Morten Hjorth-Jensen
344 lines
13 KiB
HTML
344 lines
13 KiB
HTML
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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Plans for week 35', 2, None, 'plans-for-week-35'),
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('Reading recommendations:', 3, None, 'reading-recommendations'),
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('Thursday September 1', 2, None, 'thursday-september-1'),
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('Why Linear Regression (aka Ordinary Least Squares and family), '
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'repeat from last week',
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2,
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None,
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'why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week'),
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('Regression analysis, overarching aims',
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2,
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None,
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'regression-analysis-overarching-aims'),
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('Regression analysis, overarching aims II',
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2,
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None,
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'regression-analysis-overarching-aims-ii'),
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('Examples', 2, None, 'examples'),
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('General linear models', 2, None, 'general-linear-models'),
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('Rewriting the fitting procedure as a linear algebra problem',
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2,
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None,
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'rewriting-the-fitting-procedure-as-a-linear-algebra-problem'),
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('Rewriting the fitting procedure as a linear algebra problem, '
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'more details',
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2,
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None,
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'rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details'),
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('Generalizing the fitting procedure as a linear algebra problem',
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2,
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None,
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'generalizing-the-fitting-procedure-as-a-linear-algebra-problem'),
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('Generalizing the fitting procedure as a linear algebra problem',
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2,
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None,
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'generalizing-the-fitting-procedure-as-a-linear-algebra-problem'),
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('Optimizing our parameters',
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2,
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None,
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'optimizing-our-parameters'),
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('Our model for the nuclear binding energies',
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2,
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None,
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'our-model-for-the-nuclear-binding-energies'),
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('Optimizing our parameters, more details',
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2,
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None,
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'optimizing-our-parameters-more-details'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'interpretations-and-optimizing-our-parameters'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'interpretations-and-optimizing-our-parameters'),
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('Some useful matrix and vector expressions',
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2,
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None,
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'some-useful-matrix-and-vector-expressions'),
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('Meet the Hessian Matrix', 2, None, 'meet-the-hessian-matrix'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'interpretations-and-optimizing-our-parameters'),
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('Own code for Ordinary Least Squares',
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2,
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None,
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'own-code-for-ordinary-least-squares'),
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('Adding error analysis and training set up',
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2,
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None,
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'adding-error-analysis-and-training-set-up'),
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('Splitting our Data in Training and Test data',
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2,
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None,
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'splitting-our-data-in-training-and-test-data'),
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('Examples', 2, None, 'examples'),
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('Making your own test-train splitting',
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2,
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None,
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'making-your-own-test-train-splitting'),
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('The Boston housing data example',
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2,
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None,
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'the-boston-housing-data-example'),
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('Housing data, the code', 2, None, 'housing-data-the-code'),
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('Reducing the number of degrees of freedom, overarching view',
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2,
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None,
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'reducing-the-number-of-degrees-of-freedom-overarching-view'),
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('Preprocessing our data', 2, None, 'preprocessing-our-data'),
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('Functionality in Scikit-Learn',
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2,
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None,
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'functionality-in-scikit-learn'),
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('More preprocessing', 2, None, 'more-preprocessing'),
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('Frequently used scaling functions',
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2,
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None,
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'frequently-used-scaling-functions'),
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('Example of own Standard scaling',
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2,
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None,
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'example-of-own-standard-scaling'),
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('Min-Max Scaling', 2, None, 'min-max-scaling'),
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('Testing the Means Squared Error as function of Complexity',
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2,
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None,
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'testing-the-means-squared-error-as-function-of-complexity'),
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('More preprocessing examples, Franke function and regression',
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2,
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None,
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'more-preprocessing-examples-franke-function-and-regression'),
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('Mathematical Interpretation of Ordinary Least Squares',
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2,
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None,
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'mathematical-interpretation-of-ordinary-least-squares'),
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('Residual Error', 2, None, 'residual-error'),
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('Simple case', 2, None, 'simple-case'),
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('The singular value decomposition',
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2,
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None,
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'the-singular-value-decomposition'),
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('Linear Regression Problems',
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2,
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None,
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'linear-regression-problems'),
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('Fixing the singularity', 2, None, 'fixing-the-singularity'),
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('Basic math of the SVD', 2, None, 'basic-math-of-the-svd'),
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('The SVD, a Fantastic Algorithm',
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2,
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None,
