mhjensen
228 lines
12 KiB
HTML
228 lines
12 KiB
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{'highest level': 2,
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'sections': [('Logistic Regression', 2, None, '___sec0'),
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('Optimization and Deep learning', 2, None, '___sec1'),
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('Basics', 2, None, '___sec2'),
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('Linear classifier', 2, None, '___sec3'),
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('Some selected properties', 2, None, '___sec4'),
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('The logistic function', 2, None, '___sec5'),
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('Examples of likelihood functions used in logistic regression '
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'and nueral networks',
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2,
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None,
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'___sec6'),
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('Two parameters', 2, None, '___sec7'),
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('Maximum likelihood', 2, None, '___sec8'),
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('The cost function rewritten', 2, None, '___sec9'),
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('Minimizing the cross entropy', 2, None, '___sec10'),
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('A more compact expression', 2, None, '___sec11'),
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('Extending to more predictors', 2, None, '___sec12'),
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('Including more classes', 2, None, '___sec13'),
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('More classes', 2, None, '___sec14'),
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('A simple classification problem', 2, None, '___sec15'),
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('The Credit Card example', 2, None, '___sec16'),
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('How to read the Credit Card data', 2, None, '___sec17')]}
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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-bs002.html#___sec1" style="font-size: 80%;">Optimization and Deep learning</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs003.html#___sec2" style="font-size: 80%;">Basics</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs004.html#___sec3" style="font-size: 80%;">Linear classifier</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">Some selected properties</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">The logistic function</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs007.html#___sec6" style="font-size: 80%;">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec7" style="font-size: 80%;">Two parameters</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec8" style="font-size: 80%;">Maximum likelihood</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs012.html#___sec11" style="font-size: 80%;">A more compact expression</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs013.html#___sec12" style="font-size: 80%;">Extending to more predictors</a></li>
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<!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;">A simple classification problem</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs017.html#___sec16" style="font-size: 80%;">The Credit Card example</a></li>
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<!-- navigation toc: --> <li><a href="._LogReg-bs018.html#___sec17" style="font-size: 80%;">How to read the Credit Card data</a></li>
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<h2 id="___sec15" class="anchor">A simple classification problem </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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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>
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<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, linear_model
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<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>
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">generate_data</span>():
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np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
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X, y <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>make_moons(<span style="color: #666666">200</span>, noise<span style="color: #666666">=0.20</span>)
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<span style="color: #008000; font-weight: bold">return</span> X, y
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">visualize</span>(X, y, clf):
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plot_decision_boundary(<span style="color: #008000; font-weight: bold">lambda</span> x: clf<span style="color: #666666">.</span>predict(x), X, y)
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_decision_boundary</span>(pred_func, X, y):
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<span style="color: #408080; font-style: italic"># Set min and max values and give it some padding</span>
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x_min, x_max <span style="color: #666666">=</span> X[:, <span style="color: #666666">0</span>]<span style="color: #666666">.</span>min() <span style="color: #666666">-</span> <span style="color: #666666">.5</span>, X[:, <span style="color: #666666">0</span>]<span style="color: #666666">.</span>max() <span style="color: #666666">+</span> <span style="color: #666666">.5</span>
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y_min, y_max <span style="color: #666666">=</span> X[:, <span style="color: #666666">1</span>]<span style="color: #666666">.</span>min() <span style="color: #666666">-</span> <span style="color: #666666">.5</span>, X[:, <span style="color: #666666">1</span>]<span style="color: #666666">.</span>max() <span style="color: #666666">+</span> <span style="color: #666666">.5</span>
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h <span style="color: #666666">=</span> <span style="color: #666666">0.01</span>
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<span style="color: #408080; font-style: italic"># Generate a grid of points with distance h between them</span>
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xx, yy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>meshgrid(np<span style="color: #666666">.</span>arange(x_min, x_max, h), np<span style="color: #666666">.</span>arange(y_min, y_max, h))
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<span style="color: #408080; font-style: italic"># Predict the function value for the whole gid</span>
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Z <span style="color: #666666">=</span> pred_func(np<span style="color: #666666">.</span>c_[xx<span style="color: #666666">.</span>ravel(), yy<span style="color: #666666">.</span>ravel()])
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Z <span style="color: #666666">=</span> Z<span style="color: #666666">.</span>reshape(xx<span style="color: #666666">.</span>shape)
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<span style="color: #408080; font-style: italic"># Plot the contour and training examples</span>
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plt<span style="color: #666666">.</span>contourf(xx, yy, Z, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
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plt<span style="color: #666666">.</span>scatter(X[:, <span style="color: #666666">0</span>], X[:, <span style="color: #666666">1</span>], c<span style="color: #666666">=</span>y, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>Spectral)
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plt<span style="color: #666666">.</span>show()
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">classify</span>(X, y):
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clf <span style="color: #666666">=</span> linear_model<span style="color: #666666">.</span>LogisticRegressionCV()
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clf<span style="color: #666666">.</span>fit(X, y)
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<span style="color: #008000; font-weight: bold">return</span> clf
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">main</span>():
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X, y <span style="color: #666666">=</span> generate_data()
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<span style="color: #408080; font-style: italic"># visualize(X, y)</span>
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clf <span style="color: #666666">=</span> classify(X, y)
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visualize(X, y, clf)
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<span style="color: #008000; font-weight: bold">if</span> <span style="color: #19177C">__name__</span> <span style="color: #666666">==</span> <span style="color: #BA2121">"__main__"</span>:
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main()
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</pre></div>
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