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<section id="quantification-methods">
<h1>Quantification Methods<a class="headerlink" href="#quantification-methods" title="Permalink to this heading"></a></h1>
<p>Quantification methods can be categorized as belonging to
<em>aggregative</em> and <em>non-aggregative</em> groups.
Most methods included in QuaPy at the moment are of type <em>aggregative</em>
(though we plan to add many more methods in the near future), i.e.,
are methods characterized by the fact that
quantification is performed as an aggregation function of the individual
products of classification.</p>
<p>Any quantifier in QuaPy shoud extend the class <em>BaseQuantifier</em>,
and implement some abstract methods:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="nd">@abstractmethod</span>
<span class="k">def</span> <span class="nf">fit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">LabelledCollection</span><span class="p">):</span> <span class="o">...</span>
<span class="nd">@abstractmethod</span>
<span class="k">def</span> <span class="nf">quantify</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">instances</span><span class="p">):</span> <span class="o">...</span>
</pre></div>
</div>
<p>The meaning of those functions should be familiar to those
used to work with scikit-learn since the class structure of QuaPy
is directly inspired by scikit-learn’s <em>Estimators</em>. Functions
<em>fit</em> and <em>quantify</em> are used to train the model and to provide
class estimations (the reason why
scikit-learn’ structure has not been adopted <em>as is</em> in QuaPy responds to
the fact that scikit-learn’s <em>predict</em> function is expected to return
one output for each input element –e.g., a predicted label for each
instance in a sample– while in quantification the output for a sample
is one single array of class prevalences).
Quantifiers also extend from scikit-learn’s <code class="docutils literal notranslate"><span class="pre">BaseEstimator</span></code>, in order
to simplify the use of <em>set_params</em> and <em>get_params</em> used in
<a class="reference external" href="https://github.com/HLT-ISTI/QuaPy/wiki/Model-Selection">model selector</a>.</p>
<section id="aggregative-methods">
<h2>Aggregative Methods<a class="headerlink" href="#aggregative-methods" title="Permalink to this heading"></a></h2>
<p>All quantification methods are implemented as part of the
<em>qp.method</em> package. In particular, <em>aggregative</em> methods are defined in
<em>qp.method.aggregative</em>, and extend <em>AggregativeQuantifier(BaseQuantifier)</em>.
The methods that any <em>aggregative</em> quantifier must implement are:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="nd">@abstractmethod</span>
<span class="k">def</span> <span class="nf">fit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">LabelledCollection</span><span class="p">,</span> <span class="n">fit_learner</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span> <span class="o">...</span>
<span class="nd">@abstractmethod</span>
<span class="k">def</span> <span class="nf">aggregate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">classif_predictions</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="o">...</span>
</pre></div>
</div>
<p>since, as mentioned before, aggregative methods base their prediction on the
individual predictions of a classifier. Indeed, a default implementation
of <em>BaseQuantifier.quantify</em> is already provided, which looks like:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span> <span class="k">def</span> <span class="nf">quantify</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">instances</span><span class="p">):</span>
<span class="n">classif_predictions</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">classify</span><span class="p">(</span><span class="n">instances</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">aggregate</span><span class="p">(</span><span class="n">classif_predictions</span><span class="p">)</span>
</pre></div>
</div>
<p>Aggregative quantifiers are expected to maintain a classifier (which is
accessed through the <em>&#64;property</em> <em>classifier</em>). This classifier is
given as input to the quantifier, and can be already fit
on external data (in which case, the <em>fit_learner</em> argument should
be set to False), or be fit by the quantifier’s fit (default).</p>
<p>Another class of <em>aggregative</em> methods are the <em>probabilistic</em>
aggregative methods, that should inherit from the abstract class
<em>AggregativeProbabilisticQuantifier(AggregativeQuantifier)</em>.
The particularity of <em>probabilistic</em> aggregative methods (w.r.t.
non-probabilistic ones), is that the default quantifier is defined
in terms of the posterior probabilities returned by a probabilistic
classifier, and not by the crisp decisions of a hard classifier.