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'the-svd-a-fantastic-algorithm'),
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('Economy-size SVD', 2, None, 'economy-size-svd'),
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('Codes for the SVD', 2, None, 'codes-for-the-svd'),
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('Note about SVD Calculations',
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2,
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None,
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'note-about-svd-calculations'),
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('Friday September 2', 2, None, 'friday-september-2'),
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('Mathematics of the SVD and implications',
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2,
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None,
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'mathematics-of-the-svd-and-implications'),
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('Example Matrix', 2, None, 'example-matrix'),
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('Setting up the Matrix to be inverted',
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2,
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None,
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'setting-up-the-matrix-to-be-inverted'),
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('Further properties (important for our analyses later)',
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2,
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None,
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'further-properties-important-for-our-analyses-later'),
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('Meet the Covariance Matrix',
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2,
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None,
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'meet-the-covariance-matrix'),
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('Introducing the Covariance and Correlation functions',
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2,
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None,
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'introducing-the-covariance-and-correlation-functions'),
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('Covariance and Correlation Matrix',
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2,
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None,
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'covariance-and-correlation-matrix'),
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('Correlation Function and Design/Feature Matrix',
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2,
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None,
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'correlation-function-and-design-feature-matrix'),
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('Covariance Matrix Examples',
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2,
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None,
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'covariance-matrix-examples'),
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('Correlation Matrix', 2, None, 'correlation-matrix'),
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('Correlation Matrix with Pandas',
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2,
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None,
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'correlation-matrix-with-pandas'),
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('Correlation Matrix with Pandas and the Franke function',
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2,
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None,
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'correlation-matrix-with-pandas-and-the-franke-function'),
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('Rewriting the Covariance and/or Correlation Matrix',
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2,
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None,
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'rewriting-the-covariance-and-or-correlation-matrix'),
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('Linking with the SVD', 2, None, 'linking-with-the-svd'),
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('What does it mean?', 2, None, 'what-does-it-mean'),
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('And finally $\\boldsymbol{X}\\boldsymbol{X}^T$',
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2,
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None,
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'and-finally-boldsymbol-x-boldsymbol-x-t'),
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('Ridge and LASSO Regression',
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2,
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None,
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'ridge-and-lasso-regression'),
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('Deriving the Ridge Regression Equations',
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2,
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None,
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'deriving-the-ridge-regression-equations'),
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('Interpreting the Ridge results',
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2,
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None,
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'interpreting-the-ridge-results'),
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('More interpretations', 2, None, 'more-interpretations'),
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('Deriving the Lasso Regression Equations',
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2,
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None,
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'deriving-the-lasso-regression-equations'),
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('Exercises for week 35', 2, None, 'exercises-for-week-35'),
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('Exercise 1: Setting up various Python environments',
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2,
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None,
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'exercise-1-setting-up-various-python-environments'),
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('Exercise 2: making your own data and exploring scikit-learn',
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2,
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None,
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'exercise-2-making-your-own-data-and-exploring-scikit-learn'),
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('Exercise 3: Normalizing our data',
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2,
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None,
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'exercise-3-normalizing-our-data'),
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('Exercise 4: Adding Ridge Regression',
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2,
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None,
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'exercise-4-adding-ridge-regression'),
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('Exercise 5: Analytical exercises',
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2,
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None,
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'exercise-5-analytical-exercises')]}
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end of tocinfo -->
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<body>
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<!-- ------------------- main content ---------------------- -->
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<p>ndTITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<!-- institution(s) -->
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<center>
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[1] <b>Department of Physics, University of Oslo</b>
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[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b>
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<br>
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<center>
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<h4>Sep 8, 2022</h4>
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</center> <!-- date -->
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<br>
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</p>
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<p>
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<!-- navigation buttons at the bottom of the page -->
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<ul class="pagination">
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<li class="active"><a href="._week35-bs000.html">1</a></li>
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<li><a href="._week35-bs001.html">2</a></li>
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<li><a href="._week35-bs002.html">3</a></li>
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<li><a href="._week35-bs003.html">4</a></li>
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<li><a href="._week35-bs004.html">5</a></li>
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<li><a href="._week35-bs005.html">6</a></li>
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<li><a href="._week35-bs006.html">7</a></li>
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<li><a href="._week35-bs007.html">8</a></li>
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<li><a href="._week35-bs008.html">9</a></li>
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<li><a href="._week35-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week35-bs069.html">70</a></li>
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<li><a href="._week35-bs001.html">»</a></li>
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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