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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<div class="section" id="model-complexity-influence">
<span id="example-applications-plot-model-complexity-influence-py"></span><h1>Model Complexity Influence<a class="headerlink" href="#model-complexity-influence" title="Permalink to this headline">¶</a></h1>
<p>Demonstrate how model complexity influences both prediction accuracy and
computational performance.</p>
<p>The dataset is the Boston Housing dataset (resp. 20 Newsgroups) for
regression (resp. classification).</p>
<p>For each class of models we make the model complexity vary through the choice
of relevant model parameters and measure the influence on both computational
performance (latency) and predictive power (MSE or Hamming Loss).</p>
<ul class="horizontal">
<li><a class="first reference internal image-reference" href="../../_images/plot_model_complexity_influence_0011.png"><img alt="../../_images/plot_model_complexity_influence_0011.png" src="../../_images/plot_model_complexity_influence_0011.png" style="width: 564.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_model_complexity_influence_0021.png"><img alt="../../_images/plot_model_complexity_influence_0021.png" src="../../_images/plot_model_complexity_influence_0021.png" style="width: 564.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_model_complexity_influence_0031.png"><img alt="../../_images/plot_model_complexity_influence_0031.png" src="../../_images/plot_model_complexity_influence_0031.png" style="width: 564.0px; height: 282.0px;" /></a>
</li>
</ul>
<p><strong>Script output</strong>:</p>
<div class="highlight-python"><div class="highlight"><pre>Benchmarking SGDClassifier(alpha=0.001, class_weight=None, epsilon=0.1, eta0=0.0,
fit_intercept=True, l1_ratio=0.25, learning_rate='optimal',
loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet',
power_t=0.5, random_state=None, shuffle=False, verbose=0,
warm_start=False)
Complexity: 4538 | Hamming Loss (Misclassification Ratio): 0.2554 | Pred. Time: 0.027533s
Benchmarking SGDClassifier(alpha=0.001, class_weight=None, epsilon=0.1, eta0=0.0,
fit_intercept=True, l1_ratio=0.5, learning_rate='optimal',
loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet',
power_t=0.5, random_state=None, shuffle=False, verbose=0,
warm_start=False)
Complexity: 1666 | Hamming Loss (Misclassification Ratio): 0.2920 | Pred. Time: 0.019870s
Benchmarking SGDClassifier(alpha=0.001, class_weight=None, epsilon=0.1, eta0=0.0,
fit_intercept=True, l1_ratio=0.75, learning_rate='optimal',
loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet',
power_t=0.5, random_state=None, shuffle=False, verbose=0,
warm_start=False)
Complexity: 890 | Hamming Loss (Misclassification Ratio): 0.3175 | Pred. Time: 0.015984s
Benchmarking SGDClassifier(alpha=0.001, class_weight=None, epsilon=0.1, eta0=0.0,
fit_intercept=True, l1_ratio=0.9, learning_rate='optimal',
loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet',
power_t=0.5, random_state=None, shuffle=False, verbose=0,
warm_start=False)
Complexity: 674 | Hamming Loss (Misclassification Ratio): 0.3334 | Pred. Time: 0.014499s
Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05,
kernel='rbf', max_iter=-1, nu=0.1, probability=False, random_state=None,
shrinking=True, tol=0.001, verbose=False)
Complexity: 69 | MSE: 31.8133 | Pred. Time: 0.000393s
Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05,
kernel='rbf', max_iter=-1, nu=0.25, probability=False,
random_state=None, shrinking=True, tol=0.001, verbose=False)
Complexity: 136 | MSE: 25.6140 | Pred. Time: 0.000726s
Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05,
kernel='rbf', max_iter=-1, nu=0.5, probability=False, random_state=None,
shrinking=True, tol=0.001, verbose=False)
Complexity: 243 | MSE: 22.3315 | Pred. Time: 0.001269s
Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05,
kernel='rbf', max_iter=-1, nu=0.75, probability=False,
random_state=None, shrinking=True, tol=0.001, verbose=False)
Complexity: 350 | MSE: 21.3679 | Pred. Time: 0.001808s
Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05,
kernel='rbf', max_iter=-1, nu=0.9, probability=False, random_state=None,
shrinking=True, tol=0.001, verbose=False)
Complexity: 404 | MSE: 21.0915 | Pred. Time: 0.002309s
Benchmarking GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',
max_depth=3, max_features=None, max_leaf_nodes=None,
min_samples_leaf=1, min_samples_split=2, n_estimators=10,
random_state=None, subsample=1.0, verbose=0, warm_start=False)
Complexity: 10 | MSE: 27.9672 | Pred. Time: 0.000061s
Benchmarking GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',
max_depth=3, max_features=None, max_leaf_nodes=None,
min_samples_leaf=1, min_samples_split=2, n_estimators=50,
random_state=None, subsample=1.0, verbose=0, warm_start=False)
Complexity: 50 | MSE: 8.0288 | Pred. Time: 0.000145s
Benchmarking GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',
max_depth=3, max_features=None, max_leaf_nodes=None,
min_samples_leaf=1, min_samples_split=2, n_estimators=100,
random_state=None, subsample=1.0, verbose=0, warm_start=False)
Complexity: 100 | MSE: 6.7578 | Pred. Time: 0.000241s
Benchmarking GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',
max_depth=3, max_features=None, max_leaf_nodes=None,
min_samples_leaf=1, min_samples_split=2, n_estimators=200,
random_state=None, subsample=1.0, verbose=0, warm_start=False)
Complexity: 200 | MSE: 5.8592 | Pred. Time: 0.000423s
