improving code quality in terms of pylint

docs/build/html/genindex.html

@@ -224,8 +224,6 @@
       <li><a href="quapy.html#quapy.util.create_parent_dir">create_parent_dir() (in module quapy.util)</a>
 </li>
       <li><a href="quapy.method.html#quapy.method.aggregative.cross_generate_predictions">cross_generate_predictions() (in module quapy.method.aggregative)</a>
-</li>
-      <li><a href="quapy.method.html#quapy.method.aggregative.cross_generate_predictions_depr">cross_generate_predictions_depr() (in module quapy.method.aggregative)</a>
 </li>
       <li><a href="quapy.html#quapy.model_selection.cross_val_predict">cross_val_predict() (in module quapy.model_selection)</a>
 </li>

docs/build/html/quapy.classification.html

@@ -316,11 +316,14 @@ fitting <cite>TruncatedSVD</cite> and then <cite>LogisticRegression</cite> on th
 
 <dl class="py method">
 <dt class="sig sig-object py" id="quapy.classification.methods.LowRankLogisticRegression.get_params">
-<span class="sig-name descname"><span class="pre">get_params</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#quapy.classification.methods.LowRankLogisticRegression.get_params" title="Permalink to this definition">¶</a></dt>
+<span class="sig-name descname"><span class="pre">get_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deep</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.classification.methods.LowRankLogisticRegression.get_params" title="Permalink to this definition">¶</a></dt>
 <dd><p>Get hyper-parameters for this estimator.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p>a dictionary with parameter names mapped to their values</p>
+<dd class="field-odd"><p><strong>deep</strong> – compatibility with sklearn</p>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p>a dictionary with parameter names mapped to their values</p>
 </dd>
 </dl>
 </dd></dl>
@@ -524,7 +527,7 @@ dimensionality of the embedding</p>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="quapy.classification.neural.NeuralClassifierTrainer">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">quapy.classification.neural.</span></span><span class="sig-name descname"><span class="pre">NeuralClassifierTrainer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">net</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#quapy.classification.neural.TextClassifierNet" title="quapy.classification.neural.TextClassifierNet"><span class="pre">TextClassifierNet</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">lr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">patience</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">epochs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">64</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size_test</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">512</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">padding_length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">300</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">device</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'cpu'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">checkpointpath</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'../checkpoint/classifier_net.dat'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.classification.neural.NeuralClassifierTrainer" title="Permalink to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">quapy.classification.neural.</span></span><span class="sig-name descname"><span class="pre">NeuralClassifierTrainer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">net</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#quapy.classification.neural.TextClassifierNet" title="quapy.classification.neural.TextClassifierNet"><span class="pre">TextClassifierNet</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">lr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">patience</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">epochs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">200</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">64</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">batch_size_test</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">512</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">padding_length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">300</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">device</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'cuda'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">checkpointpath</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'../checkpoint/classifier_net.dat'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.classification.neural.NeuralClassifierTrainer" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>Trains a neural network for text classification.</p>
 <dl class="field-list simple">

docs/build/html/quapy.data.html

@@ -447,8 +447,8 @@ index.</p>
 <span class="sig-name descname"><span class="pre">sampling_index</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">size</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shuffle</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.data.base.LabelledCollection.sampling_index" title="Permalink to this definition">¶</a></dt>
 <dd><p>Returns an index to be used to extract a random sample of desired size and desired prevalence values. If the
 prevalence values are not specified, then returns the index of a uniform sampling.
-For each class, the sampling is drawn without replacement if the requested prevalence is larger than
+For each class, the sampling is drawn with replacement if the requested prevalence is larger than
-the actual prevalence of the class, or with replacement otherwise.</p>
+the actual prevalence of the class, or without replacement otherwise.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -534,7 +534,7 @@ values for each class)</p>
 <dt class="sig sig-object py" id="quapy.data.base.LabelledCollection.uniform_sampling">
 <span class="sig-name descname"><span class="pre">uniform_sampling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.data.base.LabelledCollection.uniform_sampling" title="Permalink to this definition">¶</a></dt>
 <dd><p>Returns a uniform sample (an instance of <a class="reference internal" href="#quapy.data.base.LabelledCollection" title="quapy.data.base.LabelledCollection"><code class="xref py py-class docutils literal notranslate"><span class="pre">LabelledCollection</span></code></a>) of desired size. The sampling is drawn
-without replacement if the requested size is greater than the number of instances, or with replacement
+with replacement if the requested size is greater than the number of instances, or without replacement
 otherwise.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -553,7 +553,7 @@ otherwise.</p>
 <dt class="sig sig-object py" id="quapy.data.base.LabelledCollection.uniform_sampling_index">
 <span class="sig-name descname"><span class="pre">uniform_sampling_index</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.data.base.LabelledCollection.uniform_sampling_index" title="Permalink to this definition">¶</a></dt>
 <dd><p>Returns an index to be used to extract a uniform sample of desired size. The sampling is drawn
-without replacement if the requested size is greater than the number of instances, or with replacement
+with replacement if the requested size is greater than the number of instances, or without replacement
 otherwise.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>

