small update on decision trees, more to come
This commit is contained in:
mhjensen
@@ -100,7 +100,7 @@ end of tocinfo -->
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>May 30, 2018</h4></center> <!-- date -->
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<center><h4>Nov 1, 2018</h4></center> <!-- date -->
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<br>
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<p>
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<!-- potential-jumbotron-button -->
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@@ -113,6 +113,15 @@ end of tocinfo -->
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<div class="panel-body">
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<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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<p>
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Decision trees are supervised learning algorithms used for both,
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classification and regression tasks where we will concentrate on
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classification in this first part of our decision tree tutorial.
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Decision trees are assigned to the information based learning
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algorithms which use different measures of information gain for
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learning. We can use decision trees for issues where we have
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continuous but also categorical input and target features.
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<p>
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</div>
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</div>
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@@ -279,6 +288,105 @@ plt<span style="color: #666666">.</span>show()
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</pre></div>
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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: #408080; font-style: italic"># Program to test the Metropolis algorithm with one particle at given temp in</span>
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<span style="color: #408080; font-style: italic"># one dimension</span>
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<span style="color: #408080; font-style: italic">#!/usr/bin/env python</span>
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<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">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.mlab</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">mlab</span>
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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">import</span> <span style="color: #0000FF; font-weight: bold">random</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> sqrt, exp, log
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
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<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
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<span style="color: #408080; font-style: italic"># initialize the rng with a seed</span>
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random<span style="color: #666666">.</span>seed()
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<span style="color: #408080; font-style: italic"># Hard coding of input parameters</span>
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MCcycles <span style="color: #666666">=</span> <span style="color: #666666">100000</span>
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Temperature <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
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beta <span style="color: #666666">=</span> <span style="color: #666666">1./</span>Temperature
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InitialVelocity <span style="color: #666666">=</span> <span style="color: #666666">-2.0</span>
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CurrentVelocity <span style="color: #666666">=</span> InitialVelocity
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Energy <span style="color: #666666">=</span> <span style="color: #666666">0.5*</span>InitialVelocity<span style="color: #666666">*</span>InitialVelocity
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VelocityRange <span style="color: #666666">=</span> <span style="color: #666666">10*</span>sqrt(Temperature)
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VelocityStep <span style="color: #666666">=</span> <span style="color: #666666">2*</span>VelocityRange<span style="color: #666666">/10.</span>
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AverageEnergy <span style="color: #666666">=</span> Energy
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AverageEnergy2 <span style="color: #666666">=</span> Energy<span style="color: #666666">*</span>Energy
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VelocityValues <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(MCcycles)
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<span style="color: #408080; font-style: italic"># The Monte Carlo sampling with Metropolis starts here</span>
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<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span> (<span style="color: #666666">1</span>, MCcycles, <span style="color: #666666">1</span>):
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TrialVelocity <span style="color: #666666">=</span> CurrentVelocity <span style="color: #666666">+</span> (<span style="color: #666666">2.0*</span>random<span style="color: #666666">.</span>random() <span style="color: #666666">-</span> <span style="color: #666666">1.0</span>)<span style="color: #666666">*</span>VelocityStep
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EnergyChange <span style="color: #666666">=</span> <span style="color: #666666">0.5*</span>(TrialVelocity<span style="color: #666666">*</span>TrialVelocity <span style="color: #666666">-</span>CurrentVelocity<span style="color: #666666">*</span>CurrentVelocity);
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<span style="color: #008000; font-weight: bold">if</span> random<span style="color: #666666">.</span>random() <span style="color: #666666"><=</span> exp(<span style="color: #666666">-</span>beta<span style="color: #666666">*</span>EnergyChange):
