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<h1>Source code for quapy.functional</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">itertools</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</span><span class="p">,</span> <span class="n">Callable</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<div class="viewcode-block" id="prevalence_linspace">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.prevalence_linspace">[docs]</a>
<span class="k">def</span> <span class="nf">prevalence_linspace</span><span class="p">(</span><span class="n">n_prevalences</span><span class="o">=</span><span class="mi">21</span><span class="p">,</span> <span class="n">repeats</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">smooth_limits_epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Produces an array of uniformly separated values of prevalence.</span>
<span class="sd"> By default, produces an array of 21 prevalence values, with</span>
<span class="sd"> step 0.05 and with the limits smoothed, i.e.:</span>
<span class="sd"> [0.01, 0.05, 0.10, 0.15, ..., 0.90, 0.95, 0.99]</span>
<span class="sd"> :param n_prevalences: the number of prevalence values to sample from the [0,1] interval (default 21)</span>
<span class="sd"> :param repeats: number of times each prevalence is to be repeated (defaults to 1)</span>
<span class="sd"> :param smooth_limits_epsilon: the quantity to add and subtract to the limits 0 and 1</span>
<span class="sd"> :return: an array of uniformly separated prevalence values</span>
<span class="sd"> """</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="n">n_prevalences</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="n">smooth_limits_epsilon</span>
<span class="n">p</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-=</span> <span class="n">smooth_limits_epsilon</span>
<span class="k">if</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">></span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'the smoothing in the limits is greater than the prevalence step'</span><span class="p">)</span>
<span class="k">if</span> <span class="n">repeats</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">repeats</span><span class="p">)</span>
<span class="k">return</span> <span class="n">p</span></div>
<div class="viewcode-block" id="prevalence_from_labels">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.prevalence_from_labels">[docs]</a>
<span class="k">def</span> <span class="nf">prevalence_from_labels</span><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">classes</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Computed the prevalence values from a vector of labels.</span>
<span class="sd"> :param labels: array-like of shape `(n_instances)` with the label for each instance</span>
<span class="sd"> :param classes: the class labels. This is needed in order to correctly compute the prevalence vector even when</span>
<span class="sd"> some classes have no examples.</span>
<span class="sd"> :return: an ndarray of shape `(len(classes))` with the class prevalence values</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">labels</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'param labels does not seem to be a ndarray of label predictions'</span><span class="p">)</span>
<span class="n">unique</span><span class="p">,</span> <span class="n">counts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">return_counts</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">by_class</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="k">lambda</span><span class="p">:</span><span class="mi">0</span><span class="p">,</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">unique</span><span class="p">,</span> <span class="n">counts</span><span class="p">)))</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">by_class</span><span class="p">[</span><span class="n">class_</span><span class="p">]</span> <span class="k">for</span> <span class="n">class_</span> <span class="ow">in</span> <span class="n">classes</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">prevalences</span> <span class="o">/=</span> <span class="n">prevalences</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="k">return</span> <span class="n">prevalences</span></div>
<div class="viewcode-block" id="prevalence_from_probabilities">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.prevalence_from_probabilities">[docs]</a>
<span class="k">def</span> <span class="nf">prevalence_from_probabilities</span><span class="p">(</span><span class="n">posteriors</span><span class="p">,</span> <span class="n">binarize</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Returns a vector of prevalence values from a matrix of posterior probabilities.</span>
<span class="sd"> :param posteriors: array-like of shape `(n_instances, n_classes,)` with posterior probabilities for each class</span>
<span class="sd"> :param binarize: set to True (default is False) for computing the prevalence values on crisp decisions (i.e.,</span>
<span class="sd"> converting the vectors of posterior probabilities into class indices, by taking the argmax).</span>
