn"]], "The Hessian matrix": [[39, "the-hessian-matrix"], [40, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[39, "the-hessian-matrix-for-ridge-regression"], [40, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[36, "the-jacobian"]], "The MNIST dataset again": [[4, "the-mnist-dataset-again"], [45, "the-mnist-dataset-again"], [46, "the-mnist-dataset-again"]], "The Neural Network": [[43, "the-neural-network"], [44, "the-neural-network"]], "The OLS case": [[37, "the-ols-case"]], "The RELU function family": [[2, "the-relu-function-family"], [42, "the-relu-function-family"], [43, "the-relu-function-family"], [44, "the-relu-function-family"]], "The Ridge case": [[37, "the-ridge-case"]], "The SVD example": [[45, "the-svd-example"]], "The SVD, a Fantastic Algorithm": [[36, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[2, "the-softmax-function"], [43, "the-softmax-function"], [44, "the-softmax-function"]], "The Squared-Error again! Steepest Descent": [[48, "the-squared-error-again-steepest-descent"]], "The Table": [[47, "the-table"], [48, "the-table"]], "The \\chi^2 function": [[1, "the-chi-2-function"], [35, "the-chi-2-function"], [35, "id4"], [35, "id5"], [35, "id6"], [35, "id7"], [35, "id8"]], "The analytical solution": [[44, "the-analytical-solution"]], "The approximation theorem in words": [[42, "the-approximation-theorem-in-words"]], "The backward pass is linear": [[46, "the-backward-pass-is-linear"]], "The basic structure of your project": [[30, "the-basic-structure-of-your-project"]], "The bias-variance tradeoff": [[7, "the-bias-variance-tradeoff"], [38, "the-bias-variance-tradeoff"]], "The code": [[35, "the-code"]], "The code for solving the ODE": [[3, "the-code-for-solving-the-ode"], [44, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[36, "the-complete-code-with-a-simple-data-set"]], "The convolution stage": [[45, "the-convolution-stage"]], "The cost function": [[0, "the-cost-function"]], "The cost function rewritten": [[39, "the-cost-function-rewritten"]], "The cost/loss function": [[36, "the-cost-loss-function"]], "The course has two central parts": [[26, "the-course-has-two-central-parts"]], "The derivative of the Logistic funtion": [[42, "the-derivative-of-the-logistic-funtion"], [43, "the-derivative-of-the-logistic-funtion"]], "The derivative of the cost/loss function": [[39, "the-derivative-of-the-cost-loss-function"], [40, "the-derivative-of-the-cost-loss-function"]], "The derivatives": [[42, "the-derivatives"], [43, "the-derivatives"]], "The equations": [[39, "the-equations"], [40, "the-equations"]], "The equations for ordinary least squares": [[36, "the-equations-for-ordinary-least-squares"]], "The equations to solve": [[39, "the-equations-to-solve"], [40, "the-equations-to-solve"]], "The first Case": [[37, "the-first-case"]], "The forget gate": [[46, "the-forget-gate"]], "The function to solve for": [[44, "the-function-to-solve-for"]], "The gradient step": [[40, "the-gradient-step"], [41, "the-gradient-step"]], "The ideal": [[39, "the-ideal"], [40, "the-ideal"]], "The logistic function": [[0, "the-logistic-function"], [8, "the-logistic-function"], [39, "the-logistic-function"]], "The mean squared error and its derivative": [[36, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[9, "the-moons-example"]], "The multilayer  perceptron (MLP)": [[13, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[3, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"], [44, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The optimization problem": [[42, "the-optimization-problem"]], "The ouput layer": [[42, "the-ouput-layer"], [43, "the-ouput-layer"]], "The problem of exploding or vanishing gradients": [[46, "the-problem-of-exploding-or-vanishing-gradients"]], "The problem to solve for": [[44, "the-problem-to-solve-for"]], "The program using Autograd": [[44, "the-program-using-autograd"]], "The same example but now with cross-validation": [[38, "the-same-example-but-now-with-cross-validation"]], "The sensitiveness of the gradient descent": [[39, "the-sensitiveness-of-the-gradient-descent"], [40, "the-sensitiveness-of-the-gradient-descent"]], "The singular value decomposition": [[6, "the-singular-value-decomposition"], [36, "the-singular-value-decomposition"]], "The specific equation to solve for": [[44, "the-specific-equation-to-solve-for"]], "The syntax a.dot(b) when finding the dot product": [[40, "the-syntax-a-dot-b-when-finding-the-dot-product"]], "The training": [[42, "the-training"], [43, "the-training"]], "The trial solution": [[44, "the-trial-solution"], [44, "id4"], [44, "id5"], [44, "id7"]], "The two-dimensional case": [[9, "the-two-dimensional-case"]], "Time decay rate": [[40, "time-decay-rate"], [41, "time-decay-rate"]], "To our real data: nuclear binding