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CurrentVelocity <span style="color: #666666">=</span> TrialVelocity
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Energy <span style="color: #666666">+=</span> EnergyChange
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VelocityValues[i] <span style="color: #666666">=</span> CurrentVelocity
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AverageEnergy <span style="color: #666666">+=</span> Energy
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AverageEnergy2 <span style="color: #666666">+=</span> Energy<span style="color: #666666">*</span>Energy
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<span style="color: #408080; font-style: italic">#Final averages</span>
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AverageEnergy <span style="color: #666666">=</span> AverageEnergy<span style="color: #666666">/</span>MCcycles
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AverageEnergy2 <span style="color: #666666">=</span> AverageEnergy2<span style="color: #666666">/</span>MCcycles
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Variance <span style="color: #666666">=</span> AverageEnergy2 <span style="color: #666666">-</span> AverageEnergy<span style="color: #666666">*</span>AverageEnergy
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<span style="color: #008000; font-weight: bold">print</span>(AverageEnergy, Variance)
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n, bins, patches <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>hist(VelocityValues, <span style="color: #666666">400</span>, facecolor<span style="color: #666666">=</span><span style="color: #BA2121">'green'</span>)
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plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'$v$'</span>)
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plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Velocity distribution P(v)'</span>)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r'Velocity histogram at $k_BT=2$'</span>)
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plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-5</span>, <span style="color: #666666">5</span>, <span style="color: #666666">0</span>, <span style="color: #666666">600</span>])
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plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>)
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">collections</span> <span style="color: #008000; font-weight: bold">import</span> Counter
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<span style="color: #408080; font-style: italic">#print (Counter(VelocityValues))</span>
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<span style="color: #008000; font-weight: bold">print</span> (VelocityValues[:<span style="color: #666666">20</span>])
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VelocityValues<span style="color: #666666">=</span><span style="color: #008000">list</span>(Counter(VelocityValues)<span style="color: #666666">.</span>keys())
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d<span style="color: #666666">=</span><span style="color: #008000">list</span>(Counter(VelocityValues)<span style="color: #666666">.</span>values())
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VelocityValues<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(VelocityValues)[:, np<span style="color: #666666">.</span>newaxis]
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d<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(d)
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<span style="color: #008000; font-weight: bold">print</span> (VelocityValues<span style="color: #666666">.</span>shape, d<span style="color: #666666">.</span>shape)
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plt<span style="color: #666666">.</span>scatter(VelocityValues, d)
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plt<span style="color: #666666">.</span>show()
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<span style="color: #408080; font-style: italic">#2nd Degree Polynomial</span>
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poly_feat<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=20</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
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X_poly<span style="color: #666666">=</span>poly_feat<span style="color: #666666">.</span>fit_transform(VelocityValues)
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lin_reg<span style="color: #666666">=</span>LinearRegression()
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poly_fit<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly,d)
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y_plot<span style="color: #666666">=</span>poly_fit<span style="color: #666666">.</span>predict(X_poly)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Polynomial Fit"</span>)
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plt<span style="color: #666666">.</span>plot(VelocityValues, y_plot, color<span style="color: #666666">=</span><span style="color: #BA2121">'black'</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Fit"</span>)
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plt<span style="color: #666666">.</span>show()
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<span style="color: #408080; font-style: italic">#Decision Trees</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
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regr_1<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>)
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regr_2<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=5</span>)
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regr_3<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=7</span>)
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regr_1<span style="color: #666666">.</span>fit(VelocityValues, d)
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regr_2<span style="color: #666666">.</span>fit(VelocityValues, d)
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regr_3<span style="color: #666666">.</span>fit(VelocityValues, d)
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X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0.0</span>, MCcycles, <span style="color: #666666">0.01</span>)[:, np<span style="color: #666666">.</span>newaxis]