<span class="sd"> :return: array of shape `(n_classes,)` containing the prevalence values</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">posteriors</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'param posteriors does not seem to be a ndarray of posteior probabilities'</span><span class="p">)</span>
<span class="k">if</span> <span class="n">binarize</span><span class="p">:</span>
<span class="n">predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">posteriors</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="n">prevalence_from_labels</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">posteriors</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">posteriors</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">0</span><span class="p">)</span>
<span class="n">prevalences</span> <span class="o">/=</span> <span class="n">prevalences</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="k">return</span> <span class="n">prevalences</span></div>
<div class="viewcode-block" id="as_binary_prevalence">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.as_binary_prevalence">[docs]</a>
<span class="k">def</span> <span class="nf">as_binary_prevalence</span><span class="p">(</span><span class="n">positive_prevalence</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">],</span> <span class="n">clip_if_necessary</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Helper that, given a float representing the prevalence for the positive class, returns a np.ndarray of two</span>
<span class="sd"> values representing a binary distribution.</span>
<span class="sd"> :param positive_prevalence: prevalence for the positive class</span>
<span class="sd"> :param clip_if_necessary: if True, clips the value in [0,1] in order to guarantee the resulting distribution</span>
<span class="sd"> is valid. If False, it then checks that the value is in the valid range, and raises an error if not.</span>
<span class="sd"> :return: np.ndarray of shape `(2,)`</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">clip_if_necessary</span><span class="p">:</span>
<span class="n">positive_prevalence</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">positive_prevalence</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">assert</span> <span class="mi">0</span> <span class="o"><=</span> <span class="n">positive_prevalence</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">'the value provided is not a valid prevalence for the positive class'</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="mi">1</span><span class="o">-</span><span class="n">positive_prevalence</span><span class="p">,</span> <span class="n">positive_prevalence</span><span class="p">])</span><span class="o">.</span><span class="n">T</span></div>
<div class="viewcode-block" id="HellingerDistance">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.HellingerDistance">[docs]</a>
<span class="k">def</span> <span class="nf">HellingerDistance</span><span class="p">(</span><span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <span class="o">-></span> <span class="nb">float</span><span class="p">:</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Computes the Hellingher Distance (HD) between (discretized) distributions `P` and `Q`.</span>
<span class="sd"> The HD for two discrete distributions of `k` bins is defined as:</span>
<span class="sd"> .. math::</span>
<span class="sd"> HD(P,Q) = \\frac{ 1 }{ \\sqrt{ 2 } } \\sqrt{ \\sum_{i=1}^k ( \\sqrt{p_i} - \\sqrt{q_i} )^2 }</span>
<span class="sd"> :param P: real-valued array-like of shape `(k,)` representing a discrete distribution</span>
<span class="sd"> :param Q: real-valued array-like of shape `(k,)` representing a discrete distribution</span>
<span class="sd"> :return: float</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">P</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Q</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span></div>
<div class="viewcode-block" id="TopsoeDistance">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.TopsoeDistance">[docs]</a>
<span class="k">def</span> <span class="nf">TopsoeDistance</span><span class="p">(</span><span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">1e-20</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Topsoe distance between two (discretized) distributions `P` and `Q`.</span>
<span class="sd"> The Topsoe distance for two discrete distributions of `k` bins is defined as:</span>
<span class="sd"> .. math::</span>
<span class="sd"> Topsoe(P,Q) = \\sum_{i=1}^k \\left( p_i \\log\\left(\\frac{ 2 p_i + \\epsilon }{ p_i+q_i+\\epsilon }\\right) +</span>
<span class="sd"> q_i \\log\\left(\\frac{ 2 q_i + \\epsilon }{ p_i+q_i+\\epsilon }\\right) \\right)</span>
<span class="sd"> :param P: real-valued array-like of shape `(k,)` representing a discrete distribution</span>
<span class="sd"> :param Q: real-valued array-like of shape `(k,)` representing a discrete distribution</span>
