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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>bike-sharing-demand</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<style type="text/css">
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<h1 id="Goal:-improve-evaluation-a-model">Goal: improve evaluation a model<a class="anchor-link" href="#Goal:-improve-evaluation-a-model">¶</a></h1><h2 id="Evoluation-a-model-is-the-most-important-thing!">Evoluation a model is the most important thing!<a class="anchor-link" href="#Evoluation-a-model-is-the-most-important-thing!">¶</a></h2><p>Remember this point is the most important.<br>
If you don't understand your a quality function or don't have a good strategy how to evaluate model - rest is doesn't matter.</p>
<p>Check list</p>
<ol>
<li>What data set is using for evaluation? </li>
<li>What is range values for a quality function (what the value is for an ideal solution)?</li>
<li>What and how make impact on output value (a quality function)? </li>
</ol>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">ExtraTreesRegressor</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">make_scorer</span>
<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">shuffle</span>
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<h1 id="Read-data">Read data<a class="anchor-link" href="#Read-data">¶</a></h1>
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<div class=" highlight hl-ipython2"><pre><span class="n">train</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s">'train.csv'</span><span class="p">)</span>
<span class="n">train</span><span class="o">.</span><span class="n">head</span><span class="p">()</span>
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<div>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>datetime</th>
<th>season</th>
<th>holiday</th>
<th>workingday</th>
<th>weather</th>
<th>temp</th>
<th>atemp</th>
<th>humidity</th>
<th>windspeed</th>
<th>casual</th>
<th>registered</th>
<th>count</th>
</tr>
</thead>
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<tr>
<th>0</th>
<td>2011-01-01 00:00:00</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>9.84</td>
<td>14.395</td>
<td>81</td>
<td>0</td>
<td>3</td>
<td>13</td>
<td>16</td>
</tr>
<tr>
<th>1</th>
<td>2011-01-01 01:00:00</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>9.02</td>
<td>13.635</td>
<td>80</td>
<td>0</td>
<td>8</td>
<td>32</td>
<td>40</td>
</tr>
<tr>
<th>2</th>
<td>2011-01-01 02:00:00</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>9.02</td>
<td>13.635</td>
<td>80</td>
<td>0</td>
<td>5</td>
<td>27</td>
<td>32</td>
</tr>
<tr>
<th>3</th>
<td>2011-01-01 03:00:00</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>9.84</td>
<td>14.395</td>
<td>75</td>
<td>0</td>
<td>3</td>
<td>10</td>
<td>13</td>
</tr>
<tr>
<th>4</th>
<td>2011-01-01 04:00:00</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>9.84</td>
<td>14.395</td>
<td>75</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>1</td>
</tr>
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<ol>
<li><strong>datetime</strong> - hourly date + timestamp </li>
<li><strong>season</strong> - 1 = spring, 2 = summer, 3 = fall, 4 = winter </li>
<li><strong>holiday</strong> - whether the day is considered a holiday</li>
<li><strong>workingday</strong> - whether the day is neither a weekend nor holiday</li>
<li><strong>weather</strong> -
1: Clear, Few clouds, Partly cloudy, Partly cloudy
2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist
3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds
4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog </li>
<li><strong>temp</strong> - temperature in Celsius</li>
<li><strong>atemp</strong> - "feels like" temperature in Celsius</li>
<li><strong>humidity</strong> - relative humidity</li>
<li><strong>windspeed</strong> - wind speed</li>
<li><strong>casual</strong> - number of non-registered user rentals initiated</li>
<li><strong>registered</strong> - number of registered user rentals initiated</li>
<li><strong>count</strong> - number of total rentals</li>
</ol>
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<h1 id="Build-a-model">Build a model<a class="anchor-link" href="#Build-a-model">¶</a></h1>
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<div class=" highlight hl-ipython2"><pre><span class="n">model</span> <span class="o">=</span> <span class="n">ExtraTreesRegressor</span><span class="p">()</span>
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<h2 id="train-&-test-(data-sets)">train & test (data sets)<a class="anchor-link" href="#train-&-test-(data-sets)">¶</a></h2><p>Prepare two data sets (for training and for testing):</p>
<h3 id="train-data-set">train data set<a class="anchor-link" href="#train-data-set">¶</a></h3><p><strong>X_train</strong> - features (<em>matrix</em>).<br>
<strong>y_train</strong> - target variable (<em>vector</em>).</p>
<h3 id="test-data-set">test data set<a class="anchor-link" href="#test-data-set">¶</a></h3><p><strong>X_test</strong> - features (<em>matrix</em>).<br>
<strong>y_test</strong> - target variable (<em>vector</em>).</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">train</span><span class="p">[</span><span class="s">'datetime'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">to_datetime</span><span class="p">(</span> <span class="n">train</span><span class="p">[</span><span class="s">'datetime'</span><span class="p">]</span> <span class="p">)</span>
<span class="n">train</span><span class="p">[</span><span class="s">'day'</span><span class="p">]</span> <span class="o">=</span> <span class="n">train</span><span class="p">[</span><span class="s">'datetime'</span><span class="p">]</span><span class="o">.</span><span class="n">map</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">day</span><span class="p">)</span>
<span class="n">train</span><span class="o">.</span><span class="n">day</span><span class="o">.</span><span class="n">unique</span><span class="p">()</span>
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<pre>array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19])</pre>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">train_test_split</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">last_training_day</span><span class="o">=</span><span class="mf">0.3</span><span class="p">):</span>
<span class="n">days</span> <span class="o">=</span> <span class="n">train</span><span class="o">.</span><span class="n">day</span><span class="o">.</span><span class="n">unique</span><span class="p">()</span>
<span class="n">shuffle</span><span class="p">(</span><span class="n">days</span><span class="p">)</span>