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y_1<span style="color: #666666">=</span>regr_1<span style="color: #666666">.</span>predict(X_test)
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y_2<span style="color: #666666">=</span>regr_2<span style="color: #666666">.</span>predict(X_test)
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y_3<span style="color: #666666">=</span>regr_3<span style="color: #666666">.</span>predict(X_test)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Decision Tree"</span>)
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plt<span style="color: #666666">.</span>plot(X_test, y_1, color<span style="color: #666666">=</span><span style="color: #BA2121">"red"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=2"</span>, linewidth<span style="color: #666666">=2</span>)
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plt<span style="color: #666666">.</span>plot(X_test, y_2, color<span style="color: #666666">=</span><span style="color: #BA2121">"green"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=5"</span>, linewidth<span style="color: #666666">=2</span>)
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plt<span style="color: #666666">.</span>plot(X_test, y_3, color<span style="color: #666666">=</span><span style="color: #BA2121">"m"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=7"</span>, linewidth<span style="color: #666666">=2</span>)
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plt<span style="color: #666666">.</span>show()
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<span style="color: #408080; font-style: italic">#Separate each frequency not in one specific velocity, but in a range of values,</span>
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<span style="color: #408080; font-style: italic">#i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...</span>
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</pre></div>
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<p>
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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@@ -132,7 +132,7 @@ td.padding {
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p> <br>
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<center><h4>May 30, 2018</h4></center> <!-- date -->
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<center><h4>Nov 1, 2018</h4></center> <!-- date -->
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<br>
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<p>
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@@ -147,6 +147,15 @@ td.padding {
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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Decision trees are supervised learning algorithms used for both,
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classification and regression tasks where we will concentrate on
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classification in this first part of our decision tree tutorial.
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||||
Decision trees are assigned to the information based learning
|
||||
algorithms which use different measures of information gain for
|
||||
learning. We can use decision trees for issues where we have
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continuous but also categorical input and target features.
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</div>
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</section>
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@@ -309,6 +318,105 @@ plt.title(<span style="color: #CD5555">"Decision Tree Regression"</spa
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plt.legend()
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plt.show()
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</pre></div>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Program to test the Metropolis algorithm with one particle at given temp in</span>
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<span style="color: #228B22"># one dimension</span>
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<span style="color: #228B22">#!/usr/bin/env python</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.mlab</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">mlab</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">random</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">math</span> <span style="color: #8B008B; font-weight: bold">import</span> sqrt, exp, log
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
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<span style="color: #228B22"># initialize the rng with a seed</span>
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random.seed()
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<span style="color: #228B22"># Hard coding of input parameters</span>
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MCcycles = <span style="color: #B452CD">100000</span>
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Temperature = <span style="color: #B452CD">2.0</span>
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beta = <span style="color: #B452CD">1.</span>/Temperature
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InitialVelocity = -<span style="color: #B452CD">2.0</span>
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CurrentVelocity = InitialVelocity
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Energy = <span style="color: #B452CD">0.5</span>*InitialVelocity*InitialVelocity
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VelocityRange = <span style="color: #B452CD">10</span>*sqrt(Temperature)
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VelocityStep = <span style="color: #B452CD">2</span>*VelocityRange/<span style="color: #B452CD">10.</span>
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AverageEnergy = Energy
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AverageEnergy2 = Energy*Energy
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VelocityValues = np.zeros(MCcycles)
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<span style="color: #228B22"># The Monte Carlo sampling with Metropolis starts here</span>
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<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span> (<span style="color: #B452CD">1</span>, MCcycles, <span style="color: #B452CD">1</span>):