docs/build/html/quapy.html

@@ -61,6 +61,7 @@
 </section>
 <section id="module-quapy.error">
 <span id="quapy-error"></span><h2>quapy.error<a class="headerlink" href="#module-quapy.error" title="Permalink to this heading">¶</a></h2>
+<p>Implementation of error measures used for quantification</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.absolute_error">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">absolute_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.absolute_error" title="Permalink to this definition">¶</a></dt>
@@ -86,8 +87,9 @@ where <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.acc_error">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">acc_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y_true</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_pred</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.acc_error" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the error in terms of 1-accuracy. The accuracy is computed as <span class="math notranslate nohighlight">\(\frac{tp+tn}{tp+fp+fn+tn}\)</span>, with
+<dd><p>Computes the error in terms of 1-accuracy. The accuracy is computed as
-<cite>tp</cite>, <cite>fp</cite>, <cite>fn</cite>, and <cite>tn</cite> standing for true positives, false positives, false negatives, and true negatives,
+<span class="math notranslate nohighlight">\(\frac{tp+tn}{tp+fp+fn+tn}\)</span>, with <cite>tp</cite>, <cite>fp</cite>, <cite>fn</cite>, and <cite>tn</cite> standing
+for true positives, false positives, false negatives, and true negatives,
 respectively</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -105,8 +107,9 @@ respectively</p>
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.acce">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">acce</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y_true</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_pred</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.acce" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the error in terms of 1-accuracy. The accuracy is computed as <span class="math notranslate nohighlight">\(\frac{tp+tn}{tp+fp+fn+tn}\)</span>, with
+<dd><p>Computes the error in terms of 1-accuracy. The accuracy is computed as
-<cite>tp</cite>, <cite>fp</cite>, <cite>fn</cite>, and <cite>tn</cite> standing for true positives, false positives, false negatives, and true negatives,
+<span class="math notranslate nohighlight">\(\frac{tp+tn}{tp+fp+fn+tn}\)</span>, with <cite>tp</cite>, <cite>fp</cite>, <cite>fn</cite>, and <cite>tn</cite> standing
+for true positives, false positives, false negatives, and true negatives,
 respectively</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -146,10 +149,12 @@ where <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.f1_error">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">f1_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y_true</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_pred</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.f1_error" title="Permalink to this definition">¶</a></dt>
-<dd><p>F1 error: simply computes the error in terms of macro <span class="math notranslate nohighlight">\(F_1\)</span>, i.e., <span class="math notranslate nohighlight">\(1-F_1^M\)</span>,
+<dd><p>F1 error: simply computes the error in terms of macro <span class="math notranslate nohighlight">\(F_1\)</span>, i.e.,
-where <span class="math notranslate nohighlight">\(F_1\)</span> is the harmonic mean of precision and recall, defined as <span class="math notranslate nohighlight">\(\frac{2tp}{2tp+fp+fn}\)</span>,
+<span class="math notranslate nohighlight">\(1-F_1^M\)</span>, where <span class="math notranslate nohighlight">\(F_1\)</span> is the harmonic mean of precision and recall,
-with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing for true positives, false positives, and false negatives, respectively.
+defined as <span class="math notranslate nohighlight">\(\frac{2tp}{2tp+fp+fn}\)</span>, with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing
-<cite>Macro</cite> averaging means the <span class="math notranslate nohighlight">\(F_1\)</span> is computed for each category independently, and then averaged.</p>
+for true positives, false positives, and false negatives, respectively.
+<cite>Macro</cite> averaging means the <span class="math notranslate nohighlight">\(F_1\)</span> is computed for each category independently,
+and then averaged.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -166,10 +171,12 @@ with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing for true pos
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.f1e">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">f1e</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">y_true</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_pred</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.f1e" title="Permalink to this definition">¶</a></dt>
-<dd><p>F1 error: simply computes the error in terms of macro <span class="math notranslate nohighlight">\(F_1\)</span>, i.e., <span class="math notranslate nohighlight">\(1-F_1^M\)</span>,
+<dd><p>F1 error: simply computes the error in terms of macro <span class="math notranslate nohighlight">\(F_1\)</span>, i.e.,
-where <span class="math notranslate nohighlight">\(F_1\)</span> is the harmonic mean of precision and recall, defined as <span class="math notranslate nohighlight">\(\frac{2tp}{2tp+fp+fn}\)</span>,
+<span class="math notranslate nohighlight">\(1-F_1^M\)</span>, where <span class="math notranslate nohighlight">\(F_1\)</span> is the harmonic mean of precision and recall,
-with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing for true positives, false positives, and false negatives, respectively.
+defined as <span class="math notranslate nohighlight">\(\frac{2tp}{2tp+fp+fn}\)</span>, with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing
-<cite>Macro</cite> averaging means the <span class="math notranslate nohighlight">\(F_1\)</span> is computed for each category independently, and then averaged.</p>
+for true positives, false positives, and false negatives, respectively.
+<cite>Macro</cite> averaging means the <span class="math notranslate nohighlight">\(F_1\)</span> is computed for each category independently,
+and then averaged.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -186,7 +193,8 @@ with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing for true pos
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.from_name">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">from_name</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">err_name</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.from_name" title="Permalink to this definition">¶</a></dt>
-<dd><p>Gets an error function from its name. E.g., <cite>from_name(“mae”)</cite> will return function <a class="reference internal" href="#quapy.error.mae" title="quapy.error.mae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.mae()</span></code></a></p>
+<dd><p>Gets an error function from its name. E.g., <cite>from_name(“mae”)</cite>
+will return function <a class="reference internal" href="#quapy.error.mae" title="quapy.error.mae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.mae()</span></code></a></p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>err_name</strong> – string, the error name</p>
