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<h1>Source code for quapy.error</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;Implementation of error measures used for quantification&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">f1_score</span>
<span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<div class="viewcode-block" id="from_name">
<a class="viewcode-back" href="../../quapy.html#quapy.error.from_name">[docs]</a>
<span class="k">def</span> <span class="nf">from_name</span><span class="p">(</span><span class="n">err_name</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Gets an error function from its name. E.g., `from_name(&quot;mae&quot;)`</span>
<span class="sd"> will return function :meth:`quapy.error.mae`</span>
<span class="sd"> :param err_name: string, the error name</span>
<span class="sd"> :return: a callable implementing the requested error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">err_name</span> <span class="ow">in</span> <span class="n">ERROR_NAMES</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;unknown error </span><span class="si">{</span><span class="n">err_name</span><span class="si">}</span><span class="s1">&#39;</span>
<span class="n">callable_error</span> <span class="o">=</span> <span class="nb">globals</span><span class="p">()[</span><span class="n">err_name</span><span class="p">]</span>
<span class="k">return</span> <span class="n">callable_error</span></div>
<div class="viewcode-block" id="f1e">
<a class="viewcode-back" href="../../quapy.html#quapy.error.f1e">[docs]</a>
<span class="k">def</span> <span class="nf">f1e</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="w"> </span><span class="sd">&quot;&quot;&quot;F1 error: simply computes the error in terms of macro :math:`F_1`, i.e.,</span>
<span class="sd"> :math:`1-F_1^M`, where :math:`F_1` is the harmonic mean of precision and recall,</span>
<span class="sd"> defined as :math:`\\frac{2tp}{2tp+fp+fn}`, with `tp`, `fp`, and `fn` standing</span>
<span class="sd"> for true positives, false positives, and false negatives, respectively.</span>
<span class="sd"> `Macro` averaging means the :math:`F_1` is computed for each category independently,</span>
<span class="sd"> and then averaged.</span>
<span class="sd"> :param y_true: array-like of true labels</span>
<span class="sd"> :param y_pred: array-like of predicted labels</span>
<span class="sd"> :return: :math:`1-F_1^M`</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="mf">1.</span> <span class="o">-</span> <span class="n">f1_score</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">average</span><span class="o">=</span><span class="s1">&#39;macro&#39;</span><span class="p">)</span></div>
<div class="viewcode-block" id="acce">
<a class="viewcode-back" href="../../quapy.html#quapy.error.acce">[docs]</a>
<span class="k">def</span> <span class="nf">acce</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="w"> </span><span class="sd">&quot;&quot;&quot;Computes the error in terms of 1-accuracy. The accuracy is computed as</span>
<span class="sd"> :math:`\\frac{tp+tn}{tp+fp+fn+tn}`, with `tp`, `fp`, `fn`, and `tn` standing</span>
<span class="sd"> for true positives, false positives, false negatives, and true negatives,</span>
<span class="sd"> respectively</span>
<span class="sd"> :param y_true: array-like of true labels</span>
<span class="sd"> :param y_pred: array-like of predicted labels</span>
<span class="sd"> :return: 1-accuracy</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="mf">1.</span> <span class="o">-</span> <span class="p">(</span><span class="n">y_true</span> <span class="o">==</span> <span class="n">y_pred</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="mae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mae">[docs]</a>
<span class="k">def</span> <span class="nf">mae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean absolute error (see :meth:`quapy.error.ae`) across the sample pairs.</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :return: mean absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">ae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="ae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.ae">[docs]</a>
<span class="k">def</span> <span class="nf">ae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the absolute error between the two prevalence vectors.</span>
<span class="sd"> Absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as</span>
<span class="sd"> :math:`AE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}|\\hat{p}(y)-p(y)|`,</span>
<span class="sd"> where :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :return: absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">prevs</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="n">prevs_hat</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;wrong shape </span><span class="si">{</span><span class="n">prevs</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1"> vs. </span><span class="si">{</span><span class="n">prevs_hat</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">&#39;</span>
<span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="n">prevs_hat</span> <span class="o">-</span> <span class="n">prevs</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="nae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.nae">[docs]</a>