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TrialVelocity = CurrentVelocity + (<span style="color: #B452CD">2.0</span>*random.random() - <span style="color: #B452CD">1.0</span>)*VelocityStep
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EnergyChange = <span style="color: #B452CD">0.5</span>*(TrialVelocity*TrialVelocity -CurrentVelocity*CurrentVelocity);
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<span style="color: #8B008B; font-weight: bold">if</span> random.random() <= exp(-beta*EnergyChange):
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CurrentVelocity = TrialVelocity
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Energy += EnergyChange
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VelocityValues[i] = CurrentVelocity
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AverageEnergy += Energy
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AverageEnergy2 += Energy*Energy
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<span style="color: #228B22">#Final averages</span>
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AverageEnergy = AverageEnergy/MCcycles
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AverageEnergy2 = AverageEnergy2/MCcycles
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Variance = AverageEnergy2 - AverageEnergy*AverageEnergy
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<span style="color: #8B008B; font-weight: bold">print</span>(AverageEnergy, Variance)
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n, bins, patches = plt.hist(VelocityValues, <span style="color: #B452CD">400</span>, facecolor=<span style="color: #CD5555">'green'</span>)
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plt.xlabel(<span style="color: #CD5555">'$v$'</span>)
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plt.ylabel(<span style="color: #CD5555">'Velocity distribution P(v)'</span>)
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plt.title(<span style="color: #CD5555">r'Velocity histogram at $k_BT=2$'</span>)
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plt.axis([-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">0</span>, <span style="color: #B452CD">600</span>])
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plt.grid(<span style="color: #658b00">True</span>)
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">collections</span> <span style="color: #8B008B; font-weight: bold">import</span> Counter
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<span style="color: #228B22">#print (Counter(VelocityValues))</span>
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<span style="color: #8B008B; font-weight: bold">print</span> (VelocityValues[:<span style="color: #B452CD">20</span>])
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VelocityValues=<span style="color: #658b00">list</span>(Counter(VelocityValues).keys())
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d=<span style="color: #658b00">list</span>(Counter(VelocityValues).values())
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VelocityValues=np.asarray(VelocityValues)[:, np.newaxis]
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d=np.asarray(d)
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<span style="color: #8B008B; font-weight: bold">print</span> (VelocityValues.shape, d.shape)
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plt.scatter(VelocityValues, d)
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plt.show()
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<span style="color: #228B22">#2nd Degree Polynomial</span>
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poly_feat=PolynomialFeatures(degree=<span style="color: #B452CD">20</span>, include_bias=<span style="color: #658b00">False</span>)
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X_poly=poly_feat.fit_transform(VelocityValues)
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lin_reg=LinearRegression()
|
||||
poly_fit=lin_reg.fit(X_poly,d)
|
||||
|
||||
y_plot=poly_fit.predict(X_poly)
|
||||
plt.title(<span style="color: #CD5555">"Polynomial Fit"</span>)
|
||||
plt.plot(VelocityValues, y_plot, color=<span style="color: #CD5555">'black'</span>, label=<span style="color: #CD5555">"Fit"</span>)
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22">#Decision Trees</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
|
||||
regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">2</span>)
|
||||
regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
|
||||
regr_3=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
|
||||
regr_1.fit(VelocityValues, d)
|
||||
regr_2.fit(VelocityValues, d)
|
||||
regr_3.fit(VelocityValues, d)
|
||||
|
||||
X_test = np.arange(<span style="color: #B452CD">0.0</span>, MCcycles, <span style="color: #B452CD">0.01</span>)[:, np.newaxis]
|
||||
y_1=regr_1.predict(X_test)
|
||||
y_2=regr_2.predict(X_test)
|
||||
y_3=regr_3.predict(X_test)
|
||||
|
||||
plt.title(<span style="color: #CD5555">"Decision Tree"</span>)
|
||||
plt.plot(X_test, y_1, color=<span style="color: #CD5555">"red"</span>, label=<span style="color: #CD5555">"max_depth=2"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.plot(X_test, y_2, color=<span style="color: #CD5555">"green"</span>, label=<span style="color: #CD5555">"max_depth=5"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.plot(X_test, y_3, color=<span style="color: #CD5555">"m"</span>, label=<span style="color: #CD5555">"max_depth=7"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22">#Separate each frequency not in one specific velocity, but in a range of values,</span>
|
||||
<span style="color: #228B22">#i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...</span>
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
@@ -88,7 +88,7 @@ end of tocinfo -->
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>May 30, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Nov 1, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -98,6 +98,15 @@ end of tocinfo -->
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<p>
|
||||
Decision trees are supervised learning algorithms used for both,
|
||||
classification and regression tasks where we will concentrate on
|
||||
classification in this first part of our decision tree tutorial.
|
||||
Decision trees are assigned to the information based learning
|
||||
algorithms which use different measures of information gain for
|
||||
learning. We can use decision trees for issues where we have
|
||||
continuous but also categorical input and target features.