@@ -199,11 +207,13 @@ with <cite>tp</cite>, <cite>fp</cite>, and <cite>fn</cite> standing for true pos
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.kld">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">kld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.kld" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">kld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.kld" title="Permalink to this definition">¶</a></dt>
 <dd><dl class="simple">
-<dt>Computes the Kullback-Leibler divergence between the two prevalence distributions.</dt><dd><p>Kullback-Leibler divergence between two prevalence distributions <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span> is computed as
+<dt>Computes the Kullback-Leibler divergence between the two prevalence distributions.</dt><dd><p>Kullback-Leibler divergence between two prevalence distributions <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>
-<span class="math notranslate nohighlight">\(KLD(p,\hat{p})=D_{KL}(p||\hat{p})=\sum_{y\in \mathcal{Y}} p(y)\log\frac{p(y)}{\hat{p}(y)}\)</span>, where
+is computed as
-<span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.
+<span class="math notranslate nohighlight">\(KLD(p,\hat{p})=D_{KL}(p||\hat{p})=
+\sum_{y\in \mathcal{Y}} p(y)\log\frac{p(y)}{\hat{p}(y)}\)</span>,
+where <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.
 The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 </dd>
 </dl>
@@ -212,9 +222,10 @@ The distributions are smoothed using the <cite>eps</cite> factor (see <a class="
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_classes,)</cite> with the true prevalence values</p></li>
 <li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_classes,)</cite> with the predicted prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. KLD is not defined in cases in which the distributions contain zeros; <cite>eps</cite>
+<li><p><strong>eps</strong> – smoothing factor. KLD is not defined in cases in which the distributions contain
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size.
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+If <cite>eps=None</cite>, the sample size will be taken from the environment variable <cite>SAMPLE_SIZE</cite>
+(which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -231,7 +242,8 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
+prevalence values</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -248,7 +260,8 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
+prevalence values</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -259,17 +272,21 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.mean_relative_absolute_error">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mean_relative_absolute_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mean_relative_absolute_error" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mean_relative_absolute_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mean_relative_absolute_error" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the mean relative absolute error (see <a class="reference internal" href="#quapy.error.rae" title="quapy.error.rae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.rae()</span></code></a>) across the sample pairs.
+<dd><p>Computes the mean relative absolute error (see <a class="reference internal" href="#quapy.error.rae" title="quapy.error.rae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.rae()</span></code></a>) across
-The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
+the sample pairs. The distributions are smoothed using the <cite>eps</cite> factor (see
+<a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
+<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. <cite>mrae</cite> is not defined in cases in which the true distribution contains zeros; <cite>eps</cite>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+prevalence values</p></li>
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+<li><p><strong>eps</strong> – smoothing factor. <cite>mrae</cite> is not defined in cases in which the true
+distribution contains zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>,
+with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size will be taken from
+the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -281,16 +298,20 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.mkld">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mkld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mkld" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the mean Kullback-Leibler divergence (see <a class="reference internal" href="#quapy.error.kld" title="quapy.error.kld"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.kld()</span></code></a>) across the sample pairs.
+<dd><p>Computes the mean Kullback-Leibler divergence (see <a class="reference internal" href="#quapy.error.kld" title="quapy.error.kld"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.kld()</span></code></a>) across the
-The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
+sample pairs. The distributions are smoothed using the <cite>eps</cite> factor
+(see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
+<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. KLD is not defined in cases in which the distributions contain zeros; <cite>eps</cite>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+prevalence values</p></li>
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+<li><p><strong>eps</strong> – smoothing factor. KLD is not defined in cases in which the distributions contain
+zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size.
+If <cite>eps=None</cite>, the sample size will be taken from the environment variable <cite>SAMPLE_SIZE</cite>
+(which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -302,16 +323,19 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.mnkld">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mnkld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mnkld" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the mean Normalized Kullback-Leibler divergence (see <a class="reference internal" href="#quapy.error.nkld" title="quapy.error.nkld"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.nkld()</span></code></a>) across the sample pairs.
+<dd><p>Computes the mean Normalized Kullback-Leibler divergence (see <a class="reference internal" href="#quapy.error.nkld" title="quapy.error.nkld"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.nkld()</span></code></a>)
-The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
+across the sample pairs. The distributions are smoothed using the <cite>eps</cite> factor
+(see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
-<li><p><strong>eps</strong> – smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; <cite>eps</cite>
+prevalence values</p></li>
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+<li><p><strong>eps</strong> – smoothing factor. NKLD is not defined in cases in which the distributions contain
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size.
+If <cite>eps=None</cite>, the sample size will be taken from the environment variable <cite>SAMPLE_SIZE</cite>