<span class="sd"> :return: float</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">P</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">((</span><span class="mi">2</span><span class="o">*</span><span class="n">P</span><span class="o">+</span><span class="n">epsilon</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">P</span><span class="o">+</span><span class="n">Q</span><span class="o">+</span><span class="n">epsilon</span><span class="p">))</span> <span class="o">+</span> <span class="n">Q</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="mi">2</span><span class="o">*</span><span class="n">Q</span><span class="o">+</span><span class="n">epsilon</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">P</span><span class="o">+</span><span class="n">Q</span><span class="o">+</span><span class="n">epsilon</span><span class="p">)))</span></div>
<div class="viewcode-block" id="uniform_prevalence_sampling">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.uniform_prevalence_sampling">[docs]</a>
<span class="k">def</span> <span class="nf">uniform_prevalence_sampling</span><span class="p">(</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Implements the `Kraemer algorithm <http://www.cs.cmu.edu/~nasmith/papers/smith+tromble.tr04.pdf>`_</span>
<span class="sd"> for sampling uniformly at random from the unit simplex. This implementation is adapted from this</span>
<span class="sd"> `post <https://cs.stackexchange.com/questions/3227/uniform-sampling-from-a-simplex>_`.</span>
<span class="sd"> :param n_classes: integer, number of classes (dimensionality of the simplex)</span>
<span class="sd"> :param size: number of samples to return</span>
<span class="sd"> :return: `np.ndarray` of shape `(size, n_classes,)` if `size>1`, or of shape `(n_classes,)` otherwise</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">n_classes</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">size</span><span class="p">)</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="mi">1</span><span class="o">-</span><span class="n">u</span><span class="p">,</span> <span class="n">u</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">size</span><span class="p">,</span> <span class="n">n_classes</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">u</span><span class="o">.</span><span class="n">sort</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="n">_0s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">size</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="n">_1s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">size</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="n">_0s</span><span class="p">,</span> <span class="n">u</span><span class="p">])</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="n">u</span><span class="p">,</span> <span class="n">_1s</span><span class="p">])</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">b</span><span class="o">-</span><span class="n">a</span>
<span class="k">if</span> <span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">u</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
<span class="k">return</span> <span class="n">u</span></div>
<span class="n">uniform_simplex_sampling</span> <span class="o">=</span> <span class="n">uniform_prevalence_sampling</span>
<div class="viewcode-block" id="strprev">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.strprev">[docs]</a>
<span class="k">def</span> <span class="nf">strprev</span><span class="p">(</span><span class="n">prevalences</span><span class="p">,</span> <span class="n">prec</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Returns a string representation for a prevalence vector. E.g.,</span>
<span class="sd"> >>> strprev([1/3, 2/3], prec=2)</span>
<span class="sd"> >>> '[0.33, 0.67]'</span>
<span class="sd"> :param prevalences: a vector of prevalence values</span>
<span class="sd"> :param prec: float precision</span>
<span class="sd"> :return: string</span>
<span class="sd"> """</span>
<span class="k">return</span> <span class="s1">'['</span><span class="o">+</span> <span class="s1">', '</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="n">p</span><span class="si">:</span><span class="s1">.</span><span class="si">{</span><span class="n">prec</span><span class="si">}</span><span class="s1">f</span><span class="si">}</span><span class="s1">'</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">prevalences</span><span class="p">])</span> <span class="o">+</span> <span class="s1">']'</span></div>
<div class="viewcode-block" id="adjusted_quantification">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.adjusted_quantification">[docs]</a>
<span class="k">def</span> <span class="nf">adjusted_quantification</span><span class="p">(</span><span class="n">prevalence_estim</span><span class="p">,</span> <span class="n">tpr</span><span class="p">,</span> <span class="n">fpr</span><span class="p">,</span> <span class="n">clip</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Implements the adjustment of ACC and PACC for the binary case. The adjustment for a prevalence estimate of the</span>
<span class="sd"> positive class `p` comes down to computing:</span>
<span class="sd"> .. math::</span>
<span class="sd"> ACC(p) = \\frac{ p - fpr }{ tpr - fpr }</span>