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
@@ -263,6 +272,105 @@ plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># Program to test the Metropolis algorithm with one particle at given temp in</span>
|
||||
<span style="color: #228B22"># one dimension</span>
|
||||
<span style="color: #228B22">#!/usr/bin/env python</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.mlab</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">mlab</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">random</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">math</span> <span style="color: #8B008B; font-weight: bold">import</span> sqrt, exp, log
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
|
||||
<span style="color: #228B22"># initialize the rng with a seed</span>
|
||||
random.seed()
|
||||
<span style="color: #228B22"># Hard coding of input parameters</span>
|
||||
MCcycles = <span style="color: #B452CD">100000</span>
|
||||
Temperature = <span style="color: #B452CD">2.0</span>
|
||||
beta = <span style="color: #B452CD">1.</span>/Temperature
|
||||
InitialVelocity = -<span style="color: #B452CD">2.0</span>
|
||||
CurrentVelocity = InitialVelocity
|
||||
Energy = <span style="color: #B452CD">0.5</span>*InitialVelocity*InitialVelocity
|
||||
VelocityRange = <span style="color: #B452CD">10</span>*sqrt(Temperature)
|
||||
VelocityStep = <span style="color: #B452CD">2</span>*VelocityRange/<span style="color: #B452CD">10.</span>
|
||||
AverageEnergy = Energy
|
||||
AverageEnergy2 = Energy*Energy
|
||||
VelocityValues = np.zeros(MCcycles)
|
||||
<span style="color: #228B22"># The Monte Carlo sampling with Metropolis starts here</span>
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span> (<span style="color: #B452CD">1</span>, MCcycles, <span style="color: #B452CD">1</span>):
|
||||
TrialVelocity = CurrentVelocity + (<span style="color: #B452CD">2.0</span>*random.random() - <span style="color: #B452CD">1.0</span>)*VelocityStep
|
||||
EnergyChange = <span style="color: #B452CD">0.5</span>*(TrialVelocity*TrialVelocity -CurrentVelocity*CurrentVelocity);
|
||||
<span style="color: #8B008B; font-weight: bold">if</span> random.random() <= exp(-beta*EnergyChange):
|
||||
CurrentVelocity = TrialVelocity
|
||||
Energy += EnergyChange
|
||||
VelocityValues[i] = CurrentVelocity
|
||||
AverageEnergy += Energy
|
||||
AverageEnergy2 += Energy*Energy
|
||||
<span style="color: #228B22">#Final averages</span>
|
||||
AverageEnergy = AverageEnergy/MCcycles
|
||||
AverageEnergy2 = AverageEnergy2/MCcycles
|
||||
Variance = AverageEnergy2 - AverageEnergy*AverageEnergy
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(AverageEnergy, Variance)
|
||||
n, bins, patches = plt.hist(VelocityValues, <span style="color: #B452CD">400</span>, facecolor=<span style="color: #CD5555">'green'</span>)
|
||||
|
||||
plt.xlabel(<span style="color: #CD5555">'$v$'</span>)
|
||||
plt.ylabel(<span style="color: #CD5555">'Velocity distribution P(v)'</span>)
|
||||
plt.title(<span style="color: #CD5555">r'Velocity histogram at $k_BT=2$'</span>)
|
||||
plt.axis([-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">0</span>, <span style="color: #B452CD">600</span>])
|
||||
plt.grid(<span style="color: #658b00">True</span>)
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">collections</span> <span style="color: #8B008B; font-weight: bold">import</span> Counter
|
||||
|
||||