+(which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -322,17 +346,21 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.mrae">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mrae</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mrae" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">mrae</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.mrae" title="Permalink to this definition">¶</a></dt>
-<dd><p>Computes the mean relative absolute error (see <a class="reference internal" href="#quapy.error.rae" title="quapy.error.rae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.rae()</span></code></a>) across the sample pairs.
+<dd><p>Computes the mean relative absolute error (see <a class="reference internal" href="#quapy.error.rae" title="quapy.error.rae"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.rae()</span></code></a>) across
-The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
+the sample pairs. The distributions are smoothed using the <cite>eps</cite> factor (see
+<a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
+<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. <cite>mrae</cite> is not defined in cases in which the true distribution contains zeros; <cite>eps</cite>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+prevalence values</p></li>
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+<li><p><strong>eps</strong> – smoothing factor. <cite>mrae</cite> is not defined in cases in which the true
+distribution contains zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>,
+with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size will be taken from
+the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -348,8 +376,10 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the true prevalence values</p></li>
+<li><p><strong>prevs</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the
-<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the predicted prevalence values</p></li>
+true prevalence values</p></li>
+<li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_samples, n_classes,)</cite> with the
+predicted prevalence values</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -360,10 +390,12 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.nkld">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">nkld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.nkld" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">nkld</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.nkld" title="Permalink to this definition">¶</a></dt>
 <dd><dl class="simple">
-<dt>Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.</dt><dd><p>Normalized Kullback-Leibler divergence between two prevalence distributions <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>
+<dt>Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.</dt><dd><p>Normalized Kullback-Leibler divergence between two prevalence distributions <span class="math notranslate nohighlight">\(p\)</span> and
-is computed as <span class="math notranslate nohighlight">\(NKLD(p,\hat{p}) = 2\frac{e^{KLD(p,\hat{p})}}{e^{KLD(p,\hat{p})}+1}-1\)</span>, where
+<span class="math notranslate nohighlight">\(\hat{p}\)</span> is computed as
+math:<cite>NKLD(p,hat{p}) = 2frac{e^{KLD(p,hat{p})}}{e^{KLD(p,hat{p})}+1}-1</cite>,
+where
 <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.
 The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 </dd>
@@ -373,9 +405,10 @@ The distributions are smoothed using the <cite>eps</cite> factor (see <a class="
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_classes,)</cite> with the true prevalence values</p></li>
 <li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_classes,)</cite> with the predicted prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; <cite>eps</cite>
+<li><p><strong>eps</strong> – smoothing factor. NKLD is not defined in cases in which the distributions
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+contain zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+size. If <cite>eps=None</cite>, the sample size will be taken from the environment variable
+<cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -386,10 +419,12 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.rae">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">rae</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.rae" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">rae</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.rae" title="Permalink to this definition">¶</a></dt>
 <dd><dl class="simple">
-<dt>Computes the absolute relative error between the two prevalence vectors.</dt><dd><p>Relative absolute error between two prevalence vectors <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>  is computed as
+<dt>Computes the absolute relative error between the two prevalence vectors.</dt><dd><p>Relative absolute error between two prevalence vectors <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>
-<span class="math notranslate nohighlight">\(RAE(p,\hat{p})=\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}\frac{|\hat{p}(y)-p(y)|}{p(y)}\)</span>,
+is computed as
+<span class="math notranslate nohighlight">\(RAE(p,\hat{p})=
+\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}\frac{|\hat{p}(y)-p(y)|}{p(y)}\)</span>,
 where <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.
 The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 </dd>
@@ -399,9 +434,10 @@ The distributions are smoothed using the <cite>eps</cite> factor (see <a class="
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_classes,)</cite> with the true prevalence values</p></li>
 <li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_classes,)</cite> with the predicted prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. <cite>rae</cite> is not defined in cases in which the true distribution contains zeros; <cite>eps</cite>
+<li><p><strong>eps</strong> – smoothing factor. <cite>rae</cite> is not defined in cases in which the true distribution
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+contains zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+sample size. If <cite>eps=None</cite>, the sample size will be taken from the environment variable
+<cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -412,10 +448,12 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.relative_absolute_error">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">relative_absolute_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.relative_absolute_error" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">relative_absolute_error</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.relative_absolute_error" title="Permalink to this definition">¶</a></dt>
 <dd><dl class="simple">
-<dt>Computes the absolute relative error between the two prevalence vectors.</dt><dd><p>Relative absolute error between two prevalence vectors <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>  is computed as
+<dt>Computes the absolute relative error between the two prevalence vectors.</dt><dd><p>Relative absolute error between two prevalence vectors <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>
-<span class="math notranslate nohighlight">\(RAE(p,\hat{p})=\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}\frac{|\hat{p}(y)-p(y)|}{p(y)}\)</span>,
+is computed as
+<span class="math notranslate nohighlight">\(RAE(p,\hat{p})=
+\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}\frac{|\hat{p}(y)-p(y)|}{p(y)}\)</span>,
 where <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.