<span class="sd"> :param prevalence_estim: float, the estimated value for the positive class</span>
<span class="sd"> :param tpr: float, the true positive rate of the classifier</span>
<span class="sd"> :param fpr: float, the false positive rate of the classifier</span>
<span class="sd"> :param clip: set to True (default) to clip values that might exceed the range [0,1]</span>
<span class="sd"> :return: float, the adjusted count</span>
<span class="sd"> """</span>
<span class="n">den</span> <span class="o">=</span> <span class="n">tpr</span> <span class="o">-</span> <span class="n">fpr</span>
<span class="k">if</span> <span class="n">den</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">den</span> <span class="o">+=</span> <span class="mf">1e-8</span>
<span class="n">adjusted</span> <span class="o">=</span> <span class="p">(</span><span class="n">prevalence_estim</span> <span class="o">-</span> <span class="n">fpr</span><span class="p">)</span> <span class="o">/</span> <span class="n">den</span>
<span class="k">if</span> <span class="n">clip</span><span class="p">:</span>
<span class="n">adjusted</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">adjusted</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">)</span>
<span class="k">return</span> <span class="n">adjusted</span></div>
<div class="viewcode-block" id="normalize_prevalence">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.normalize_prevalence">[docs]</a>
<span class="k">def</span> <span class="nf">normalize_prevalence</span><span class="p">(</span><span class="n">prevalences</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Normalize a vector or matrix of prevalence values. The normalization consists of applying a L1 normalization in</span>
<span class="sd"> cases in which the prevalence values are not all-zeros, and to convert the prevalence values into `1/n_classes` in</span>
<span class="sd"> cases in which all values are zero.</span>
<span class="sd"> :param prevalences: array-like of shape `(n_classes,)` or of shape `(n_samples, n_classes,)` with prevalence values</span>
<span class="sd"> :return: a normalized vector or matrix of prevalence values</span>
<span class="sd"> """</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">prevalences</span><span class="p">)</span>
<span class="n">n_classes</span> <span class="o">=</span> <span class="n">prevalences</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="n">accum</span> <span class="o">=</span> <span class="n">prevalences</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="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">true_divide</span><span class="p">(</span><span class="n">prevalences</span><span class="p">,</span> <span class="n">accum</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">accum</span><span class="o">></span><span class="mi">0</span><span class="p">)</span>
<span class="n">allzeros</span> <span class="o">=</span> <span class="n">accum</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span><span class="o">==</span><span class="mi">0</span>
<span class="k">if</span> <span class="nb">any</span><span class="p">(</span><span class="n">allzeros</span><span class="p">):</span>
<span class="k">if</span> <span class="n">prevalences</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">fill_value</span><span class="o">=</span><span class="mf">1.</span><span class="o">/</span><span class="n">n_classes</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">prevalences</span><span class="p">[</span><span class="n">accum</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span><span class="o">==</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">fill_value</span><span class="o">=</span><span class="mf">1.</span><span class="o">/</span><span class="n">n_classes</span><span class="p">)</span>
<span class="k">return</span> <span class="n">prevalences</span></div>
<span class="k">def</span> <span class="nf">__num_prevalence_combinations_depr</span><span class="p">(</span><span class="n">n_prevpoints</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_repeats</span><span class="p">:</span><span class="nb">int</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Computes the number of prevalence combinations in the n_classes-dimensional simplex if `nprevpoints` equally distant</span>
<span class="sd"> prevalence values are generated and `n_repeats` repetitions are requested.</span>
<span class="sd"> :param n_classes: integer, number of classes</span>
<span class="sd"> :param n_prevpoints: integer, number of prevalence points.</span>
<span class="sd"> :param n_repeats: integer, number of repetitions for each prevalence combination</span>
<span class="sd"> :return: The number of possible combinations. For example, if n_classes=2, n_prevpoints=5, n_repeats=1, then the</span>
<span class="sd"> number of possible combinations are 5, i.e.: [0,1], [0.25,0.75], [0.50,0.50], [0.75,0.25], and [1.0,0.0]</span>
<span class="sd"> """</span>
<span class="n">__cache</span><span class="o">=</span><span class="p">{}</span>