<span class="k">def</span> <span class="nf">nae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the normalized absolute error between the two prevalence vectors.</span>
<span class="sd"> Normalized absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as</span>
<span class="sd"> :math:`NAE(p,\\hat{p})=\\frac{AE(p,\\hat{p})}{z_{AE}}`,</span>
<span class="sd"> where :math:`z_{AE}=\\frac{2(1-\\min_{y\\in \\mathcal{Y}} p(y))}{|\\mathcal{Y}|}`, and :math:`\\mathcal{Y}`</span>
<span class="sd"> are the classes of interest.</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :return: normalized absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">prevs</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="n">prevs_hat</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;wrong shape </span><span class="si">{</span><span class="n">prevs</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1"> vs. </span><span class="si">{</span><span class="n">prevs_hat</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">&#39;</span>
<span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="n">prevs_hat</span> <span class="o">-</span> <span class="n">prevs</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">prevs</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)))</span></div>
<div class="viewcode-block" id="mnae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mnae">[docs]</a>
<span class="k">def</span> <span class="nf">mnae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean normalized absolute error (see :meth:`quapy.error.nae`) across the sample pairs.</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :return: mean normalized absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">nae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="mse">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mse">[docs]</a>
<span class="k">def</span> <span class="nf">mse</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean squared error (see :meth:`quapy.error.se`) across the sample pairs.</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the</span>
<span class="sd"> true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the</span>
<span class="sd"> predicted prevalence values</span>
<span class="sd"> :return: mean squared error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">se</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="se">
<a class="viewcode-back" href="../../quapy.html#quapy.error.se">[docs]</a>
<span class="k">def</span> <span class="nf">se</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the squared error between the two prevalence vectors.</span>
<span class="sd"> Squared error between two prevalence vectors :math:`p` and :math:`\\hat{p}` is computed as</span>
<span class="sd"> :math:`SE(p,\\hat{p})=\\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}(\\hat{p}(y)-p(y))^2`,</span>
<span class="sd"> where</span>
<span class="sd"> :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :return: absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="p">((</span><span class="n">prevs_hat</span> <span class="o">-</span> <span class="n">prevs</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="mkld">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mkld">[docs]</a>
<span class="k">def</span> <span class="nf">mkld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean Kullback-Leibler divergence (see :meth:`quapy.error.kld`) across the</span>
<span class="sd"> sample pairs. The distributions are smoothed using the `eps` factor</span>
<span class="sd"> (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain</span>
<span class="sd"> zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.</span>
<span class="sd"> If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`</span>
<span class="sd"> (which has thus to be set beforehand).</span>
<span class="sd"> :return: mean Kullback-Leibler distribution</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">kld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="kld">
<a class="viewcode-back" href="../../quapy.html#quapy.error.kld">[docs]</a>
<span class="k">def</span> <span class="nf">kld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Kullback-Leibler divergence between the two prevalence distributions.</span>
<span class="sd"> Kullback-Leibler divergence between two prevalence distributions :math:`p` and :math:`\\hat{p}`</span>
<span class="sd"> is computed as</span>
<span class="sd"> :math:`KLD(p,\\hat{p})=D_{KL}(p||\\hat{p})=</span>
<span class="sd"> \\sum_{y\\in \\mathcal{Y}} p(y)\\log\\frac{p(y)}{\\hat{p}(y)}`,</span>
<span class="sd"> where :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :param eps: smoothing factor. KLD is not defined in cases in which the distributions contain</span>
<span class="sd"> zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.</span>
<span class="sd"> If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`</span>
<span class="sd"> (which has thus to be set beforehand).</span>
<span class="sd"> :return: Kullback-Leibler divergence between the two distributions</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">__check_eps</span><span class="p">(</span><span class="n">eps</span><span class="p">)</span>