 The distributions are smoothed using the <cite>eps</cite> factor (see <a class="reference internal" href="#quapy.error.smooth" title="quapy.error.smooth"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quapy.error.smooth()</span></code></a>).</p>
 </dd>
@@ -425,9 +463,10 @@ The distributions are smoothed using the <cite>eps</cite> factor (see <a class="
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>prevs</strong> – array-like of shape <cite>(n_classes,)</cite> with the true prevalence values</p></li>
 <li><p><strong>prevs_hat</strong> – array-like of shape <cite>(n_classes,)</cite> with the predicted prevalence values</p></li>
-<li><p><strong>eps</strong> – smoothing factor. <cite>rae</cite> is not defined in cases in which the true distribution contains zeros; <cite>eps</cite>
+<li><p><strong>eps</strong> – smoothing factor. <cite>rae</cite> is not defined in cases in which the true distribution
-is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the sample size. If <cite>eps=None</cite>, the sample size
+contains zeros; <cite>eps</cite> is typically set to be <span class="math notranslate nohighlight">\(\frac{1}{2T}\)</span>, with <span class="math notranslate nohighlight">\(T\)</span> the
-will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
+sample size. If <cite>eps=None</cite>, the sample size will be taken from the environment variable
+<cite>SAMPLE_SIZE</cite> (which has thus to be set beforehand).</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
@@ -438,10 +477,11 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.error.se">
-<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">se</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p_hat</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.se" title="Permalink to this definition">¶</a></dt>
+<span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">se</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prevs_hat</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.se" title="Permalink to this definition">¶</a></dt>
 <dd><dl class="simple">
 <dt>Computes the squared error between the two prevalence vectors.</dt><dd><p>Squared error between two prevalence vectors <span class="math notranslate nohighlight">\(p\)</span> and <span class="math notranslate nohighlight">\(\hat{p}\)</span>  is computed as
-<span class="math notranslate nohighlight">\(SE(p,\hat{p})=\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}(\hat{p}(y)-p(y))^2\)</span>, where
+<span class="math notranslate nohighlight">\(SE(p,\hat{p})=\frac{1}{|\mathcal{Y}|}\sum_{y\in \mathcal{Y}}(\hat{p}(y)-p(y))^2\)</span>,
+where
 <span class="math notranslate nohighlight">\(\mathcal{Y}\)</span> are the classes of interest.</p>
 </dd>
 </dl>
@@ -462,7 +502,8 @@ will be taken from the environment variable <cite>SAMPLE_SIZE</cite> (which has
 <dt class="sig sig-object py" id="quapy.error.smooth">
 <span class="sig-prename descclassname"><span class="pre">quapy.error.</span></span><span class="sig-name descname"><span class="pre">smooth</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prevs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.error.smooth" title="Permalink to this definition">¶</a></dt>
 <dd><p>Smooths a prevalence distribution with <span class="math notranslate nohighlight">\(\epsilon\)</span> (<cite>eps</cite>) as:
-<span class="math notranslate nohighlight">\(\underline{p}(y)=\frac{\epsilon+p(y)}{\epsilon|\mathcal{Y}|+\displaystyle\sum_{y\in \mathcal{Y}}p(y)}\)</span></p>
+<span class="math notranslate nohighlight">\(\underline{p}(y)=\frac{\epsilon+p(y)}{\epsilon|\mathcal{Y}|+
+\displaystyle\sum_{y\in \mathcal{Y}}p(y)}\)</span></p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -601,7 +642,7 @@ convenient or not. Set to False to deactivate.</p></li>
 </div>
 <span class="target" id="module-quapy.protocol"></span><dl class="py class">
 <dt class="sig sig-object py" id="quapy.protocol.APP">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">quapy.protocol.</span></span><span class="sig-name descname"><span class="pre">APP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="quapy.data.html#quapy.data.base.LabelledCollection" title="quapy.data.base.LabelledCollection"><span class="pre">LabelledCollection</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_prevalences</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">21</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">repeats</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">smooth_limits_epsilon</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sample_prev'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.protocol.APP" title="Permalink to this definition">¶</a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">quapy.protocol.</span></span><span class="sig-name descname"><span class="pre">APP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="quapy.data.html#quapy.data.base.LabelledCollection" title="quapy.data.base.LabelledCollection"><span class="pre">LabelledCollection</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_prevalences</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">21</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">repeats</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">smooth_limits_epsilon</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sanity_check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">return_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sample_prev'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.protocol.APP" title="Permalink to this definition">¶</a></dt>
 <dd><p>Bases: <a class="reference internal" href="#quapy.protocol.AbstractStochasticSeededProtocol" title="quapy.protocol.AbstractStochasticSeededProtocol"><code class="xref py py-class docutils literal notranslate"><span class="pre">AbstractStochasticSeededProtocol</span></code></a>, <a class="reference internal" href="#quapy.protocol.OnLabelledCollectionProtocol" title="quapy.protocol.OnLabelledCollectionProtocol"><code class="xref py py-class docutils literal notranslate"><span class="pre">OnLabelledCollectionProtocol</span></code></a></p>
 <p>Implementation of the artificial prevalence protocol (APP).
 The APP consists of exploring a grid of prevalence values containing <cite>n_prevalences</cite> points (e.g.,
@@ -621,6 +662,8 @@ grid (default is 21)</p></li>
 <li><p><strong>smooth_limits_epsilon</strong> – the quantity to add and subtract to the limits 0 and 1</p></li>
 <li><p><strong>random_state</strong> – allows replicating samples across runs (default 0, meaning that the sequence of samples
 will be the same every time the protocol is called)</p></li>
+<li><p><strong>sanity_check</strong> – int, raises an exception warning the user that the number of examples to be generated exceed
+this number; set to None for skipping this check</p></li>
 <li><p><strong>return_type</strong> – set to “sample_prev” (default) to get the pairs of (sample, prevalence) at each iteration, or
 to “labelled_collection” to get instead instances of LabelledCollection</p></li>
 </ul>
@@ -1819,6 +1862,7 @@ this function is invoked, it loads the pickled resource. Example:</p>
 </section>
 <section id="module-quapy">
 <span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-quapy" title="Permalink to this heading">¶</a></h2>
+<p>QuaPy module for quantification</p>
 </section>
 </section>
 