<span class="k">def</span> <span class="nf">__f</span><span class="p">(</span><span class="n">nc</span><span class="p">,</span><span class="n">np</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="n">nc</span><span class="p">,</span><span class="n">np</span><span class="p">)</span> <span class="ow">in</span> <span class="n">__cache</span><span class="p">:</span> <span class="c1"># cached result</span>
<span class="k">return</span> <span class="n">__cache</span><span class="p">[(</span><span class="n">nc</span><span class="p">,</span><span class="n">np</span><span class="p">)]</span>
<span class="k">if</span> <span class="n">nc</span><span class="o">==</span><span class="mi">1</span><span class="p">:</span> <span class="c1"># stop condition</span>
<span class="k">return</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># recursive call</span>
<span class="n">x</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">__f</span><span class="p">(</span><span class="n">nc</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">-</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">np</span><span class="p">)])</span>
<span class="n">__cache</span><span class="p">[(</span><span class="n">nc</span><span class="p">,</span><span class="n">np</span><span class="p">)]</span> <span class="o">=</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">__f</span><span class="p">(</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">n_prevpoints</span><span class="p">)</span> <span class="o">*</span> <span class="n">n_repeats</span>
<div class="viewcode-block" id="num_prevalence_combinations">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.num_prevalence_combinations">[docs]</a>
<span class="k">def</span> <span class="nf">num_prevalence_combinations</span><span class="p">(</span><span class="n">n_prevpoints</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_repeats</span><span class="p">:</span><span class="nb">int</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Computes the number of valid prevalence combinations in the n_classes-dimensional simplex if `n_prevpoints` equally</span>
<span class="sd"> distant prevalence values are generated and `n_repeats` repetitions are requested.</span>
<span class="sd"> The computation comes down to calculating:</span>
<span class="sd"> .. math::</span>
<span class="sd"> \\binom{N+C-1}{C-1} \\times r</span>
<span class="sd"> where `N` is `n_prevpoints-1`, i.e., the number of probability mass blocks to allocate, `C` is the number of</span>
<span class="sd"> classes, and `r` is `n_repeats`. This solution comes from the</span>
<span class="sd"> `Stars and Bars <https://brilliant.org/wiki/integer-equations-star-and-bars/>`_ problem.</span>
<span class="sd"> :param n_classes: integer, number of classes</span>
<span class="sd"> :param n_prevpoints: integer, number of prevalence points.</span>
<span class="sd"> :param n_repeats: integer, number of repetitions for each prevalence combination</span>
<span class="sd"> :return: The number of possible combinations. For example, if n_classes=2, n_prevpoints=5, n_repeats=1, then the</span>
<span class="sd"> number of possible combinations are 5, i.e.: [0,1], [0.25,0.75], [0.50,0.50], [0.75,0.25], and [1.0,0.0]</span>
<span class="sd"> """</span>
<span class="n">N</span> <span class="o">=</span> <span class="n">n_prevpoints</span><span class="o">-</span><span class="mi">1</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">n_classes</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">n_repeats</span>
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">special</span><span class="o">.</span><span class="n">binom</span><span class="p">(</span><span class="n">N</span> <span class="o">+</span> <span class="n">C</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">C</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span><span class="p">)</span></div>
<div class="viewcode-block" id="get_nprevpoints_approximation">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.get_nprevpoints_approximation">[docs]</a>
<span class="k">def</span> <span class="nf">get_nprevpoints_approximation</span><span class="p">(</span><span class="n">combinations_budget</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">:</span><span class="nb">int</span><span class="p">,</span> <span class="n">n_repeats</span><span class="p">:</span><span class="nb">int</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Searches for the largest number of (equidistant) prevalence points to define for each of the `n_classes` classes so</span>
<span class="sd"> that the number of valid prevalence values generated as combinations of prevalence points (points in a</span>
<span class="sd"> `n_classes`-dimensional simplex) do not exceed combinations_budget.</span>
<span class="sd"> :param combinations_budget: integer, maximum number of combinations allowed</span>
<span class="sd"> :param n_classes: integer, number of classes</span>
<span class="sd"> :param n_repeats: integer, number of repetitions for each prevalence combination</span>
<span class="sd"> :return: the largest number of prevalence points that generate less than combinations_budget valid prevalences</span>
<span class="sd"> """</span>