<span class="n">smooth_prevs</span> <span class="o">=</span> <span class="n">prevs</span> <span class="o">+</span> <span class="n">eps</span>
<span class="n">smooth_prevs_hat</span> <span class="o">=</span> <span class="n">prevs_hat</span> <span class="o">+</span> <span class="n">eps</span>
<span class="k">return</span> <span class="p">(</span><span class="n">smooth_prevs</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">smooth_prevs</span><span class="o">/</span><span class="n">smooth_prevs_hat</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="mnkld">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mnkld">[docs]</a>
<span class="k">def</span> <span class="nf">mnkld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean Normalized Kullback-Leibler divergence (see :meth:`quapy.error.nkld`)</span>
<span class="sd"> across the sample pairs. The distributions are smoothed using the `eps` factor</span>
<span class="sd"> (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param eps: smoothing factor. NKLD is not defined in cases in which the distributions contain</span>
<span class="sd"> zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample size.</span>
<span class="sd"> If `eps=None`, the sample size will be taken from the environment variable `SAMPLE_SIZE`</span>
<span class="sd"> (which has thus to be set beforehand).</span>
<span class="sd"> :return: mean Normalized Kullback-Leibler distribution</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">nkld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="nkld">
<a class="viewcode-back" href="../../quapy.html#quapy.error.nkld">[docs]</a>
<span class="k">def</span> <span class="nf">nkld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Normalized Kullback-Leibler divergence between the two prevalence distributions.</span>
<span class="sd"> Normalized Kullback-Leibler divergence between two prevalence distributions :math:`p` and</span>
<span class="sd"> :math:`\\hat{p}` is computed as</span>
<span class="sd"> math:`NKLD(p,\\hat{p}) = 2\\frac{e^{KLD(p,\\hat{p})}}{e^{KLD(p,\\hat{p})}+1}-1`,</span>
<span class="sd"> where</span>
<span class="sd"> :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :param eps: smoothing factor. NKLD is not defined in cases in which the distributions</span>
<span class="sd"> contain zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the sample</span>
<span class="sd"> size. If `eps=None`, the sample size will be taken from the environment variable</span>
<span class="sd"> `SAMPLE_SIZE` (which has thus to be set beforehand).</span>
<span class="sd"> :return: Normalized Kullback-Leibler divergence between the two distributions</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">ekld</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">kld</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">))</span>
<span class="k">return</span> <span class="mf">2.</span> <span class="o">*</span> <span class="n">ekld</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">ekld</span><span class="p">)</span> <span class="o">-</span> <span class="mf">1.</span></div>
<div class="viewcode-block" id="mrae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mrae">[docs]</a>
<span class="k">def</span> <span class="nf">mrae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean relative absolute error (see :meth:`quapy.error.rae`) across</span>
<span class="sd"> the sample pairs. The distributions are smoothed using the `eps` factor (see</span>
<span class="sd"> :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param eps: smoothing factor. `mrae` is not defined in cases in which the true</span>
<span class="sd"> distribution contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`,</span>
<span class="sd"> with :math:`T` the sample size. If `eps=None`, the sample size will be taken from</span>
<span class="sd"> the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).</span>
<span class="sd"> :return: mean relative absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">rae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="rae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.rae">[docs]</a>
<span class="k">def</span> <span class="nf">rae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the absolute relative error between the two prevalence vectors.</span>
<span class="sd"> Relative absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}`</span>
<span class="sd"> is computed as</span>
<span class="sd"> :math:`RAE(p,\\hat{p})=</span>
<span class="sd"> \\frac{1}{|\\mathcal{Y}|}\\sum_{y\\in \\mathcal{Y}}\\frac{|\\hat{p}(y)-p(y)|}{p(y)}`,</span>
<span class="sd"> where :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :param eps: smoothing factor. `rae` is not defined in cases in which the true distribution</span>
<span class="sd"> contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the</span>
<span class="sd"> sample size. If `eps=None`, the sample size will be taken from the environment variable</span>
<span class="sd"> `SAMPLE_SIZE` (which has thus to be set beforehand).</span>
<span class="sd"> :return: relative absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">__check_eps</span><span class="p">(</span><span class="n">eps</span><span class="p">)</span>