docs/build/html/quapy.method.html

@@ -1064,11 +1064,6 @@ validation data, or as an integer, indicating that the misclassification rates s
 <span class="sig-prename descclassname"><span class="pre">quapy.method.aggregative.</span></span><span class="sig-name descname"><span class="pre">cross_generate_predictions</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">classifier</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">val_split</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">probabilistic</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fit_classifier</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_jobs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.method.aggregative.cross_generate_predictions" title="Permalink to this definition">¶</a></dt>
 <dd></dd></dl>
 
-<dl class="py function">
-<dt class="sig sig-object py" id="quapy.method.aggregative.cross_generate_predictions_depr">
-<span class="sig-prename descclassname"><span class="pre">quapy.method.aggregative.</span></span><span class="sig-name descname"><span class="pre">cross_generate_predictions_depr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">classifier</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">val_split</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">probabilistic</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fit_classifier</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">''</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.method.aggregative.cross_generate_predictions_depr" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
-
 <dl class="py function">
 <dt class="sig sig-object py" id="quapy.method.aggregative.newELM">
 <span class="sig-prename descclassname"><span class="pre">quapy.method.aggregative.</span></span><span class="sig-name descname"><span class="pre">newELM</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">svmperf_base</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">loss</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'01'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">C</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#quapy.method.aggregative.newELM" title="Permalink to this definition">¶</a></dt>

quapy/error.py

@@ -1,10 +1,13 @@
-import quapy as qp
+"""Implementation of error measures used for quantification"""
+
 import numpy as np
 from sklearn.metrics import f1_score
+import quapy as qp
 
 
 def from_name(err_name):
-    """Gets an error function from its name. E.g., `from_name("mae")` will return function :meth:`quapy.error.mae`
+    """Gets an error function from its name. E.g., `from_name("mae")`
+    will return function :meth:`quapy.error.mae`
 
     :param err_name: string, the error name
     :return: a callable implementing the requested error
@@ -15,10 +18,12 @@ def from_name(err_name):
 
 
 def f1e(y_true, y_pred):
-    """F1 error: simply computes the error in terms of macro :math:`F_1`, i.e., :math:`1-F_1^M`,
+    """F1 error: simply computes the error in terms of macro :math:`F_1`, i.e.,
-    where :math:`F_1` is the harmonic mean of precision and recall, defined as :math:`\\frac{2tp}{2tp+fp+fn}`,
+    :math:`1-F_1^M`, where :math:`F_1` is the harmonic mean of precision and recall,
-    with `tp`, `fp`, and `fn` standing for true positives, false positives, and false negatives, respectively.
+    defined as :math:`\\frac{2tp}{2tp+fp+fn}`, with `tp`, `fp`, and `fn` standing
-    `Macro` averaging means the :math:`F_1` is computed for each category independently, and then averaged.
+    for true positives, false positives, and false negatives, respectively.
+    `Macro` averaging means the :math:`F_1` is computed for each category independently,
+    and then averaged.
 
     :param y_true: array-like of true labels
     :param y_pred: array-like of predicted labels
@@ -28,8 +33,9 @@ def f1e(y_true, y_pred):
 
 
 def acce(y_true, y_pred):
-    """Computes the error in terms of 1-accuracy. The accuracy is computed as :math:`\\frac{tp+tn}{tp+fp+fn+tn}`, with
+    """Computes the error in terms of 1-accuracy. The accuracy is computed as
-    `tp`, `fp`, `fn`, and `tn` standing for true positives, false positives, false negatives, and true negatives,
+    :math:`\\frac{tp+tn}{tp+fp+fn+tn}`, with `tp`, `fp`, `fn`, and `tn` standing
+    for true positives, false positives, false negatives, and true negatives,
     respectively
 
     :param y_true: array-like of true labels
@@ -43,7 +49,8 @@ def mae(prevs, prevs_hat):
     """Computes the mean absolute error (see :meth:`quapy.error.ae`) across the sample pairs.
 
     :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
-    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
+    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted
+        prevalence values
     :return: mean absolute error
     """
     return ae(prevs, prevs_hat).mean()
@@ -52,7 +59,7 @@ def mae(prevs, prevs_hat):
 def ae(prevs, prevs_hat):
     """Computes the absolute error between the two prevalence vectors.
      Absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}`  is computed as
-     :math:`AE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}|\\hat{p}(y)-p(y)|`,
+     :math:`AE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}|\\hat{p}(y)-p(y)|`,
      where :math:`\\mathcal{Y}` are the classes of interest.
 
     :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
@@ -66,129 +73,153 @@ def ae(prevs, prevs_hat):
 def mse(prevs, prevs_hat):
     """Computes the mean squared error (see :meth:`quapy.error.se`) across the sample pairs.
 