<span class="k">assert</span> <span class="n">n_classes</span> <span class="o">></span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">n_repeats</span> <span class="o">></span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">combinations_budget</span> <span class="o">></span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'parameters must be positive integers'</span>
<span class="n">n_prevpoints</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="n">combinations</span> <span class="o">=</span> <span class="n">num_prevalence_combinations</span><span class="p">(</span><span class="n">n_prevpoints</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">,</span> <span class="n">n_repeats</span><span class="p">)</span>
<span class="k">if</span> <span class="n">combinations</span> <span class="o">></span> <span class="n">combinations_budget</span><span class="p">:</span>
<span class="k">return</span> <span class="n">n_prevpoints</span><span class="o">-</span><span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">n_prevpoints</span> <span class="o">+=</span> <span class="mi">1</span></div>
<div class="viewcode-block" id="check_prevalence_vector">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.check_prevalence_vector">[docs]</a>
<span class="k">def</span> <span class="nf">check_prevalence_vector</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">raise_exception</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">toleranze</span><span class="o">=</span><span class="mf">1e-08</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Checks that p is a valid prevalence vector, i.e., that it contains values in [0,1] and that the values sum up to 1.</span>
<span class="sd"> :param p: the prevalence vector to check</span>
<span class="sd"> :return: True if `p` is valid, False otherwise</span>
<span class="sd"> """</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="n">p</span><span class="o">>=</span><span class="mi">0</span><span class="p">):</span>
<span class="k">if</span> <span class="n">raise_exception</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'the prevalence vector contains negative numbers'</span><span class="p">)</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="n">p</span><span class="o"><=</span><span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">raise_exception</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'the prevalence vector contains values >1'</span><span class="p">)</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="mi">1</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="n">toleranze</span><span class="p">):</span>
<span class="k">if</span> <span class="n">raise_exception</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'the prevalence vector does not sum up to 1'</span><span class="p">)</span>
<span class="k">return</span> <span class="kc">False</span>
<span class="k">return</span> <span class="kc">True</span></div>
<div class="viewcode-block" id="get_divergence">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.get_divergence">[docs]</a>
<span class="k">def</span> <span class="nf">get_divergence</span><span class="p">(</span><span class="n">divergence</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">Callable</span><span class="p">]):</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">divergence</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
<span class="k">if</span> <span class="n">divergence</span><span class="o">==</span><span class="s1">'HD'</span><span class="p">:</span>
<span class="k">return</span> <span class="n">HellingerDistance</span>
<span class="k">elif</span> <span class="n">divergence</span><span class="o">==</span><span class="s1">'topsoe'</span><span class="p">:</span>
<span class="k">return</span> <span class="n">TopsoeDistance</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'unknown divergence </span><span class="si">{</span><span class="n">divergence</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">callable</span><span class="p">(</span><span class="n">divergence</span><span class="p">):</span>
<span class="k">return</span> <span class="n">divergence</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">'argument "divergence" not understood; use a str or a callable function'</span><span class="p">)</span></div>
<div class="viewcode-block" id="argmin_prevalence">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.argmin_prevalence">[docs]</a>
<span class="k">def</span> <span class="nf">argmin_prevalence</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'optim_minimize'</span><span class="p">):</span>
<span class="k">if</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">'optim_minimize'</span><span class="p">:</span>
<span class="k">return</span> <span class="n">optim_minimize</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">'linear_search'</span><span class="p">:</span>
<span class="k">return</span> <span class="n">linear_search</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">'ternary_search'</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span></div>
