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added more scikit-learn functionality

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mhjensen
2018-05-28 08:41:15 -04:00
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doc/pub/How2ReadData/html/How2ReadData.html
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@@ -156,7 +156,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 27, 2018</h4></center> <!-- date -->
<center><h4>May 28, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -253,9 +253,9 @@ into the hassle of exploring how to set up dependencies and paths, we
recommend two widely used distrubutions which set up all relevant
dependencies for Python, namely
<ol>
<ul>
<li> <a href="https://docs.anaconda.com/" target="_blank">Anaconda</a>,</li>
</ol>
</ul>
which is an open source
distribution of the Python and R programming languages for large-scale
@@ -263,9 +263,9 @@ data processing, predictive analytics, and scientific computing, that
aims to simplify package management and deployment. Package versions
are managed by the package management system <b>conda</b>.
<ol>
<ul>
<li> <a href="https://www.enthought.com/product/canopy/" target="_blank">Enthought canopy</a></li>
</ol>
</ul>
is a Python
distribution for scientific and analytic computing distribution and
@@ -492,16 +492,18 @@ relative error.
As mentioned above, <b>scikit-learn</b> has an impressive functionality.
We can for example extract the values of \( \alpha \) and \( \beta \) and
their error estimates, or the variance and standard deviation and many
other properties from the statistical data analysis. Here we show an
example of the functionality of scikit-learn.
other properties from the statistical data analysis.
<p>
Here we show an
example of the functionality of scikit-learn.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error, r2_score
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">2.0+</span> <span style="color: #666666">5*</span>x<span style="color: #666666">+0.5</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
@@ -514,6 +516,10 @@ ypredict <span style="color: #666666">=</span> linreg<span style="color: #666666
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Mean squared error: </span><span style="color: #BB6688; font-weight: bold">%.2f</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> mean_squared_error(y, ypredict))
<span style="color: #408080; font-style: italic"># Explained variance score: 1 is perfect prediction </span>
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Variance score: </span><span style="color: #BB6688; font-weight: bold">%.2f</span><span style="color: #BA2121">&#39;</span> <span style="color: #666666">%</span> r2_score(y, ypredict))
<span style="color: #408080; font-style: italic"># Mean squared log error </span>
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Mean squared log error: </span><span style="color: #BB6688; font-weight: bold">%.2f</span><span style="color: #BA2121">&#39;</span> <span style="color: #666666">%</span> mean_squared_log_error(y, ypredict) )
<span style="color: #408080; font-style: italic"># Mean absolute error </span>
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&#39;Mean absolute error: </span><span style="color: #BB6688; font-weight: bold">%.2f</span><span style="color: #BA2121">&#39;</span> <span style="color: #666666">%</span> mean_absolute_error(y, ypredict))
plt<span style="color: #666666">.</span>plot(x, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0.0</span>,<span style="color: #666666">1.0</span>,<span style="color: #666666">1.5</span>, <span style="color: #666666">7.0</span>])
@@ -543,17 +549,38 @@ constant model that always predicts the expected value of \( \hat{y} \),
disregarding the input features, would get a \( R^2 \) score of \( 0.0 \).
<p>
If \( \tilde{\hat{y}}_i \) is the predicted value of the i-th sample and \( y_i \) is the corresponding true value, then the score \( R^2 \) is defined as
If \( \tilde{\hat{y}}_i \) is the predicted value of the \( i-th \) sample and \( y_i \) is the corresponding true value, then the score \( R^2 \) is defined as
$$
R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
$$
where the mean value
where we have defined the mean value of \( \hat{y} \) as
$$
\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
$$
We will discuss in more detail these and more function in the various lectures.
Another quantity will meet again in our discussions of regression analysis is
mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the \( l1 \)-norm loss. In our discussion above we presented the relative error.
The MAE is defined as follows
$$
\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|.
$$
Finally we present the
squared logarithmic (quadratic) error
$$
\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2,
$$
<p>
where \( \log_e (x) \) stands for the natural logarithm of \( x \). This error
estimate is best to use when targets having exponential growth, such
as population counts, average sales of a commodity over a span of
years etc.
<p>
We will discuss in more
detail these and more function in the various lectures.
<p>
Another useful Python package is