-    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
+    :param prevs: array-like of shape `(n_samples, n_classes,)` with the
-    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
+        true prevalence values
+    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the
+        predicted prevalence values
     :return: mean squared error
     """
     return se(prevs, prevs_hat).mean()
 
 
-def se(p, p_hat):
+def se(prevs, prevs_hat):
     """Computes the squared error between the two prevalence vectors.
      Squared error between two prevalence vectors :math:`p` and :math:`\\hat{p}`  is computed as
-     :math:`SE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}(\\hat{p}(y)-p(y))^2`, where
+     :math:`SE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}(\\hat{p}(y)-p(y))^2`,
+     where
      :math:`\\mathcal{Y}` are the classes of interest.
 
     :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
     :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
     :return: absolute error
     """
-    return ((p_hat-p)**2).mean(axis=-1)
+    return ((prevs_hat - prevs) ** 2).mean(axis=-1)
 
 
 def mkld(prevs, prevs_hat, eps=None):
-    """Computes the mean Kullback-Leibler divergence (see :meth:`quapy.error.kld`) across the sample pairs.
+    """Computes the mean Kullback-Leibler divergence (see :meth:`quapy.error.kld`) across the
-    The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
+    sample pairs. The distributions are smoothed using the `eps` factor
+    (see :meth:`quapy.error.smooth`).
 
-    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
+    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true
-    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
+        prevalence values
-    :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain zeros; `eps`
+    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
+        prevalence values
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
+    :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain
+        zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.
+        If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`
+        (which has thus to be set beforehand).
     :return: mean Kullback-Leibler distribution
     """
     return kld(prevs, prevs_hat, eps).mean()
 
 
-def kld(p, p_hat, eps=None):
+def kld(prevs, prevs_hat, eps=None):
     """Computes the Kullback-Leibler divergence between the two prevalence distributions.
-     Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}` is computed as
+     Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}`
-     :math:`KLD(p,\\hat{p})=D_{KL}(p||\\hat{p})=\\sum_{y\\in \\mathcal{Y}} p(y)\\log\\frac{p(y)}{\\hat{p}(y)}`, where
+     is computed as
-     :math:`\\mathcal{Y}` are the classes of interest.
+     :math:`KLD(p,\\hat{p})=D_{KL}(p||\\hat{p})=
-     The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
+     \\sum_{y\\in \\mathcal{Y}} p(y)\\log\\frac{p(y)}{\\hat{p}(y)}`,
-
-    :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
-    :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
-    :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain zeros; `eps`
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
-    :return: Kullback-Leibler divergence between the two distributions
-    """
-    eps = __check_eps(eps)
-    sp = p+eps
-    sp_hat = p_hat + eps
-    return (sp*np.log(sp/sp_hat)).sum(axis=-1)
-
-
-def mnkld(prevs, prevs_hat, eps=None):
-    """Computes the mean Normalized Kullback-Leibler divergence (see :meth:`quapy.error.nkld`) across the sample pairs.
-    The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
-
-    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
-    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
-    :param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; `eps`
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
-    :return: mean Normalized Kullback-Leibler distribution
-    """
-    return nkld(prevs, prevs_hat, eps).mean()
-
-
-def nkld(p, p_hat, eps=None):
-    """Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.
-     Normalized Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}`
-     is computed as :math:`NKLD(p,\\hat{p}) = 2\\frac{e^{KLD(p,\\hat{p})}}{e^{KLD(p,\\hat{p})}+1}-1`, where
-     :math:`\\mathcal{Y}` are the classes of interest.
-     The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
-
-    :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
-    :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
-    :param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain zeros; `eps`
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
-    :return: Normalized Kullback-Leibler divergence between the two distributions
-    """
-    ekld = np.exp(kld(p, p_hat, eps))
-    return 2. * ekld / (1 + ekld) - 1.
-
-
-def mrae(p, p_hat, eps=None):
-    """Computes the mean relative absolute error (see :meth:`quapy.error.rae`) across the sample pairs.
-    The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
-
-    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
-    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted prevalence values
-    :param eps: smoothing factor. `mrae` is not defined in cases in which the true distribution contains zeros; `eps`
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
-    :return: mean relative absolute error
-    """
-    return rae(p, p_hat, eps).mean()
-
-
-def rae(p, p_hat, eps=None):
-    """Computes the absolute relative error between the two prevalence vectors.
-     Relative absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}`  is computed as
-     :math:`RAE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\in \mathcal{Y}}\\frac{|\\hat{p}(y)-p(y)|}{p(y)}`,
      where :math:`\\mathcal{Y}` are the classes of interest.
      The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
 