In any case, the interface <em>classify(instances)</em> remains unchanged.</p>
<p>One advantage of <em>aggregative</em> methods (either probabilistic or not)
is that the evaluation according to any sampling procedure (e.g.,
the <a class="reference external" href="https://github.com/HLT-ISTI/QuaPy/wiki/Evaluation">artificial sampling protocol</a>)
can be achieved very efficiently, since the entire set can be pre-classified
once, and the quantification estimations for different samples can directly
reuse these predictions, without requiring to classify each element every time.
QuaPy leverages this property to speed-up any procedure having to do with
quantification over samples, as is customarily done in model selection or
in evaluation.</p>
<section id="the-classify-count-variants">
<h3>The Classify &amp; Count variants<a class="headerlink" href="#the-classify-count-variants" title="Permalink to this heading"></a></h3>
<p>QuaPy implements the four CC variants, i.e.:</p>
<ul class="simple">
<li><p><em>CC</em> (Classify &amp; Count), the simplest aggregative quantifier; one that
simply relies on the label predictions of a classifier to deliver class estimates.</p></li>
<li><p><em>ACC</em> (Adjusted Classify &amp; Count), the adjusted variant of CC.</p></li>
<li><p><em>PCC</em> (Probabilistic Classify &amp; Count), the probabilistic variant of CC that
relies on the soft estimations (or posterior probabilities) returned by a (probabilistic) classifier.</p></li>
<li><p><em>PACC</em> (Probabilistic Adjusted Classify &amp; Count), the adjusted variant of PCC.</p></li>
</ul>
<p>The following code serves as a complete example using CC equipped
with a SVM as the classifier:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">import</span> <span class="nn">quapy.functional</span> <span class="k">as</span> <span class="nn">F</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">LinearSVC</span>
<span class="n">training</span><span class="p">,</span> <span class="n">test</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_twitter</span><span class="p">(</span><span class="s1">&#39;hcr&#39;</span><span class="p">,</span> <span class="n">pickle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span><span class="o">.</span><span class="n">train_test</span>
<span class="c1"># instantiate a classifier learner, in this case a SVM</span>
<span class="n">svm</span> <span class="o">=</span> <span class="n">LinearSVC</span><span class="p">()</span>
<span class="c1"># instantiate a Classify &amp; Count with the SVM</span>
<span class="c1"># (an alias is available in qp.method.aggregative.ClassifyAndCount)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">CC</span><span class="p">(</span><span class="n">svm</span><span class="p">)</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
<p>The same code could be used to instantiate an ACC, by simply replacing
the instantiation of the model with:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">ACC</span><span class="p">(</span><span class="n">svm</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that the adjusted variants (ACC and PACC) need to estimate
some parameters for performing the adjustment (e.g., the
<em>true positive rate</em> and the <em>false positive rate</em> in case of
binary classification) that are estimated on a validation split
of the labelled set. In this case, the <strong>init</strong> method of
ACC defines an additional parameter, <em>val_split</em> which, by
default, is set to 0.4 and so, the 40% of the labelled data
will be used for estimating the parameters for adjusting the
predictions. This parameters can also be set with an integer,
indicating that the parameters should be estimated by means of
<em>k</em>-fold cross-validation, for which the integer indicates the
number <em>k</em> of folds. Finally, <em>val_split</em> can be set to a
specific held-out validation set (i.e., an instance of <em>LabelledCollection</em>).</p>
<p>The specification of <em>val_split</em> can be
postponed to the invokation of the fit method (if <em>val_split</em> was also
set in the constructor, the one specified at fit time would prevail),
e.g.:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">ACC</span><span class="p">(</span><span class="n">svm</span><span class="p">)</span>
<span class="c1"># perform 5-fold cross validation for estimating ACC&#39;s parameters</span>