Benchmarking GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',
max_depth=3, max_features=None, max_leaf_nodes=None,
min_samples_leaf=1, min_samples_split=2, n_estimators=500,
random_state=None, subsample=1.0, verbose=0, warm_start=False)
Complexity: 500 | MSE: 6.0492 | Pred. Time: 0.001017s
</pre></div>
</div>
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_model_complexity_influence.py"><tt class="xref download docutils literal"><span class="pre">plot_model_complexity_influence.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="n">__doc__</span><span class="p">)</span>
<span class="c"># Author: Eustache Diemert <[email protected]></span>
<span class="c"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.axes_grid1.parasite_axes</span> <span class="kn">import</span> <span class="n">host_subplot</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.axisartist.axislines</span> <span class="kn">import</span> <span class="n">Axes</span>
<span class="kn">from</span> <span class="nn">scipy.sparse.csr</span> <span class="kn">import</span> <a href="http://docs.scipy.org/doc/scipy-0.11.0/reference/generated/scipy.sparse.csr_matrix.getH.html#scipy.sparse.csr_matrix"><span class="n">csr_matrix</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.utils.shuffle.html#sklearn.utils.shuffle"><span class="n">shuffle</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.mean_squared_error.html#sklearn.metrics.mean_squared_error"><span class="n">mean_squared_error</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm.classes</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.NuSVR.html#sklearn.svm.NuSVR"><span class="n">NuSVR</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble.gradient_boosting</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor"><span class="n">GradientBoostingRegressor</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model.stochastic_gradient</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.SGDClassifier.html#sklearn.linear_model.SGDClassifier"><span class="n">SGDClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.hamming_loss.html#sklearn.metrics.hamming_loss"><span class="n">hamming_loss</span></a>
<span class="c">###############################################################################</span>
<span class="c"># Routines</span>
<span class="c"># initialize random generator</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">generate_data</span><span class="p">(</span><span class="n">case</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
<span class="sd">"""Generate regression/classification data."""</span>
<span class="n">bunch</span> <span class="o">=</span> <span class="bp">None</span>
<span class="k">if</span> <span class="n">case</span> <span class="o">==</span> <span class="s">'regression'</span><span class="p">:</span>
<span class="n">bunch</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_boston.html#sklearn.datasets.load_boston"><span class="n">datasets</span><span class="o">.</span><span class="n">load_boston</span></a><span class="p">()</span>
<span class="k">elif</span> <span class="n">case</span> <span class="o">==</span> <span class="s">'classification'</span><span class="p">:</span>
<span class="n">bunch</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_20newsgroups_vectorized.html#sklearn.datasets.fetch_20newsgroups_vectorized"><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_20newsgroups_vectorized</span></a><span class="p">(</span><span class="n">subset</span><span class="o">=</span><span class="s">'all'</span><span class="p">)</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.utils.shuffle.html#sklearn.utils.shuffle"><span class="n">shuffle</span></a><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">bunch</span><span class="o">.</span><span class="n">target</span><span class="p">)</span>
<span class="n">offset</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mf">0.8</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="n">offset</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">offset</span><span class="p">]</span>
<span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">offset</span><span class="p">:],</span> <span class="n">y</span><span class="p">[</span><span class="n">offset</span><span class="p">:]</span>
<span class="k">if</span> <span class="n">sparse</span><span class="p">:</span>
<span class="n">X_train</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/scipy-0.11.0/reference/generated/scipy.sparse.csr_matrix.getH.html#scipy.sparse.csr_matrix"><span class="n">csr_matrix</span></a><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_test</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/scipy-0.11.0/reference/generated/scipy.sparse.csr_matrix.getH.html#scipy.sparse.csr_matrix"><span class="n">csr_matrix</span></a><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">X_train</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.array.html#numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">X_test</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.array.html#numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">y_test</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.array.html#numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">)</span>
