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Morten Hjorth-Jensen
2022-09-10 21:33:46 +02:00
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>4. Ridge and Lasso Regression &#8212; Applied Data Analysis and Machine Learning</title>
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</a>
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<p aria-level="2" class="caption" role="heading">
<p class="caption" role="heading">
<span class="caption-text">
About the course
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</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<p class="caption" role="heading">
<span class="caption-text">
Review of Statistics with Resampling Techniques and Linear Algebra
</span>
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</a>
</li>
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<p aria-level="2" class="caption" role="heading">
<p class="caption" role="heading">
<span class="caption-text">
From Regression to Support Vector Machines
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</a>
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<p aria-level="2" class="caption" role="heading">
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<span class="caption-text">
Decision Trees, Ensemble Methods and Boosting
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Dimensionality Reduction
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Deep Learning Methods
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<i class="fas fa-list"></i> Contents
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<h1>Ridge and Lasso Regression</h1>
<!-- Table of contents -->
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">
4.1. Mathematical Interpretation of Ordinary Least Squares
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<a class="reference internal nav-link" href="#the-singular-value-decomposition">
4.2. The singular value decomposition
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<a class="reference internal nav-link" href="#basic-math-of-the-svd">
4.3. Basic math of the SVD
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<a class="reference internal nav-link" href="#codes-for-the-svd">
4.4. Codes for the SVD
</a>
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<a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">
4.5. Code for SVD and Inversion of Matrices
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">
4.6. Mathematics of the SVD and implications
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">
4.7. Further properties (important for our analyses later)
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#meet-the-covariance-matrix">
4.8. Meet the Covariance Matrix
</a>
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#linking-with-the-svd">
4.9. Linking with the SVD
</a>
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<a class="reference internal nav-link" href="#id1">
4.10. Ridge and Lasso Regression
</a>
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
4.11. Linking the regression analysis with a statistical interpretation
</a>
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
4.12. Deriving OLS from a probability distribution
</a>
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<a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
4.13. Bayes’ Theorem and Ridge and Lasso Regression
</a>
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#linking-bayes-theorem-with-ridge-and-lasso-regression">
4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression
</a>
</li>
</ul>
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</div>
<div>
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