<span class="c1"># (overrides the default val_split=0.4 in the constructor)</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">,</span> <span class="n">val_split</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<p>The following code illustrates the case in which PCC is used:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">PCC</span><span class="p">(</span><span class="n">svm</span><span class="p">)</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;classifier:&#39;</span><span class="p">,</span> <span class="n">model</span><span class="o">.</span><span class="n">classifier</span><span class="p">)</span>
</pre></div>
</div>
<p>In this case, QuaPy will print:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">The</span> <span class="n">learner</span> <span class="n">LinearSVC</span> <span class="n">does</span> <span class="ow">not</span> <span class="n">seem</span> <span class="n">to</span> <span class="n">be</span> <span class="n">probabilistic</span><span class="o">.</span> <span class="n">The</span> <span class="n">learner</span> <span class="n">will</span> <span class="n">be</span> <span class="n">calibrated</span><span class="o">.</span>
<span class="n">classifier</span><span class="p">:</span> <span class="n">CalibratedClassifierCV</span><span class="p">(</span><span class="n">base_estimator</span><span class="o">=</span><span class="n">LinearSVC</span><span class="p">(),</span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<p>The first output indicates that the learner (<em>LinearSVC</em> in this case)
is not a probabilistic classifier (i.e., it does not implement the
<em>predict_proba</em> method) and so, the classifier will be converted to
a probabilistic one through <a class="reference external" href="https://scikit-learn.org/stable/modules/calibration.html">calibration</a>.
As a result, the classifier that is printed in the second line points
to a <em>CalibratedClassifier</em> instance. Note that calibration can only
be applied to hard classifiers when <em>fit_learner=True</em>; an exception
will be raised otherwise.</p>
<p>Lastly, everything we said aboud ACC and PCC
applies to PACC as well.</p>
</section>
<section id="expectation-maximization-emq">
<h3>Expectation Maximization (EMQ)<a class="headerlink" href="#expectation-maximization-emq" title="Permalink to this heading"></a></h3>
<p>The Expectation Maximization Quantifier (EMQ), also known as
the SLD, is available at <em>qp.method.aggregative.EMQ</em> or via the
alias <em>qp.method.aggregative.ExpectationMaximizationQuantifier</em>.
The method is described in:</p>
<p><em>Saerens, M., Latinne, P., and Decaestecker, C. (2002). Adjusting the outputs of a classifier
to new a priori probabilities: A simple procedure. Neural Computation, 14(1):21–41.</em></p>
<p>EMQ works with a probabilistic classifier (if the classifier
given as input is a hard one, a calibration will be attempted).
Although this method was originally proposed for improving the
posterior probabilities of a probabilistic classifier, and not
for improving the estimation of prior probabilities, EMQ ranks
almost always among the most effective quantifiers in the
experiments we have carried out.</p>
<p>An example of use can be found below:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_twitter</span><span class="p">(</span><span class="s1">&#39;hcr&#39;</span><span class="p">,</span> <span class="n">pickle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">EMQ</span><span class="p">(</span><span class="n">LogisticRegression</span><span class="p">())</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
<p><em>New in v0.1.7</em>: EMQ now accepts two new parameters in the construction method, namely
<em>exact_train_prev</em> which allows to use the true training prevalence as the departing
prevalence estimation (default behaviour), or instead an approximation of it as
suggested by <a class="reference external" href="http://proceedings.mlr.press/v119/alexandari20a.html">Alexandari et al. (2020)</a>
(by setting <em>exact_train_prev=False</em>).
The other parameter is <em>recalib</em> which allows to indicate a calibration method, among those
proposed by <a class="reference external" href="http://proceedings.mlr.press/v119/alexandari20a.html">Alexandari et al. (2020)</a>,
including the Bias-Corrected Temperature Scaling, Vector Scaling, etc.