<span class="n">y_train</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.array.html#numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">y_train</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="p">{</span><span class="s">'X_train'</span><span class="p">:</span> <span class="n">X_train</span><span class="p">,</span> <span class="s">'X_test'</span><span class="p">:</span> <span class="n">X_test</span><span class="p">,</span> <span class="s">'y_train'</span><span class="p">:</span> <span class="n">y_train</span><span class="p">,</span>
<span class="s">'y_test'</span><span class="p">:</span> <span class="n">y_test</span><span class="p">}</span>
<span class="k">return</span> <span class="n">data</span>
<span class="k">def</span> <span class="nf">benchmark_influence</span><span class="p">(</span><span class="n">conf</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Benchmark influence of :changing_param: on both MSE and latency.</span>
<span class="sd"> """</span>
<span class="n">prediction_times</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">prediction_powers</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">complexities</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">param_value</span> <span class="ow">in</span> <span class="n">conf</span><span class="p">[</span><span class="s">'changing_param_values'</span><span class="p">]:</span>
<span class="n">conf</span><span class="p">[</span><span class="s">'tuned_params'</span><span class="p">][</span><span class="n">conf</span><span class="p">[</span><span class="s">'changing_param'</span><span class="p">]]</span> <span class="o">=</span> <span class="n">param_value</span>
<span class="n">estimator</span> <span class="o">=</span> <span class="n">conf</span><span class="p">[</span><span class="s">'estimator'</span><span class="p">](</span><span class="o">**</span><span class="n">conf</span><span class="p">[</span><span class="s">'tuned_params'</span><span class="p">])</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Benchmarking </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">estimator</span><span class="p">)</span>
<span class="n">estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">conf</span><span class="p">[</span><span class="s">'data'</span><span class="p">][</span><span class="s">'X_train'</span><span class="p">],</span> <span class="n">conf</span><span class="p">[</span><span class="s">'data'</span><span class="p">][</span><span class="s">'y_train'</span><span class="p">])</span>
<span class="n">conf</span><span class="p">[</span><span class="s">'postfit_hook'</span><span class="p">](</span><span class="n">estimator</span><span class="p">)</span>
<span class="n">complexity</span> <span class="o">=</span> <span class="n">conf</span><span class="p">[</span><span class="s">'complexity_computer'</span><span class="p">](</span><span class="n">estimator</span><span class="p">)</span>
<span class="n">complexities</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">complexity</span><span class="p">)</span>
<span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">conf</span><span class="p">[</span><span class="s">'n_samples'</span><span class="p">]):</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">conf</span><span class="p">[</span><span class="s">'data'</span><span class="p">][</span><span class="s">'X_test'</span><span class="p">])</span>
<span class="n">elapsed_time</span> <span class="o">=</span> <span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start_time</span><span class="p">)</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">conf</span><span class="p">[</span><span class="s">'n_samples'</span><span class="p">])</span>
<span class="n">prediction_times</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">elapsed_time</span><span class="p">)</span>
<span class="n">pred_score</span> <span class="o">=</span> <span class="n">conf</span><span class="p">[</span><span class="s">'prediction_performance_computer'</span><span class="p">](</span>
<span class="n">conf</span><span class="p">[</span><span class="s">'data'</span><span class="p">][</span><span class="s">'y_test'</span><span class="p">],</span> <span class="n">y_pred</span><span class="p">)</span>
<span class="n">prediction_powers</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pred_score</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Complexity: </span><span class="si">%d</span><span class="s"> | </span><span class="si">%s</span><span class="s">: </span><span class="si">%.4f</span><span class="s"> | Pred. Time: </span><span class="si">%f</span><span class="s">s</span><span class="se">\n</span><span class="s">"</span> <span class="o">%</span> <span class="p">(</span>
<span class="n">complexity</span><span class="p">,</span> <span class="n">conf</span><span class="p">[</span><span class="s">'prediction_performance_label'</span><span class="p">],</span> <span class="n">pred_score</span><span class="p">,</span>
<span class="n">elapsed_time</span><span class="p">))</span>
<span class="k">return</span> <span class="n">prediction_powers</span><span class="p">,</span> <span class="n">prediction_times</span><span class="p">,</span> <span class="n">complexities</span>
<span class="k">def</span> <span class="nf">plot_influence</span><span class="p">(</span><span class="n">conf</span><span class="p">,</span> <span class="n">mse_values</span><span class="p">,</span> <span class="n">prediction_times</span><span class="p">,</span> <span class="n">complexities</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Plot influence of model complexity on both accuracy and latency.</span>
<span class="sd"> """</span>