<span class="n">prevs</span> <span class="o">=</span> <span class="n">smooth</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
<span class="n">prevs_hat</span> <span class="o">=</span> <span class="n">smooth</span><span class="p">(</span><span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">prevs</span> <span class="o">-</span> <span class="n">prevs_hat</span><span class="p">)</span> <span class="o">/</span> <span class="n">prevs</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></div>
<div class="viewcode-block" id="nrae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.nrae">[docs]</a>
<span class="k">def</span> <span class="nf">nrae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the normalized absolute relative error between the two prevalence vectors.</span>
<span class="sd"> Relative absolute error between two prevalence vectors :math:`p` and :math:`\\hat{p}`</span>
<span class="sd"> is computed as</span>
<span class="sd"> :math:`NRAE(p,\\hat{p})= \\frac{RAE(p,\\hat{p})}{z_{RAE}}`,</span>
<span class="sd"> where</span>
<span class="sd"> :math:`z_{RAE} = \\frac{|\\mathcal{Y}|-1+\\frac{1-\\min_{y\\in \\mathcal{Y}} p(y)}{\\min_{y\\in \\mathcal{Y}} p(y)}}{|\\mathcal{Y}|}`</span>
<span class="sd"> and :math:`\\mathcal{Y}` are the classes of interest.</span>
<span class="sd"> The distributions are smoothed using the `eps` factor (see :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_classes,)` with the predicted prevalence values</span>
<span class="sd"> :param eps: smoothing factor. `nrae` is not defined in cases in which the true distribution</span>
<span class="sd"> contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`, with :math:`T` the</span>
<span class="sd"> sample size. If `eps=None`, the sample size will be taken from the environment variable</span>
<span class="sd"> `SAMPLE_SIZE` (which has thus to be set beforehand).</span>
<span class="sd"> :return: normalized relative absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">eps</span> <span class="o">=</span> <span class="n">__check_eps</span><span class="p">(</span><span class="n">eps</span><span class="p">)</span>
<span class="n">prevs</span> <span class="o">=</span> <span class="n">smooth</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
<span class="n">prevs_hat</span> <span class="o">=</span> <span class="n">smooth</span><span class="p">(</span><span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span>
<span class="n">min_p</span> <span class="o">=</span> <span class="n">prevs</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">prevs</span> <span class="o">-</span> <span class="n">prevs_hat</span><span class="p">)</span> <span class="o">/</span> <span class="n">prevs</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">prevs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="o">+</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">min_p</span><span class="p">)</span><span class="o">/</span><span class="n">min_p</span><span class="p">)</span></div>
<div class="viewcode-block" id="mnrae">
<a class="viewcode-back" href="../../quapy.html#quapy.error.mnrae">[docs]</a>
<span class="k">def</span> <span class="nf">mnrae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the mean normalized relative absolute error (see :meth:`quapy.error.nrae`) across</span>
<span class="sd"> the sample pairs. The distributions are smoothed using the `eps` factor (see</span>
<span class="sd"> :meth:`quapy.error.smooth`).</span>
<span class="sd"> :param prevs: array-like of shape `(n_samples, n_classes,)` with the true</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param prevs_hat: array-like of shape `(n_samples, n_classes,)` with the predicted</span>
<span class="sd"> prevalence values</span>
<span class="sd"> :param eps: smoothing factor. `mnrae` is not defined in cases in which the true</span>
<span class="sd"> distribution contains zeros; `eps` is typically set to be :math:`\\frac{1}{2T}`,</span>
<span class="sd"> with :math:`T` the sample size. If `eps=None`, the sample size will be taken from</span>
<span class="sd"> the environment variable `SAMPLE_SIZE` (which has thus to be set beforehand).</span>
<span class="sd"> :return: mean normalized relative absolute error</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">nrae</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">prevs_hat</span><span class="p">,</span> <span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></div>
<div class="viewcode-block" id="smooth">
<a class="viewcode-back" href="../../quapy.html#quapy.error.smooth">[docs]</a>
<span class="k">def</span> <span class="nf">smooth</span><span class="p">(</span><span class="n">prevs</span><span class="p">,</span> <span class="n">eps</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot; Smooths a prevalence distribution with :math:`\\epsilon` (`eps`) as:</span>
<span class="sd"> :math:`\\underline{p}(y)=\\frac{\\epsilon+p(y)}{\\epsilon|\\mathcal{Y}|+</span>
<span class="sd"> \\displaystyle\\sum_{y\\in \\mathcal{Y}}p(y)}`</span>
<span class="sd"> :param prevs: array-like of shape `(n_classes,)` with the true prevalence values</span>
<span class="sd"> :param eps: smoothing factor</span>