See the API documentation for further details.</p>
</section>
<section id="hellinger-distance-y-hdy">
<h3>Hellinger Distance y (HDy)<a class="headerlink" href="#hellinger-distance-y-hdy" title="Permalink to this heading"></a></h3>
<p>Implementation of the method based on the Hellinger Distance y (HDy) proposed by
<a class="reference external" href="https://www.sciencedirect.com/science/article/pii/S0020025512004069">González-Castro, V., Alaiz-Rodrı́guez, R., and Alegre, E. (2013). Class distribution
estimation based on the Hellinger distance. Information Sciences, 218:146–164.</a></p>
<p>It is implemented in <em>qp.method.aggregative.HDy</em> (also accessible
through the allias <em>qp.method.aggregative.HellingerDistanceY</em>).
This method works with a probabilistic classifier (hard classifiers
can be used as well and will be calibrated) and requires a validation
set to estimate parameter for the mixture model. Just like
ACC and PACC, this quantifier receives a <em>val_split</em> argument
in the constructor (or in the fit method, in which case the previous
value is overridden) that can either be a float indicating the proportion
of training data to be taken as the validation set (in a random
stratified split), or a validation set (i.e., an instance of
<em>LabelledCollection</em>) itself.</p>
<p>HDy was proposed as a binary classifier and the implementation
provided in QuaPy accepts only binary datasets.</p>
<p>The following code shows an example of use:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="c1"># load a binary dataset</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_reviews</span><span class="p">(</span><span class="s1">&#39;hp&#39;</span><span class="p">,</span> <span class="n">pickle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">qp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">preprocessing</span><span class="o">.</span><span class="n">text2tfidf</span><span class="p">(</span><span class="n">dataset</span><span class="p">,</span> <span class="n">min_df</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">HDy</span><span class="p">(</span><span class="n">LogisticRegression</span><span class="p">())</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
<p><em>New in v0.1.7:</em> QuaPy now provides an implementation of the generalized
“Distribution Matching” approaches for multiclass, inspired by the framework
of <a class="reference external" href="https://arxiv.org/abs/1606.00868">Firat (2016)</a>. One can instantiate
a variant of HDy for multiclass quantification as follows:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">mutliclassHDy</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">DistributionMatching</span><span class="p">(</span><span class="n">classifier</span><span class="o">=</span><span class="n">LogisticRegression</span><span class="p">(),</span> <span class="n">divergence</span><span class="o">=</span><span class="s1">&#39;HD&#39;</span><span class="p">,</span> <span class="n">cdf</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
</pre></div>
</div>
<p><em>New in v0.1.7:</em> QuaPy now provides an implementation of the “DyS”
framework proposed by <a class="reference external" href="https://ojs.aaai.org/index.php/AAAI/article/view/4376">Maletzke et al (2020)</a>
and the “SMM” method proposed by <a class="reference external" href="https://ieeexplore.ieee.org/document/9260028">Hassan et al (2019)</a>
(thanks to <em>Pablo González</em> for the contributions!)</p>
</section>
<section id="threshold-optimization-methods">
<h3>Threshold Optimization methods<a class="headerlink" href="#threshold-optimization-methods" title="Permalink to this heading"></a></h3>
<p><em>New in v0.1.7:</em> QuaPy now implements Forman’s threshold optimization methods;
see, e.g., <a class="reference external" href="https://dl.acm.org/doi/abs/10.1145/1150402.1150423">(Forman 2006)</a>
and <a class="reference external" href="https://link.springer.com/article/10.1007/s10618-008-0097-y">(Forman 2008)</a>.
These include: T50, MAX, X, Median Sweep (MS), and its variant MS2.</p>
</section>
<section id="explicit-loss-minimization">
<h3>Explicit Loss Minimization<a class="headerlink" href="#explicit-loss-minimization" title="Permalink to this heading"></a></h3>
<p>The Explicit Loss Minimization (ELM) represent a family of methods
based on structured output learning, i.e., quantifiers relying on
classifiers that have been optimized targeting a
quantification-oriented evaluation measure.