<a href="http://matplotlib.org/api/figure_api.html#matplotlib.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<span class="n">host</span> <span class="o">=</span> <span class="n">host_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">,</span> <span class="n">axes_class</span><span class="o">=</span><span class="n">Axes</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplots_adjust"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">right</span><span class="o">=</span><span class="mf">0.75</span><span class="p">)</span>
<span class="n">par1</span> <span class="o">=</span> <span class="n">host</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
<span class="n">host</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">'Model Complexity (</span><span class="si">%s</span><span class="s">)'</span> <span class="o">%</span> <span class="n">conf</span><span class="p">[</span><span class="s">'complexity_label'</span><span class="p">])</span>
<span class="n">y1_label</span> <span class="o">=</span> <span class="n">conf</span><span class="p">[</span><span class="s">'prediction_performance_label'</span><span class="p">]</span>
<span class="n">y2_label</span> <span class="o">=</span> <span class="s">"Time (s)"</span>
<span class="n">host</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y1_label</span><span class="p">)</span>
<span class="n">par1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y2_label</span><span class="p">)</span>
<span class="n">p1</span><span class="p">,</span> <span class="o">=</span> <span class="n">host</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">complexities</span><span class="p">,</span> <span class="n">mse_values</span><span class="p">,</span> <span class="s">'b-'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"prediction error"</span><span class="p">)</span>
<span class="n">p2</span><span class="p">,</span> <span class="o">=</span> <span class="n">par1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">complexities</span><span class="p">,</span> <span class="n">prediction_times</span><span class="p">,</span> <span class="s">'r-'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s">"latency"</span><span class="p">)</span>
<span class="n">host</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s">'upper right'</span><span class="p">)</span>
<span class="n">host</span><span class="o">.</span><span class="n">axis</span><span class="p">[</span><span class="s">"left"</span><span class="p">]</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="n">p1</span><span class="o">.</span><span class="n">get_color</span><span class="p">())</span>
<span class="n">par1</span><span class="o">.</span><span class="n">axis</span><span class="p">[</span><span class="s">"right"</span><span class="p">]</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="n">p2</span><span class="o">.</span><span class="n">get_color</span><span class="p">())</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s">'Influence of Model Complexity - </span><span class="si">%s</span><span class="s">'</span> <span class="o">%</span> <span class="n">conf</span><span class="p">[</span><span class="s">'estimator'</span><span class="p">]</span><span class="o">.</span><span class="n">__name__</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
<span class="k">def</span> <span class="nf">_count_nonzero_coefficients</span><span class="p">(</span><span class="n">estimator</span><span class="p">):</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="n">coef_</span><span class="o">.</span><span class="n">toarray</span><span class="p">()</span>
<span class="k">return</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.count_nonzero.html#numpy.count_nonzero"><span class="n">np</span><span class="o">.</span><span class="n">count_nonzero</span></a><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="c">###############################################################################</span>
<span class="c"># main code</span>
<span class="n">regression_data</span> <span class="o">=</span> <span class="n">generate_data</span><span class="p">(</span><span class="s">'regression'</span><span class="p">)</span>
<span class="n">classification_data</span> <span class="o">=</span> <span class="n">generate_data</span><span class="p">(</span><span class="s">'classification'</span><span class="p">,</span> <span class="n">sparse</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">configurations</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">{</span><span class="s">'estimator'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.SGDClassifier.html#sklearn.linear_model.SGDClassifier"><span class="n">SGDClassifier</span></a><span class="p">,</span>
<span class="s">'tuned_params'</span><span class="p">:</span> <span class="p">{</span><span class="s">'penalty'</span><span class="p">:</span> <span class="s">'elasticnet'</span><span class="p">,</span> <span class="s">'alpha'</span><span class="p">:</span> <span class="mf">0.001</span><span class="p">,</span> <span class="s">'loss'</span><span class="p">:</span>
<span class="s">'modified_huber'</span><span class="p">,</span> <span class="s">'fit_intercept'</span><span class="p">:</span> <span class="bp">True</span><span class="p">},</span>
<span class="s">'changing_param'</span><span class="p">:</span> <span class="s">'l1_ratio'</span><span class="p">,</span>
<span class="s">'changing_param_values'</span><span class="p">:</span> <span class="p">[</span><span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.75</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">],</span>