     :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
     :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
-    :param eps: smoothing factor. `rae` is not defined in cases in which the true distribution contains zeros; `eps`
+    :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain
-        is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size. If `eps=None`, the sample size
+        zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.
-        will be taken from the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
+        If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`
+        (which has thus to be set beforehand).
+    :return: Kullback-Leibler divergence between the two distributions
+    """
+    eps = __check_eps(eps)
+    smooth_prevs = prevs + eps
+    smooth_prevs_hat = prevs_hat + eps
+    return (smooth_prevs*np.log(smooth_prevs/smooth_prevs_hat)).sum(axis=-1)
+
+
+def mnkld(prevs, prevs_hat, eps=None):
+    """Computes the mean Normalized Kullback-Leibler divergence (see :meth:`quapy.error.nkld`)
+    across the sample pairs. The distributions are smoothed using the `eps` factor
+    (see :meth:`quapy.error.smooth`).
+
+    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values
+    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted
+        prevalence values
+    :param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain
+        zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.
+        If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`
+        (which has thus to be set beforehand).
+    :return: mean Normalized Kullback-Leibler distribution
+    """
+    return nkld(prevs, prevs_hat, eps).mean()
+
+
+def nkld(prevs, prevs_hat, eps=None):
+    """Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.
+     Normalized Kullback-Leibler divergence between two prevalence distributions :math:`p` and
+     :math:`\\hat{p}` is computed as
+     math:`NKLD(p,\\hat{p}) = 2\\frac{e^{KLD(p,\\hat{p})}}{e^{KLD(p,\\hat{p})}+1}-1`,
+     where
+     :math:`\\mathcal{Y}` are the classes of interest.
+     The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
+
+    :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
+    :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
+    :param eps: smoothing factor. NKLD is not defined in cases in which the distributions
+        contain zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample
+        size. If `eps=None`, the sample size will be taken from the environment variable
+        `SAMPLE_SIZE` (which has thus to be set beforehand).
+    :return: Normalized Kullback-Leibler divergence between the two distributions
+    """
+    ekld = np.exp(kld(prevs, prevs_hat, eps))
+    return 2. * ekld / (1 + ekld) - 1.
+
+
+def mrae(prevs, prevs_hat, eps=None):
+    """Computes the mean relative absolute error (see :meth:`quapy.error.rae`) across
+    the sample pairs. The distributions are smoothed using the `eps` factor (see
+    :meth:`quapy.error.smooth`).
+
+    :param prevs: array-like of shape `(n_samples, n_classes,)` with the true
+        prevalence values
+    :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted
+        prevalence values
+    :param eps: smoothing factor. `mrae` is not defined in cases in which the true
+        distribution contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`,
+        with :math:`T` the sample size. If `eps=None`, the sample size will be taken from
+        the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).
+    :return: mean relative absolute error
+    """
+    return rae(prevs, prevs_hat, eps).mean()
+
+
+def rae(prevs, prevs_hat, eps=None):
+    """Computes the absolute relative error between the two prevalence vectors.
+     Relative absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}`
+     is computed as
+     :math:`RAE(p,\\hat{p})=
+     \\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}\\frac{|\\hat{p}(y)-p(y)|}{p(y)}`,
+     where :math:`\\mathcal{Y}` are the classes of interest.
+     The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).
+
+    :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
+    :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values
+    :param eps: smoothing factor. `rae` is not defined in cases in which the true distribution
+        contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the
+        sample size. If `eps=None`, the sample size will be taken from the environment variable
+        `SAMPLE_SIZE` (which has thus to be set beforehand).
     :return: relative absolute error
     """
     eps = __check_eps(eps)
-    p = smooth(p, eps)
+    prevs = smooth(prevs, eps)
-    p_hat = smooth(p_hat, eps)
+    prevs_hat = smooth(prevs_hat, eps)
-    return (abs(p-p_hat)/p).mean(axis=-1)
+    return (abs(prevs - prevs_hat) / prevs).mean(axis=-1)
 
 
 def smooth(prevs, eps):
-    """ Smooths a prevalence distribution with :math:`\epsilon` (`eps`) as:
+    """ Smooths a prevalence distribution with :math:`\\epsilon` (`eps`) as:
-    :math:`\\underline{p}(y)=\\frac{\\epsilon+p(y)}{\\epsilon|\\mathcal{Y}|+\\displaystyle\\sum_{y\\in \\mathcal{Y}}p(y)}`
+    :math:`\\underline{p}(y)=\\frac{\\epsilon+p(y)}{\\epsilon|\\mathcal{Y}|+
+    \\displaystyle\\sum_{y\\in \\mathcal{Y}}p(y)}`
 
     :param prevs: array-like of shape `(n_classes,)` with the true prevalence values
     :param eps: smoothing factor
@@ -200,12 +231,10 @@ def smooth(prevs, eps):
 
 def __check_eps(eps=None):
     if eps is None:
-        import quapy as qp
         sample_size = qp.environ['SAMPLE_SIZE']
         if sample_size is None:
             raise ValueError('eps was not defined, and qp.environ["SAMPLE_SIZE"] was not set')
-        else:
+        eps = 1. / (2. * sample_size)
-            eps = 1. / (2. * sample_size)
     return eps
 
 
@@ -217,7 +246,8 @@ CLASSIFICATION_ERROR_NAMES = {func.__name__ for func in CLASSIFICATION_ERROR}
 QUANTIFICATION_ERROR_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR}
 QUANTIFICATION_ERROR_SINGLE_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR_SINGLE}
 QUANTIFICATION_ERROR_SMOOTH_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR_SMOOTH}
-ERROR_NAMES = CLASSIFICATION_ERROR_NAMES | QUANTIFICATION_ERROR_NAMES | QUANTIFICATION_ERROR_SINGLE_NAMES
+ERROR_NAMES = \
+    CLASSIFICATION_ERROR_NAMES | QUANTIFICATION_ERROR_NAMES | QUANTIFICATION_ERROR_SINGLE_NAMES
 
 f1_error = f1e
 acc_error = acce
@@ -225,4 +255,3 @@ mean_absolute_error = mae
 absolute_error = ae
 mean_relative_absolute_error = mrae
 relative_absolute_error = rae
-