mhjensen
283 lines
13 KiB
HTML
283 lines
13 KiB
HTML
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<title>Week 35: Linear Regression and Review of Statistical Analysis and Probability Theory</title>
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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Plans for week 35, August 24-28', 2, None, '___sec0'),
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('Thursday August 27', 2, None, '___sec1'),
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('Why Linear Regression (aka Ordinary Least Squares and family)',
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2,
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None,
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'___sec2'),
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('Regression analysis, overarching aims', 2, None, '___sec3'),
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('Regression analysis, overarching aims II', 2, None, '___sec4'),
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('Examples', 2, None, '___sec5'),
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('General linear models', 2, None, '___sec6'),
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('Rewriting the fitting procedure as a linear algebra problem',
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'___sec7'),
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('Rewriting the fitting procedure as a linear algebra problem, '
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None,
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'___sec8'),
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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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'___sec9'),
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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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'___sec10'),
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('Optimizing our parameters', 2, None, '___sec11'),
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('Our model for the nuclear binding energies',
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2,
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'___sec12'),
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('Optimizing our parameters, more details', 2, None, '___sec13'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'___sec14'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'___sec15'),
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('Some useful matrix and vector expressions',
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2,
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None,
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'___sec16'),
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('Interpretations and optimizing our parameters',
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2,
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None,
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'___sec17'),
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('Own code for Ordinary Least Squares', 2, None, '___sec18'),
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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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'___sec19'),
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('The $\\chi^2$ function', 2, None, '___sec20'),
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('The $\\chi^2$ function', 2, None, '___sec21'),
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('The $\\chi^2$ function', 2, None, '___sec22'),
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('The $\\chi^2$ function', 2, None, '___sec23'),
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('The $\\chi^2$ function', 2, None, '___sec24'),
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('The $\\chi^2$ function', 2, None, '___sec25'),
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('Fitting an Equation of State for Dense Nuclear Matter',
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2,
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None,
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'___sec26'),
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('The code', 2, None, '___sec27'),
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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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'___sec28'),
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('The Boston housing data example', 2, None, '___sec29'),
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('Housing data, the code', 2, None, '___sec30'),
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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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'___sec31'),
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('Preprocessing our data', 2, None, '___sec32'),
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('More preprocessing', 2, None, '___sec33'),
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('Simple preprocessing examples, Franke function and regression',
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2,
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None,
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('Friday August 28', 2, None, '___sec35')]}
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<a class="navbar-brand" href="week35-bs.html">Week 35: Linear Regression and Review of Statistical Analysis and Probability Theory</a>
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</div>
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<ul class="nav navbar-nav navbar-right">
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<li class="dropdown">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week35-bs001.html#___sec0" style="font-size: 80%;">Plans for week 35, August 24-28</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs002.html#___sec1" style="font-size: 80%;">Thursday August 27</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs003.html#___sec2" style="font-size: 80%;">Why Linear Regression (aka Ordinary Least Squares and family)</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs004.html#___sec3" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs005.html#___sec4" style="font-size: 80%;">Regression analysis, overarching aims II</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs006.html#___sec5" style="font-size: 80%;">Examples</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs007.html#___sec6" style="font-size: 80%;">General linear models</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs008.html#___sec7" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs009.html#___sec8" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem, more details</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs010.html#___sec9" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs011.html#___sec10" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs012.html#___sec11" style="font-size: 80%;">Optimizing our parameters</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs013.html#___sec12" style="font-size: 80%;">Our model for the nuclear binding energies</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs014.html#___sec13" style="font-size: 80%;">Optimizing our parameters, more details</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs015.html#___sec14" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs016.html#___sec15" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs017.html#___sec16" style="font-size: 80%;">Some useful matrix and vector expressions</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs018.html#___sec17" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs019.html#___sec18" style="font-size: 80%;">Own code for Ordinary Least Squares</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs020.html#___sec19" style="font-size: 80%;">Adding error analysis and training set up</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs022.html#___sec21" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs023.html#___sec22" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs024.html#___sec23" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs025.html#___sec24" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs026.html#___sec25" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs027.html#___sec26" style="font-size: 80%;">Fitting an Equation of State for Dense Nuclear Matter</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs028.html#___sec27" style="font-size: 80%;">The code</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs029.html#___sec28" style="font-size: 80%;">Splitting our Data in Training and Test data</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs030.html#___sec29" style="font-size: 80%;">The Boston housing data example</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs031.html#___sec30" style="font-size: 80%;">Housing data, the code</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs032.html#___sec31" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs033.html#___sec32" style="font-size: 80%;">Preprocessing our data</a></li>
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<!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;">More preprocessing</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs035.html#___sec34" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs036.html#___sec35" style="font-size: 80%;">Friday August 28</a></li>
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</ul>
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</li>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0034"></a>
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<!-- !split -->
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<h2 id="___sec33" class="anchor">More preprocessing </h2>
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<p>
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The <b>Normalizer</b> scales each data
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point such that the feature vector has a euclidean length of one. In other words, it
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projects a data point on the circle (or sphere in the case of higher dimensions) with a
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radius of 1. This means every data point is scaled by a different number (by the
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inverse of it’s length).
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This normalization is often used when only the direction (or angle) of the data matters,
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not the length of the feature vector.
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<p>
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The <b>RobustScaler</b> works similarly to the StandardScaler in that it
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ensures statistical properties for each feature that guarantee that
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they are on the same scale. However, the RobustScaler uses the median
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and quartiles, instead of mean and variance. This makes the
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RobustScaler ignore data points that are very different from the rest
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(like measurement errors). These odd data points are also called
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outliers, and might often lead to trouble for other scaling
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techniques.
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<p>
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</div>
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</div>
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<p>
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<p>
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<li><a href="._week35-bs033.html">«</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week35-bs026.html">27</a></li>
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<li><a href="._week35-bs027.html">28</a></li>
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<li><a href="._week35-bs028.html">29</a></li>
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<li><a href="._week35-bs029.html">30</a></li>
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<li class="active"><a href="._week35-bs034.html">35</a></li>
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<li><a href="._week35-bs035.html">36</a></li>
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<li><a href="._week35-bs036.html">37</a></li>
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