The original methods are implemented in QuaPy as classify &amp; count (CC)
quantifiers that use Joachim’s <a class="reference external" href="https://www.cs.cornell.edu/people/tj/svm_light/svm_perf.html">SVMperf</a>
as the underlying classifier, properly set to optimize for the desired loss.</p>
<p>In QuaPy, this can be more achieved by calling the functions:</p>
<ul class="simple">
<li><p><em>newSVMQ</em>: returns the quantification method called SVM(Q) that optimizes for the metric <em>Q</em> defined
in <a class="reference external" href="https://www.sciencedirect.com/science/article/pii/S003132031400291X"><em>Barranquero, J., Díez, J., and del Coz, J. J. (2015). Quantification-oriented learning based
on reliable classifiers. Pattern Recognition, 48(2):591–604.</em></a></p></li>
<li><p><em>newSVMKLD</em> and <em>newSVMNKLD</em>: returns the quantification method called SVM(KLD) and SVM(nKLD), standing for
Kullback-Leibler Divergence and Normalized Kullback-Leibler Divergence, as proposed in <a class="reference external" href="https://dl.acm.org/doi/abs/10.1145/2700406"><em>Esuli, A. and Sebastiani, F. (2015).
Optimizing text quantifiers for multivariate loss functions.
ACM Transactions on Knowledge Discovery and Data, 9(4):Article 27.</em></a></p></li>
<li><p><em>newSVMAE</em> and <em>newSVMRAE</em>: returns a quantification method called SVM(AE) and SVM(RAE) that optimizes for the (Mean) Absolute Error and for the
(Mean) Relative Absolute Error, as first used by
<a class="reference external" href="https://arxiv.org/abs/2011.02552"><em>Moreo, A. and Sebastiani, F. (2021). Tweet sentiment quantification: An experimental re-evaluation. PLOS ONE 17 (9), 1-23.</em></a></p></li>
</ul>
<p>the last two methods (SVM(AE) and SVM(RAE)) have been implemented in
QuaPy in order to make available ELM variants for what nowadays
are considered the most well-behaved evaluation metrics in quantification.</p>
<p>In order to make these models work, you would need to run the script
<em>prepare_svmperf.sh</em> (distributed along with QuaPy) that
downloads <em>SVMperf</em>’ source code, applies a patch that
implements the quantification oriented losses, and compiles the
sources.</p>
<p>If you want to add any custom loss, you would need to modify
the source code of <em>SVMperf</em> in order to implement it, and
assign a valid loss code to it. Then you must re-compile
the whole thing and instantiate the quantifier in QuaPy
as follows:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># you can either set the path to your custom svm_perf_quantification implementation</span>
<span class="c1"># in the environment variable, or as an argument to the constructor of ELM</span>
<span class="n">qp</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;SVMPERF_HOME&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;./path/to/svm_perf_quantification&#39;</span>
<span class="c1"># assign an alias to your custom loss and the id you have assigned to it</span>
<span class="n">svmperf</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">classification</span><span class="o">.</span><span class="n">svmperf</span><span class="o">.</span><span class="n">SVMperf</span>
<span class="n">svmperf</span><span class="o">.</span><span class="n">valid_losses</span><span class="p">[</span><span class="s1">&#39;mycustomloss&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">28</span>
<span class="c1"># instantiate the ELM method indicating the loss</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">method</span><span class="o">.</span><span class="n">aggregative</span><span class="o">.</span><span class="n">ELM</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="s1">&#39;mycustomloss&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>All ELM are binary quantifiers since they rely on <em>SVMperf</em>, that
currently supports only binary classification.
ELM variants (any binary quantifier in general) can be extended
to operate in single-label scenarios trivially by adopting a
“one-vs-all” strategy (as, e.g., in
<a class="reference external" href="https://link.springer.com/article/10.1007/s13278-016-0327-z"><em>Gao, W. and Sebastiani, F. (2016). From classification to quantification in tweet sentiment
analysis. Social Network Analysis and Mining, 6(19):1–22</em></a>).