<span style="color: #228B22">#print (Counter(VelocityValues))</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span> (VelocityValues[:<span style="color: #B452CD">20</span>])
|
||||
VelocityValues=<span style="color: #658b00">list</span>(Counter(VelocityValues).keys())
|
||||
d=<span style="color: #658b00">list</span>(Counter(VelocityValues).values())
|
||||
|
||||
VelocityValues=np.asarray(VelocityValues)[:, np.newaxis]
|
||||
d=np.asarray(d)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span> (VelocityValues.shape, d.shape)
|
||||
|
||||
plt.scatter(VelocityValues, d)
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22">#2nd Degree Polynomial</span>
|
||||
poly_feat=PolynomialFeatures(degree=<span style="color: #B452CD">20</span>, include_bias=<span style="color: #658b00">False</span>)
|
||||
X_poly=poly_feat.fit_transform(VelocityValues)
|
||||
lin_reg=LinearRegression()
|
||||
poly_fit=lin_reg.fit(X_poly,d)
|
||||
|
||||
y_plot=poly_fit.predict(X_poly)
|
||||
plt.title(<span style="color: #CD5555">"Polynomial Fit"</span>)
|
||||
plt.plot(VelocityValues, y_plot, color=<span style="color: #CD5555">'black'</span>, label=<span style="color: #CD5555">"Fit"</span>)
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22">#Decision Trees</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
|
||||
regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">2</span>)
|
||||
regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
|
||||
regr_3=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
|
||||
regr_1.fit(VelocityValues, d)
|
||||
regr_2.fit(VelocityValues, d)
|
||||
regr_3.fit(VelocityValues, d)
|
||||
|
||||
X_test = np.arange(<span style="color: #B452CD">0.0</span>, MCcycles, <span style="color: #B452CD">0.01</span>)[:, np.newaxis]
|
||||
y_1=regr_1.predict(X_test)
|
||||
y_2=regr_2.predict(X_test)
|
||||
y_3=regr_3.predict(X_test)
|
||||
|
||||
plt.title(<span style="color: #CD5555">"Decision Tree"</span>)
|
||||
plt.plot(X_test, y_1, color=<span style="color: #CD5555">"red"</span>, label=<span style="color: #CD5555">"max_depth=2"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.plot(X_test, y_2, color=<span style="color: #CD5555">"green"</span>, label=<span style="color: #CD5555">"max_depth=5"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.plot(X_test, y_3, color=<span style="color: #CD5555">"m"</span>, label=<span style="color: #CD5555">"max_depth=7"</span>, linewidth=<span style="color: #B452CD">2</span>)
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22">#Separate each frequency not in one specific velocity, but in a range of values,</span>
|
||||
<span style="color: #228B22">#i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...</span>
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
|
||||
|
||||
@@ -93,7 +93,7 @@ end of tocinfo -->
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>May 30, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Nov 1, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -103,6 +103,15 @@ end of tocinfo -->
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<p>
|
||||
Decision trees are supervised learning algorithms used for both,
|
||||
classification and regression tasks where we will concentrate on
|
||||
classification in this first part of our decision tree tutorial.
|
||||
Decision trees are assigned to the information based learning
|
||||
algorithms which use different measures of information gain for
|
||||
learning. We can use decision trees for issues where we have
|
||||
continuous but also categorical input and target features.