energies. Brief reminder on masses and binding energies": [[35, "to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies"]], "To think about, first part": [[36, "to-think-about-first-part"]], "Toeplitz matrices": [[45, "toeplitz-matrices"]], "Topics covered in this course: Statistical analysis and optimization of data": [[35, "topics-covered-in-this-course-statistical-analysis-and-optimization-of-data"]], "Tossing coins": [[47, "tossing-coins"], [48, "tossing-coins"]], "Towards the PCA theorem": [[12, "towards-the-pca-theorem"]], "Train and test datasets": [[2, "train-and-test-datasets"], [43, "train-and-test-datasets"], [44, "train-and-test-datasets"]], "Transforming images": [[45, "transforming-images"]], "Two first-order differential equations": [[46, "two-first-order-differential-equations"]], "Two parameters": [[0, "two-parameters"], [39, "two-parameters"]], "Two-dimensional Objects": [[4, "two-dimensional-objects"]], "Two-dimensional objects": [[45, "two-dimensional-objects"]], "Type of problem": [[3, "type-of-problem"], [44, "type-of-problem"]], "Types of Machine Learning": [[35, "types-of-machine-learning"]], "Understanding what happens": [[38, "understanding-what-happens"]], "Universal approximation theorem": [[42, "universal-approximation-theorem"]], "Unsupported functions": [[40, "unsupported-functions"]], "Updating the gradients": [[42, "updating-the-gradients"], [43, "updating-the-gradients"], [44, "updating-the-gradients"]], "Usage of CNN code": [[45, "usage-of-cnn-code"], [46, "usage-of-cnn-code"]], "Usage of activation functions": [[45, "usage-of-activation-functions"], [46, "usage-of-activation-functions"]], "Usage of cost functions": [[45, "usage-of-cost-functions"], [46, "usage-of-cost-functions"]], "Usage of schedulers": [[45, "usage-of-schedulers"], [46, "usage-of-schedulers"]], "Usage of the above learning rate schedulers": [[43, "usage-of-the-above-learning-rate-schedulers"], [44, "usage-of-the-above-learning-rate-schedulers"]], "Useful Python libraries": [[26, "useful-python-libraries"], [35, "useful-python-libraries"]], "Using Autograd": [[14, "using-autograd"]], "Using Autograd with OLS": [[40, "using-autograd-with-ols"], [41, "using-autograd-with-ols"]], "Using Automatic differentation with OLS": [[22, "using-automatic-differentation-with-ols"]], "Using Automatic differentiation": [[44, "using-automatic-differentiation"]], "Using Keras": [[43, "using-keras"], [44, "using-keras"]], "Using autograd": [[40, "using-autograd"], [41, "using-autograd"]], "Using forward Euler to solve the ODE": [[3, "using-forward-euler-to-solve-the-ode"], [44, "using-forward-euler-to-solve-the-ode"]], "Using gradient descent methods, limitations": [[14, "using-gradient-descent-methods-limitations"], [39, "using-gradient-descent-methods-limitations"], [40, "using-gradient-descent-methods-limitations"]], "Using recursion": [[40, "using-recursion"], [41, "using-recursion"]], "Using the Voting Classifier": [[47, "using-the-voting-classifier"], [48, "using-the-voting-classifier"]], "Using the chain rule and summing over all k entries": [[42, "using-the-chain-rule-and-summing-over-all-k-entries"], [43, "using-the-chain-rule-and-summing-over-all-k-entries"]], "Using the correlation matrix": [[0, "using-the-correlation-matrix"], [39, "using-the-correlation-matrix"]], "Vanishing gradients": [[42, "vanishing-gradients"], [43, "vanishing-gradients"], [46, "vanishing-gradients"]], "Various steps in cross-validation": [[38, "various-steps-in-cross-validation"], [39, "various-steps-in-cross-validation"]], "Velocity only": [[46, "velocity-only"]], "Verifying the data set": [[45, "verifying-the-data-set"], [46, "verifying-the-data-set"]], "Visualization": [[2, "visualization"], [2, "id1"], [43, "visualization"], [43, "id1"], [44, "visualization"], [44, "id1"]], "Visualizing the Tree, Classification": [[10, "visualizing-the-tree-classification"], [47, "visualizing-the-tree-classification"], [48, "visualizing-the-tree-classification"]], "Visualizing the Tree, The Moons": [[47, "visualizing-the-tree-the-moons"], [48, "visualizing-the-tree-the-moons"]], "Voting and Bagging": [[47, "voting-and-bagging"], [48, "voting-and-bagging"]], "Week 34: Introduction to the course, Logistics and Practicalities": [[35, null]], "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression": [[36, null]], "Week 36: Linear Regression and Statistical interpretations": [[37, null]], "Week 37: Statistical interpretations and Resampling Methods": [[38, null]], "Week 38: Logistic Regression and Optimization": [[39, null]], "Week 39: Optimization and  Gradient Methods": [[40, null]], "Week 40: Gradient descent methods (continued) and start Neural networks": [[41, null]], "Week 41 Neural networks and constructing a neural