In QuaPy this is possible by using the <em>OneVsAll</em> class.</p>
<p>There are two ways for instantiating this class, <em>OneVsAllGeneric</em> that works for
any quantifier, and <em>OneVsAllAggregative</em> that is optimized for aggregative quantifiers.
In general, you can simply use the <em>getOneVsAll</em> function and QuaPy will choose
the more convenient of the two.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">quapy.method.aggregative</span> <span class="kn">import</span> <span class="n">SVMQ</span>
<span class="c1"># load a single-label dataset (this one contains 3 classes)</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_twitter</span><span class="p">(</span><span class="s1">&#39;hcr&#39;</span><span class="p">,</span> <span class="n">pickle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># let qp know where svmperf is</span>
<span class="n">qp</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;SVMPERF_HOME&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;../svm_perf_quantification&#39;</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">getOneVsAll</span><span class="p">(</span><span class="n">SVMQ</span><span class="p">(),</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># run them on parallel</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
<p>Check the examples <em><span class="xref myst">explicit_loss_minimization.py</span></em>
and <span class="xref myst">one_vs_all.py</span> for more details.</p>
</section>
</section>
<section id="meta-models">
<h2>Meta Models<a class="headerlink" href="#meta-models" title="Permalink to this heading"></a></h2>
<p>By <em>meta</em> models we mean quantification methods that are defined on top of other
quantification methods, and that thus do not squarely belong to the aggregative nor
the non-aggregative group (indeed, <em>meta</em> models could use quantifiers from any of those
groups).
<em>Meta</em> models are implemented in the <em>qp.method.meta</em> module.</p>
<section id="ensembles">
<h3>Ensembles<a class="headerlink" href="#ensembles" title="Permalink to this heading"></a></h3>
<p>QuaPy implements (some of) the variants proposed in:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://www.sciencedirect.com/science/article/pii/S1566253516300628"><em>Pérez-Gállego, P., Quevedo, J. R., &amp; del Coz, J. J. (2017).
Using ensembles for problems with characterizable changes in data distribution: A case study on quantification.
Information Fusion, 34, 87-100.</em></a></p></li>
<li><p><a class="reference external" href="https://www.sciencedirect.com/science/article/pii/S1566253517303652"><em>Pérez-Gállego, P., Castano, A., Quevedo, J. R., &amp; del Coz, J. J. (2019).
Dynamic ensemble selection for quantification tasks.
Information Fusion, 45, 1-15.</em></a></p></li>
</ul>
<p>The following code shows how to instantiate an Ensemble of 30 <em>Adjusted Classify &amp; Count</em> (ACC)
quantifiers operating with a <em>Logistic Regressor</em> (LR) as the base classifier, and using the
<em>average</em> as the aggregation policy (see the original article for further details).
The last parameter indicates to use all processors for parallelization.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">quapy.method.aggregative</span> <span class="kn">import</span> <span class="n">ACC</span>
<span class="kn">from</span> <span class="nn">quapy.method.meta</span> <span class="kn">import</span> <span class="n">Ensemble</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_UCIDataset</span><span class="p">(</span><span class="s1">&#39;haberman&#39;</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">Ensemble</span><span class="p">(</span><span class="n">quantifier</span><span class="o">=</span><span class="n">ACC</span><span class="p">(</span><span class="n">LogisticRegression</span><span class="p">()),</span> <span class="n">size</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">policy</span><span class="o">=</span><span class="s1">&#39;ave&#39;</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
<p>Other aggregation policies implemented in QuaPy include:</p>
<ul class="simple">
<li><p>‘ptr’ for applying a dynamic selection based on the training prevalence of the ensemble’s members</p></li>
<li><p>‘ds’ for applying a dynamic selection based on the Hellinger Distance</p></li>
<li><p><em>any valid quantification measure</em> (e.g., ‘mse’) for performing a static selection based on
the performance estimated for each member of the ensemble in terms of that evaluation metric.</p></li>
</ul>
<p>When using any of the above options, it is important to set the <em>red_size</em> parameter, which
informs of the number of members to retain.</p>
<p>Please, check the <a class="reference external" href="https://github.com/HLT-ISTI/QuaPy/wiki/Model-Selection">model selection</a>
wiki if you want to optimize the hyperparameters of ensemble for classification or quantification.</p>
</section>
<section id="the-quanet-neural-network">
<h3>The QuaNet neural network<a class="headerlink" href="#the-quanet-neural-network" title="Permalink to this heading"></a></h3>
<p>QuaPy offers an implementation of QuaNet, a deep learning model presented in:</p>
<p><a class="reference external" href="https://dl.acm.org/doi/abs/10.1145/3269206.3269287"><em>Esuli, A., Moreo, A., &amp; Sebastiani, F. (2018, October).