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
@@ -268,6 +277,105 @@ plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<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: #408080; font-style: italic"># Program to test the Metropolis algorithm with one particle at given temp in</span>
|
||||
<span style="color: #408080; font-style: italic"># one dimension</span>
|
||||
<span style="color: #408080; font-style: italic">#!/usr/bin/env python</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.mlab</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">mlab</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">import</span> <span style="color: #0000FF; font-weight: bold">random</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> sqrt, exp, log
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
|
||||
<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: #408080; font-style: italic"># initialize the rng with a seed</span>
|
||||
random<span style="color: #666666">.</span>seed()
|
||||
<span style="color: #408080; font-style: italic"># Hard coding of input parameters</span>
|
||||
MCcycles <span style="color: #666666">=</span> <span style="color: #666666">100000</span>
|
||||
Temperature <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
|
||||
beta <span style="color: #666666">=</span> <span style="color: #666666">1./</span>Temperature
|
||||
InitialVelocity <span style="color: #666666">=</span> <span style="color: #666666">-2.0</span>
|
||||
CurrentVelocity <span style="color: #666666">=</span> InitialVelocity
|
||||
Energy <span style="color: #666666">=</span> <span style="color: #666666">0.5*</span>InitialVelocity<span style="color: #666666">*</span>InitialVelocity
|
||||
VelocityRange <span style="color: #666666">=</span> <span style="color: #666666">10*</span>sqrt(Temperature)
|
||||
VelocityStep <span style="color: #666666">=</span> <span style="color: #666666">2*</span>VelocityRange<span style="color: #666666">/10.</span>
|
||||
AverageEnergy <span style="color: #666666">=</span> Energy
|
||||
AverageEnergy2 <span style="color: #666666">=</span> Energy<span style="color: #666666">*</span>Energy
|
||||
VelocityValues <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(MCcycles)
|
||||
<span style="color: #408080; font-style: italic"># The Monte Carlo sampling with Metropolis starts here</span>
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span> (<span style="color: #666666">1</span>, MCcycles, <span style="color: #666666">1</span>):
|
||||
TrialVelocity <span style="color: #666666">=</span> CurrentVelocity <span style="color: #666666">+</span> (<span style="color: #666666">2.0*</span>random<span style="color: #666666">.</span>random() <span style="color: #666666">-</span> <span style="color: #666666">1.0</span>)<span style="color: #666666">*</span>VelocityStep
|
||||
EnergyChange <span style="color: #666666">=</span> <span style="color: #666666">0.5*</span>(TrialVelocity<span style="color: #666666">*</span>TrialVelocity <span style="color: #666666">-</span>CurrentVelocity<span style="color: #666666">*</span>CurrentVelocity);
|
||||
<span style="color: #008000; font-weight: bold">if</span> random<span style="color: #666666">.</span>random() <span style="color: #666666"><=</span> exp(<span style="color: #666666">-</span>beta<span style="color: #666666">*</span>EnergyChange):
|
||||
CurrentVelocity <span style="color: #666666">=</span> TrialVelocity
|
||||
Energy <span style="color: #666666">+=</span> EnergyChange
|
||||
VelocityValues[i] <span style="color: #666666">=</span> CurrentVelocity
|
||||
AverageEnergy <span style="color: #666666">+=</span> Energy
|
||||
AverageEnergy2 <span style="color: #666666">+=</span> Energy<span style="color: #666666">*</span>Energy
|
||||
<span style="color: #408080; font-style: italic">#Final averages</span>
|
||||
AverageEnergy <span style="color: #666666">=</span> AverageEnergy<span style="color: #666666">/</span>MCcycles
|
||||
AverageEnergy2 <span style="color: #666666">=</span> AverageEnergy2<span style="color: #666666">/</span>MCcycles
|
||||
Variance <span style="color: #666666">=</span> AverageEnergy2 <span style="color: #666666">-</span> AverageEnergy<span style="color: #666666">*</span>AverageEnergy
|
||||
<span style="color: #008000; font-weight: bold">print</span>(AverageEnergy, Variance)
|
||||
n, bins, patches <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>hist(VelocityValues, <span style="color: #666666">400</span>, facecolor<span style="color: #666666">=</span><span style="color: #BA2121">'green'</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'$v$'</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'Velocity distribution P(v)'</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r'Velocity histogram at $k_BT=2$'</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-5</span>, <span style="color: #666666">5</span>, <span style="color: #666666">0</span>, <span style="color: #666666">600</span>])