<span class="sd"> :return: array-like of shape `(n_classes,)` with the smoothed distribution</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">n_classes</span> <span class="o">=</span> <span class="n">prevs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <span class="p">(</span><span class="n">prevs</span> <span class="o">+</span> <span class="n">eps</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">eps</span> <span class="o">*</span> <span class="n">n_classes</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span></div>
<span class="k">def</span> <span class="nf">__check_eps</span><span class="p">(</span><span class="n">eps</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">eps</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">sample_size</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;SAMPLE_SIZE&#39;</span><span class="p">]</span>
<span class="k">if</span> <span class="n">sample_size</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;eps was not defined, and qp.environ[&quot;SAMPLE_SIZE&quot;] was not set&#39;</span><span class="p">)</span>
<span class="n">eps</span> <span class="o">=</span> <span class="mf">1.</span> <span class="o">/</span> <span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">sample_size</span><span class="p">)</span>
<span class="k">return</span> <span class="n">eps</span>
<span class="n">CLASSIFICATION_ERROR</span> <span class="o">=</span> <span class="p">{</span><span class="n">f1e</span><span class="p">,</span> <span class="n">acce</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR</span> <span class="o">=</span> <span class="p">{</span><span class="n">mae</span><span class="p">,</span> <span class="n">mnae</span><span class="p">,</span> <span class="n">mrae</span><span class="p">,</span> <span class="n">mnrae</span><span class="p">,</span> <span class="n">mse</span><span class="p">,</span> <span class="n">mkld</span><span class="p">,</span> <span class="n">mnkld</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR_SINGLE</span> <span class="o">=</span> <span class="p">{</span><span class="n">ae</span><span class="p">,</span> <span class="n">nae</span><span class="p">,</span> <span class="n">rae</span><span class="p">,</span> <span class="n">nrae</span><span class="p">,</span> <span class="n">se</span><span class="p">,</span> <span class="n">kld</span><span class="p">,</span> <span class="n">nkld</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR_SMOOTH</span> <span class="o">=</span> <span class="p">{</span><span class="n">kld</span><span class="p">,</span> <span class="n">nkld</span><span class="p">,</span> <span class="n">rae</span><span class="p">,</span> <span class="n">nrae</span><span class="p">,</span> <span class="n">mkld</span><span class="p">,</span> <span class="n">mnkld</span><span class="p">,</span> <span class="n">mrae</span><span class="p">}</span>
<span class="n">CLASSIFICATION_ERROR_NAMES</span> <span class="o">=</span> <span class="p">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__name__</span> <span class="k">for</span> <span class="n">func</span> <span class="ow">in</span> <span class="n">CLASSIFICATION_ERROR</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR_NAMES</span> <span class="o">=</span> <span class="p">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__name__</span> <span class="k">for</span> <span class="n">func</span> <span class="ow">in</span> <span class="n">QUANTIFICATION_ERROR</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR_SINGLE_NAMES</span> <span class="o">=</span> <span class="p">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__name__</span> <span class="k">for</span> <span class="n">func</span> <span class="ow">in</span> <span class="n">QUANTIFICATION_ERROR_SINGLE</span><span class="p">}</span>
<span class="n">QUANTIFICATION_ERROR_SMOOTH_NAMES</span> <span class="o">=</span> <span class="p">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__name__</span> <span class="k">for</span> <span class="n">func</span> <span class="ow">in</span> <span class="n">QUANTIFICATION_ERROR_SMOOTH</span><span class="p">}</span>
<span class="n">ERROR_NAMES</span> <span class="o">=</span> \
<span class="n">CLASSIFICATION_ERROR_NAMES</span> <span class="o">|</span> <span class="n">QUANTIFICATION_ERROR_NAMES</span> <span class="o">|</span> <span class="n">QUANTIFICATION_ERROR_SINGLE_NAMES</span>
<span class="n">f1_error</span> <span class="o">=</span> <span class="n">f1e</span>
<span class="n">acc_error</span> <span class="o">=</span> <span class="n">acce</span>
<span class="n">mean_absolute_error</span> <span class="o">=</span> <span class="n">mae</span>
<span class="n">absolute_error</span> <span class="o">=</span> <span class="n">ae</span>
<span class="n">mean_relative_absolute_error</span> <span class="o">=</span> <span class="n">mrae</span>
<span class="n">relative_absolute_error</span> <span class="o">=</span> <span class="n">rae</span>
<span class="n">normalized_absolute_error</span> <span class="o">=</span> <span class="n">nae</span>
<span class="n">normalized_relative_absolute_error</span> <span class="o">=</span> <span class="n">nrae</span>
<span class="n">mean_normalized_absolute_error</span> <span class="o">=</span> <span class="n">mnae</span>
<span class="n">mean_normalized_relative_absolute_error</span> <span class="o">=</span> <span class="n">mnrae</span>
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