<span class="n">test_days</span> <span class="o">=</span> <span class="n">days</span><span class="p">[:</span> <span class="nb">len</span><span class="p">(</span><span class="n">days</span><span class="p">)</span> <span class="o">*</span> <span class="mf">0.3</span><span class="p">]</span>
<span class="n">data</span><span class="p">[</span><span class="s">'is_test'</span><span class="p">]</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">day</span><span class="o">.</span><span class="n">isin</span><span class="p">(</span><span class="n">test_days</span><span class="p">)</span>
<span class="n">df_train</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">data</span><span class="o">.</span><span class="n">is_test</span> <span class="o">==</span> <span class="bp">False</span><span class="p">]</span>
<span class="n">df_test</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">data</span><span class="o">.</span><span class="n">is_test</span> <span class="o">==</span> <span class="bp">True</span><span class="p">]</span>
<span class="k">return</span> <span class="n">df_train</span><span class="p">,</span> <span class="n">df_test</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">features</span> <span class="o">=</span> <span class="p">[</span><span class="s">'season'</span><span class="p">,</span> <span class="s">'holiday'</span><span class="p">,</span> <span class="s">'workingday'</span><span class="p">,</span> <span class="s">'weather'</span><span class="p">,</span> <span class="s">'temp'</span><span class="p">,</span> <span class="s">'atemp'</span><span class="p">,</span> <span class="s">'humidity'</span><span class="p">,</span> <span class="s">'windspeed'</span><span class="p">]</span>
<span class="n">df_train</span><span class="p">,</span> <span class="n">df_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">train</span><span class="p">)</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="n">df_train</span><span class="p">[</span><span class="n">features</span><span class="p">]</span><span class="o">.</span><span class="n">values</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">df_test</span><span class="p">[</span><span class="n">features</span><span class="p">]</span><span class="o">.</span><span class="n">values</span>
<span class="n">y_train</span> <span class="o">=</span> <span class="n">df_train</span><span class="p">[</span><span class="s">'count'</span><span class="p">]</span><span class="o">.</span><span class="n">values</span>
<span class="n">y_test</span> <span class="o">=</span> <span class="n">df_test</span><span class="p">[</span><span class="s">'count'</span><span class="p">]</span><span class="o">.</span><span class="n">values</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
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<pre>ExtraTreesRegressor(bootstrap=False, criterion='mse', max_depth=None,
max_features='auto', max_leaf_nodes=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=10, n_jobs=1, oob_score=False, random_state=None,
verbose=0, warm_start=False)</pre>
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<h1 id="Evaluation-a-model">Evaluation a model<a class="anchor-link" href="#Evaluation-a-model">¶</a></h1>
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$$ \sqrt{\frac{1}{n} \sum_{i=1}^n (\log(p_i + 1) - \log(a_i+1))^2 }$$<p>where<br>
<strong>n</strong> is the number of hours in the test set<br>
<strong>pi</strong> is your predicted count<br>
<strong>ai</strong> is the actual count<br>
<strong>log(x)</strong> is the natural logarithm</p>
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<h3 id="Why-we-have-+1-for-logarithm-algorithm?-Let's-recall-a-shape-logarithm-function.">Why we have +1 for logarithm algorithm? Let's recall a shape logarithm function.<a class="anchor-link" href="#Why-we-have-+1-for-logarithm-algorithm?-Let's-recall-a-shape-logarithm-function.">¶</a></h3><p>Argument should be greater than 0. In our case <strong>pi</strong> and <strong>ai</strong> can be equals to 0.
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Binary_logarithm_plot_with_ticks.svg/408px-Binary_logarithm_plot_with_ticks.svg.png" /></p>
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<h3 id="Let's-play-around-with-a-quality-function">Let's play around with a quality function<a class="anchor-link" href="#Let's-play-around-with-a-quality-function">¶</a></h3><table>
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<th>pi</th>
<th>ai</th>
<th>result</th>
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<td>1000</td>
<td>0</td>
<td>6.909</td>
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<td>100</td>
<td>0</td>
<td>4.615</td>
</tr>
<tr>
<td>10</td>
<td>0</td>
<td>2.397</td>
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<td>5</td>
<td>0</td>
<td>1.792</td>
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<td>1</td>
<td>0</td>
<td>0.693</td>
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<td>0.5</td>
<td>0</td>
<td>0.405</td>
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<td>0.2</td>
<td>0</td>
<td>0.182</td>
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<tr>
<td>0</td>
<td>0</td>
<td>0.0</td>
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<p>For sample above <code>rmsle(pi, ai)</code> is <strong>3.644</strong>.
<em>Note: but average column result is</em> <strong>2.918</strong>.</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">rmsle</span><span class="p">(</span><span class="n">y_true</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">):</span>
<span class="n">diff</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">y_pred</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">y_true</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">mean_error</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">diff</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">mean_error</span><span class="p">)</span>
<span class="n">scorer</span> <span class="o">=</span> <span class="n">make_scorer</span><span class="p">(</span><span class="n">rmsle</span><span class="p">,</span> <span class="n">greater_is_better</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">rmsle</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">)</span>
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<pre>1.4272746457576084</pre>
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<h2 id="Looks-better-:)">Looks better :)<a class="anchor-link" href="#Looks-better-:)">¶</a></h2><p>We improved evaluation a model. Next step is understand better data and figure out how we can improve result.</p>
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