<div class="viewcode-block" id="optim_minimize">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.optim_minimize">[docs]</a>
<span class="k">def</span> <span class="nf">optim_minimize</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Searches for the optimal prevalence values, i.e., an `n_classes`-dimensional vector of the (`n_classes`-1)-simplex</span>
<span class="sd"> that yields the smallest lost. This optimization is carried out by means of a constrained search using scipy's</span>
<span class="sd"> SLSQP routine.</span>
<span class="sd"> :param loss: (callable) the function to minimize</span>
<span class="sd"> :param n_classes: (int) the number of classes, i.e., the dimensionality of the prevalence vector</span>
<span class="sd"> :return: (ndarray) the best prevalence vector found</span>
<span class="sd"> """</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">optimize</span>
<span class="c1"># the initial point is set as the uniform distribution</span>
<span class="n">uniform_distribution</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">fill_value</span><span class="o">=</span><span class="mi">1</span> <span class="o">/</span> <span class="n">n_classes</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">n_classes</span><span class="p">,))</span>
<span class="c1"># solutions are bounded to those contained in the unit-simplex</span>
<span class="n">bounds</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_classes</span><span class="p">))</span> <span class="c1"># values in [0,1]</span>
<span class="n">constraints</span> <span class="o">=</span> <span class="p">({</span><span class="s1">'type'</span><span class="p">:</span> <span class="s1">'eq'</span><span class="p">,</span> <span class="s1">'fun'</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="mi">1</span> <span class="o">-</span> <span class="nb">sum</span><span class="p">(</span><span class="n">x</span><span class="p">)})</span> <span class="c1"># values summing up to 1</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">optimize</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="n">uniform_distribution</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'SLSQP'</span><span class="p">,</span> <span class="n">bounds</span><span class="o">=</span><span class="n">bounds</span><span class="p">,</span> <span class="n">constraints</span><span class="o">=</span><span class="n">constraints</span><span class="p">)</span>
<span class="k">return</span> <span class="n">r</span><span class="o">.</span><span class="n">x</span></div>
<div class="viewcode-block" id="linear_search">
<a class="viewcode-back" href="../../quapy.html#quapy.functional.linear_search">[docs]</a>
<span class="k">def</span> <span class="nf">linear_search</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Performs a linear search for the best prevalence value in binary problems. The search is carried out by exploring</span>
<span class="sd"> the range [0,1] stepping by 0.01. This search is inefficient, and is added only for completeness (some of the</span>
<span class="sd"> early methods in quantification literature used it, e.g., HDy). A most powerful alternative is `optim_minimize`.</span>
<span class="sd"> :param loss: (callable) the function to minimize</span>
<span class="sd"> :param n_classes: (int) the number of classes, i.e., the dimensionality of the prevalence vector</span>
<span class="sd"> :return: (ndarray) the best prevalence vector found</span>
<span class="sd"> """</span>
<span class="k">assert</span> <span class="n">n_classes</span><span class="o">==</span><span class="mi">2</span><span class="p">,</span> <span class="s1">'linear search is only available for binary problems'</span>
<span class="n">prev_selected</span><span class="p">,</span> <span class="n">min_score</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
<span class="k">for</span> <span class="n">prev</span> <span class="ow">in</span> <span class="n">prevalence_linspace</span><span class="p">(</span><span class="n">n_prevalences</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">repeats</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">smooth_limits_epsilon</span><span class="o">=</span><span class="mf">0.0</span><span class="p">):</span>
<span class="n">score</span> <span class="o">=</span> <span class="n">loss</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="mi">1</span> <span class="o">-</span> <span class="n">prev</span><span class="p">,</span> <span class="n">prev</span><span class="p">]))</span>
<span class="k">if</span> <span class="n">min_score</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">score</span> <span class="o"><</span> <span class="n">min_score</span><span class="p">:</span>
<span class="n">prev_selected</span><span class="p">,</span> <span class="n">min_score</span> <span class="o">=</span> <span class="n">prev</span><span class="p">,</span> <span class="n">score</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="mi">1</span> <span class="o">-</span> <span class="n">prev_selected</span><span class="p">,</span> <span class="n">prev_selected</span><span class="p">])</span></div>
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