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mhjensen 4f4c4e6946 update on log reg
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<!-- navigation toc: --> <li><a href="._LogReg-bs001.html#___sec0" style="font-size: 80%;">Logistic Regression</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec7" style="font-size: 80%;">Maximum likelihood</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs010.html#___sec9" style="font-size: 80%;">Minimizing the cross entropy</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs011.html#___sec10" style="font-size: 80%;">A more compact expression</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs012.html#___sec11" style="font-size: 80%;">Extending to more predictors</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs013.html#___sec12" style="font-size: 80%;">Including more classes</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs014.html#___sec13" style="font-size: 80%;">The Softmax function</a></li>
<!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs016.html#___sec15" style="font-size: 80%;">A simple classification problem</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs017.html#___sec16" style="font-size: 80%;">The two-dimensional Ising model, Predicting phase transition of the two-dimensional Ising model</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs018.html#___sec17" style="font-size: 80%;">Reading in the data</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs019.html#___sec18" style="font-size: 80%;">Logistic regression</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs020.html#___sec19" style="font-size: 80%;">Exploring the logistic regression</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs021.html#___sec20" style="font-size: 80%;">Accuracy of a classification model</a></li>
<!-- navigation toc: --> <li><a href="._LogReg-bs022.html#___sec21" style="font-size: 80%;">Analyzing the results</a></li>
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<h2 id="___sec14" class="anchor">A <b>scikit-learn</b> example </h2>
<p>
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<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</span> <span style="color: #008000; font-weight: bold">import</span> datasets
iris <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_iris()
<span style="color: #008000">list</span>(iris<span style="color: #666666">.</span>keys())
[<span style="color: #BA2121">&#39;data&#39;</span>, <span style="color: #BA2121">&#39;target_names&#39;</span>, <span style="color: #BA2121">&#39;feature_names&#39;</span>, <span style="color: #BA2121">&#39;target&#39;</span>, <span style="color: #BA2121">&#39;DESCR&#39;</span>]
X <span style="color: #666666">=</span> iris[<span style="color: #BA2121">&quot;data&quot;</span>][:, <span style="color: #666666">3</span>:] <span style="color: #408080; font-style: italic"># petal width</span>
y <span style="color: #666666">=</span> (iris[<span style="color: #BA2121">&quot;target&quot;</span>] <span style="color: #666666">==</span> <span style="color: #666666">2</span>)<span style="color: #666666">.</span>astype(np<span style="color: #666666">.</span>int) <span style="color: #408080; font-style: italic"># 1 if Iris-Virginica, else 0</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> LogisticRegression
log_reg <span style="color: #666666">=</span> LogisticRegression()
log_reg<span style="color: #666666">.</span>fit(X, y)
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>, <span style="color: #666666">3</span>, <span style="color: #666666">1000</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
y_proba <span style="color: #666666">=</span> log_reg<span style="color: #666666">.</span>predict_proba(X_new)
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">&quot;g-&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;Iris-Virginica&quot;</span>)
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">0</span>], <span style="color: #BA2121">&quot;b--&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;Not Iris-Virginica&quot;</span>)
plt<span style="color: #666666">.</span>show()
</pre></div>
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