network code": [[42, null]], "Week 42 Constructing a Neural Network code with examples": [[43, null]], "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations": [[44, null]], "Week 44,  Convolutional Neural Networks (CNN)": [[45, null]], "Week 45,  Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)": [[46, null]], "Week 46: Decision Trees, Ensemble methods  and Random Forests": [[47, null]], "Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods": [[48, null]], "Weekly Schedule": [[31, "weekly-schedule"]], "Weights and biases": [[43, "weights-and-biases"], [44, "weights-and-biases"]], "What does centering (subtracting the mean values) mean mathematically?": [[36, "what-does-centering-subtracting-the-mean-values-mean-mathematically"]], "What does it mean?": [[36, "what-does-it-mean"], [37, "what-does-it-mean"]], "What is Machine Learning?": [[1, "what-is-machine-learning"]], "What is a good model?": [[1, "what-is-a-good-model"], [35, "what-is-a-good-model"]], "What is a good model? Can we define it?": [[35, "what-is-a-good-model-can-we-define-it"]], "What is boosting? Additive Modelling/Iterative Fitting": [[47, "what-is-boosting-additive-modelling-iterative-fitting"], [48, "what-is-boosting-additive-modelling-iterative-fitting"]], "What is the Difference": [[45, "what-is-the-difference"], [46, "what-is-the-difference"]], "What kinds of behaviour can RNNs exhibit?": [[46, "what-kinds-of-behaviour-can-rnns-exhibit"]], "When do we stop?": [[40, "when-do-we-stop"], [41, "when-do-we-stop"]], "Which activation function should I use?": [[2, "which-activation-function-should-i-use"]], "Which activation function should we use?": [[42, "which-activation-function-should-we-use"], [43, "which-activation-function-should-we-use"], [44, "which-activation-function-should-we-use"]], "Why CNNS for images, sound files, medical images from CT scans etc?": [[45, "why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc"], [46, "why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc"]], "Why Linear Regression (aka Ordinary Least Squares and family)": 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</span>Resampling Methods", "<span class=\"section-number\">6. </span>Logistic Regression", "<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims", "<span class=\"section-number\">9. </span>Decision trees, overarching aims", "<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods", "<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)", "<span class=\"section-number\">13. </span>Neural networks", "<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm", "<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning", "Exercises week 34", "Exercises week 35", "Exercises week 36", "Exercises week 37", "Exercises week 38", "Exercises week 39", "Exercises week 41", "Exercises week 42", "Exercises week 43", "Exercise week 47", "Applied Data Analysis and Machine Learning", "<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features", "Project 1 on Machine Learning, deadline October 7 (midnight), 2024", "Project 2 on Machine Learning, deadline November 4 (Midnight)", "Project 3 on Machine Learning, deadline December 9 (midnight), 2024", "Teaching schedule with links to material", "<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis", "Teachers and Grading", "Textbooks", "Week 34: Introduction to the course, Logistics and Practicalities", "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression", "Week 36: Linear Regression and Statistical interpretations", "Week 37: Statistical interpretations and Resampling Methods", "Week 38: Logistic Regression and Optimization", "Week 39: Optimization and  Gradient Methods", "Week 40: Gradient descent methods (continued) and start Neural networks", "Week 41 Neural networks and constructing a neural network code", "Week 42 Constructing a Neural Network code with examples", "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations", "Week 44,  Convolutional Neural Networks (CNN)", "Week 45,  Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)", "Week 46: Decision Trees, Ensemble methods  and Random Forests", "Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods"], "titleterms": {"": [9, 11, 22, 38, 39, 40, 41, 47, 48], "0": 43, "1": [1, 16, 17, 18, 19, 23, 24, 25, 28, 35, 36, 42, 43, 44, 46], "11": 42, "14": 43, "16": 39, "2": [1, 16, 17, 18, 19, 23, 24, 25, 29, 35, 36, 37, 42, 43, 44, 46], "2023": 33, "2024": [28, 30, 40, 41, 42, 43], "21": 44, "23": 40, "26": 36, "27": 40, "28": 45, "3": [1, 16, 17, 23, 24, 25, 30, 35, 36, 42, 43, 44, 46], "30": 41, "34": [16, 35], "35": [17, 36], "36": [18, 37], "37": [19, 38], "38": [0, 20, 39], "39": [21, 22, 40], "3d": [45, 46], "4": [1, 23, 24, 25, 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