<span class="s">'complexity_label'</span><span class="p">:</span> <span class="s">'non_zero coefficients'</span><span class="p">,</span>
<span class="s">'complexity_computer'</span><span class="p">:</span> <span class="n">_count_nonzero_coefficients</span><span class="p">,</span>
<span class="s">'prediction_performance_computer'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.metrics.hamming_loss.html#sklearn.metrics.hamming_loss"><span class="n">hamming_loss</span></a><span class="p">,</span>
<span class="s">'prediction_performance_label'</span><span class="p">:</span> <span class="s">'Hamming Loss (Misclassification Ratio)'</span><span class="p">,</span>
<span class="s">'postfit_hook'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">sparsify</span><span class="p">(),</span>
<span class="s">'data'</span><span class="p">:</span> <span class="n">classification_data</span><span class="p">,</span>
<span class="s">'n_samples'</span><span class="p">:</span> <span class="mi">30</span><span class="p">},</span>
<span class="p">{</span><span class="s">'estimator'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.svm.NuSVR.html#sklearn.svm.NuSVR"><span class="n">NuSVR</span></a><span class="p">,</span>
<span class="s">'tuned_params'</span><span class="p">:</span> <span class="p">{</span><span class="s">'C'</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span> <span class="s">'gamma'</span><span class="p">:</span> <span class="mi">2</span><span class="o">**-</span><span class="mi">15</span><span class="p">},</span>
<span class="s">'changing_param'</span><span class="p">:</span> <span class="s">'nu'</span><span class="p">,</span>
<span class="s">'changing_param_values'</span><span class="p">:</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.75</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">],</span>
<span class="s">'complexity_label'</span><span class="p">:</span> <span class="s">'n_support_vectors'</span><span class="p">,</span>
<span class="s">'complexity_computer'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">support_vectors_</span><span class="p">),</span>
<span class="s">'data'</span><span class="p">:</span> <span class="n">regression_data</span><span class="p">,</span>
<span class="s">'postfit_hook'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="p">,</span>
<span class="s">'prediction_performance_computer'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.metrics.mean_squared_error.html#sklearn.metrics.mean_squared_error"><span class="n">mean_squared_error</span></a><span class="p">,</span>
<span class="s">'prediction_performance_label'</span><span class="p">:</span> <span class="s">'MSE'</span><span class="p">,</span>
<span class="s">'n_samples'</span><span class="p">:</span> <span class="mi">30</span><span class="p">},</span>
<span class="p">{</span><span class="s">'estimator'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingRegressor.html#sklearn.ensemble.GradientBoostingRegressor"><span class="n">GradientBoostingRegressor</span></a><span class="p">,</span>
<span class="s">'tuned_params'</span><span class="p">:</span> <span class="p">{</span><span class="s">'loss'</span><span class="p">:</span> <span class="s">'ls'</span><span class="p">},</span>
<span class="s">'changing_param'</span><span class="p">:</span> <span class="s">'n_estimators'</span><span class="p">,</span>
<span class="s">'changing_param_values'</span><span class="p">:</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">500</span><span class="p">],</span>
<span class="s">'complexity_label'</span><span class="p">:</span> <span class="s">'n_trees'</span><span class="p">,</span>
<span class="s">'complexity_computer'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">n_estimators</span><span class="p">,</span>
<span class="s">'data'</span><span class="p">:</span> <span class="n">regression_data</span><span class="p">,</span>
<span class="s">'postfit_hook'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="p">,</span>
<span class="s">'prediction_performance_computer'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.metrics.mean_squared_error.html#sklearn.metrics.mean_squared_error"><span class="n">mean_squared_error</span></a><span class="p">,</span>
<span class="s">'prediction_performance_label'</span><span class="p">:</span> <span class="s">'MSE'</span><span class="p">,</span>
<span class="s">'n_samples'</span><span class="p">:</span> <span class="mi">30</span><span class="p">},</span>
<span class="p">]</span>
<span class="k">for</span> <span class="n">conf</span> <span class="ow">in</span> <span class="n">configurations</span><span class="p">:</span>
<span class="n">prediction_performances</span><span class="p">,</span> <span class="n">prediction_times</span><span class="p">,</span> <span class="n">complexities</span> <span class="o">=</span> \
<span class="n">benchmark_influence</span><span class="p">(</span><span class="n">conf</span><span class="p">)</span>
<span class="n">plot_influence</span><span class="p">(</span><span class="n">conf</span><span class="p">,</span> <span class="n">prediction_performances</span><span class="p">,</span> <span class="n">prediction_times</span><span class="p">,</span>
<span class="n">complexities</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>Total running time of the example:</strong> 20.01 seconds
( 0 minutes 20.01 seconds)</p>
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