A recurrent neural network for sentiment quantification.
In Proceedings of the 27th ACM International Conference on
Information and Knowledge Management (pp. 1775-1778).</em></a></p>
<p>This model requires <em>torch</em> to be installed.
QuaNet also requires a classifier that can provide embedded representations
of the inputs.
In the original paper, QuaNet was tested using an LSTM as the base classifier.
In the following example, we show an instantiation of QuaNet that instead uses CNN as a probabilistic classifier, taking its last layer representation as the document embedding:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">quapy.method.meta</span> <span class="kn">import</span> <span class="n">QuaNet</span>
<span class="kn">from</span> <span class="nn">quapy.classification.neural</span> <span class="kn">import</span> <span class="n">NeuralClassifierTrainer</span><span class="p">,</span> <span class="n">CNNnet</span>
<span class="c1"># use samples of 100 elements</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="o">=</span> <span class="mi">100</span>
<span class="c1"># load the kindle dataset as text, and convert words to numerical indexes</span>
<span class="n">dataset</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_reviews</span><span class="p">(</span><span class="s1">&#39;kindle&#39;</span><span class="p">,</span> <span class="n">pickle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">qp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">preprocessing</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="n">dataset</span><span class="p">,</span> <span class="n">min_df</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># the text classifier is a CNN trained by NeuralClassifierTrainer</span>
<span class="n">cnn</span> <span class="o">=</span> <span class="n">CNNnet</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">vocabulary_size</span><span class="p">,</span> <span class="n">dataset</span><span class="o">.</span><span class="n">n_classes</span><span class="p">)</span>
<span class="n">learner</span> <span class="o">=</span> <span class="n">NeuralClassifierTrainer</span><span class="p">(</span><span class="n">cnn</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="s1">&#39;cuda&#39;</span><span class="p">)</span>
<span class="c1"># train QuaNet</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">QuaNet</span><span class="p">(</span><span class="n">learner</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="s1">&#39;cuda&#39;</span><span class="p">)</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">training</span><span class="p">)</span>
<span class="n">estim_prevalence</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">quantify</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="o">.</span><span class="n">instances</span><span class="p">)</span>
</pre></div>
</div>
</section>
</section>
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<h3><a href="index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Quantification Methods</a><ul>
<li><a class="reference internal" href="#aggregative-methods">Aggregative Methods</a><ul>
<li><a class="reference internal" href="#the-classify-count-variants">The Classify &amp; Count variants</a></li>
<li><a class="reference internal" href="#expectation-maximization-emq">Expectation Maximization (EMQ)</a></li>
<li><a class="reference internal" href="#hellinger-distance-y-hdy">Hellinger Distance y (HDy)</a></li>
<li><a class="reference internal" href="#threshold-optimization-methods">Threshold Optimization methods</a></li>
<li><a class="reference internal" href="#explicit-loss-minimization">Explicit Loss Minimization</a></li>
</ul>
</li>
<li><a class="reference internal" href="#meta-models">Meta Models</a><ul>
<li><a class="reference internal" href="#ensembles">Ensembles</a></li>
<li><a class="reference internal" href="#the-quanet-neural-network">The QuaNet neural network</a></li>
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