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>)
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">collections</span> <span style="color: #008000; font-weight: bold">import</span> Counter
|
||||
|
||||
<span style="color: #408080; font-style: italic">#print (Counter(VelocityValues))</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span> (VelocityValues[:<span style="color: #666666">20</span>])
|
||||
VelocityValues<span style="color: #666666">=</span><span style="color: #008000">list</span>(Counter(VelocityValues)<span style="color: #666666">.</span>keys())
|
||||
d<span style="color: #666666">=</span><span style="color: #008000">list</span>(Counter(VelocityValues)<span style="color: #666666">.</span>values())
|
||||
|
||||
VelocityValues<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(VelocityValues)[:, np<span style="color: #666666">.</span>newaxis]
|
||||
d<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(d)
|
||||
<span style="color: #008000; font-weight: bold">print</span> (VelocityValues<span style="color: #666666">.</span>shape, d<span style="color: #666666">.</span>shape)
|
||||
|
||||
plt<span style="color: #666666">.</span>scatter(VelocityValues, d)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #408080; font-style: italic">#2nd Degree Polynomial</span>
|
||||
poly_feat<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=20</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
|
||||
X_poly<span style="color: #666666">=</span>poly_feat<span style="color: #666666">.</span>fit_transform(VelocityValues)
|
||||
lin_reg<span style="color: #666666">=</span>LinearRegression()
|
||||
poly_fit<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly,d)
|
||||
|
||||
y_plot<span style="color: #666666">=</span>poly_fit<span style="color: #666666">.</span>predict(X_poly)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Polynomial Fit"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(VelocityValues, y_plot, color<span style="color: #666666">=</span><span style="color: #BA2121">'black'</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Fit"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #408080; font-style: italic">#Decision Trees</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
|
||||
regr_1<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>)
|
||||
regr_2<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=5</span>)
|
||||
regr_3<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=7</span>)
|
||||
regr_1<span style="color: #666666">.</span>fit(VelocityValues, d)
|
||||
regr_2<span style="color: #666666">.</span>fit(VelocityValues, d)
|
||||
regr_3<span style="color: #666666">.</span>fit(VelocityValues, d)
|
||||
|
||||
X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0.0</span>, MCcycles, <span style="color: #666666">0.01</span>)[:, np<span style="color: #666666">.</span>newaxis]
|
||||
y_1<span style="color: #666666">=</span>regr_1<span style="color: #666666">.</span>predict(X_test)
|
||||
y_2<span style="color: #666666">=</span>regr_2<span style="color: #666666">.</span>predict(X_test)
|
||||
y_3<span style="color: #666666">=</span>regr_3<span style="color: #666666">.</span>predict(X_test)
|
||||
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Decision Tree"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X_test, y_1, color<span style="color: #666666">=</span><span style="color: #BA2121">"red"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=2"</span>, linewidth<span style="color: #666666">=2</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X_test, y_2, color<span style="color: #666666">=</span><span style="color: #BA2121">"green"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=5"</span>, linewidth<span style="color: #666666">=2</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X_test, y_3, color<span style="color: #666666">=</span><span style="color: #BA2121">"m"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"max_depth=7"</span>, linewidth<span style="color: #666666">=2</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #408080; font-style: italic">#Separate each frequency not in one specific velocity, but in a range of values,</span>
|
||||
<span style="color: #408080; font-style: italic">#i.e. frequency of all velocities in range -5 to -4.9, -4.9 to -4.8, etc...</span>
|
||||
</pre></div>
|
||||
<p>
|
||||
|
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<!-- ------------------- end of main content --------------- -->
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|
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|
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|
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Reference in New Issue
Block a user