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<div class="tex2jax_ignore mathjax_ignore section" id="model-selection">
<h1>Model Selection<a class="headerlink" href="#model-selection" title="Permalink to this headline"></a></h1>
<p>As a supervised machine learning task, quantification methods
can strongly depend on a good choice of model hyper-parameters.
The process whereby those hyper-parameters are chosen is
typically known as <em>Model Selection</em>, and typically consists of
testing different settings and picking the one that performed
best in a held-out validation set in terms of any given
evaluation measure.</p>
<div class="section" id="targeting-a-quantification-oriented-loss">
<h2>Targeting a Quantification-oriented loss<a class="headerlink" href="#targeting-a-quantification-oriented-loss" title="Permalink to this headline"></a></h2>
<p>The task being optimized determines the evaluation protocol,
i.e., the criteria according to which the performance of
any given method for solving is to be assessed.
As a task on its own right, quantification should impose
its own model selection strategies, i.e., strategies
aimed at finding appropriate configurations
specifically designed for the task of quantification.</p>
<p>Quantification has long been regarded as an add-on of
classification, and thus the model selection strategies
customarily adopted in classification have simply been
applied to quantification (see the next section).
It has been argued in <em>Moreo, Alejandro, and Fabrizio Sebastiani.
“Re-Assessing the” Classify and Count” Quantification Method.”
arXiv preprint arXiv:2011.02552 (2020).</em>
that specific model selection strategies should
be adopted for quantification. That is, model selection
strategies for quantification should target
quantification-oriented losses and be tested in a variety
of scenarios exhibiting different degrees of prior
probability shift.</p>
<p>The class
<em>qp.model_selection.GridSearchQ</em>
implements a grid-search exploration over the space of
hyper-parameter combinations that evaluates each<br />
combination of hyper-parameters
by means of a given quantification-oriented
error metric (e.g., any of the error functions implemented
in <em>qp.error</em>) and according to the
<a class="reference external" href="https://github.com/HLT-ISTI/QuaPy/wiki/Evaluation"><em>artificial sampling protocol</em></a>.</p>
<p>The following is an example of model selection for quantification:</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">PCC</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="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="c1"># set a seed to replicate runs</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</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">500</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">tfidf</span><span class="o">=</span><span class="kc">True</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="c1"># The model will be returned by the fit method of GridSearchQ.</span>
<span class="c1"># Model selection will be performed with a fixed budget of 1000 evaluations</span>
<span class="c1"># for each hyper-parameter combination. The error to optimize is the MAE for</span>
<span class="c1"># quantification, as evaluated on artificially drawn samples at prevalences </span>
<span class="c1"># covering the entire spectrum on a held-out portion (40%) of the training set.</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">model_selection</span><span class="o">.</span><span class="n">GridSearchQ</span><span class="p">(</span>
<span class="n">model</span><span class="o">=</span><span class="n">PCC</span><span class="p">(</span><span class="n">LogisticRegression</span><span class="p">()),</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;C&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">10</span><span class="p">),</span> <span class="s1">&#39;class_weight&#39;</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;balanced&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">]},</span>
<span class="n">sample_size</span><span class="o">=</span><span class="n">qp</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;SAMPLE_SIZE&#39;</span><span class="p">],</span>
<span class="n">eval_budget</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
<span class="n">error</span><span class="o">=</span><span class="s1">&#39;mae&#39;</span><span class="p">,</span>
<span class="n">refit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="c1"># retrain on the whole labelled set</span>
<span class="n">val_split</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span>
<span class="n">verbose</span><span class="o">=</span><span class="kc">True</span> <span class="c1"># show information as the process goes on</span>
<span class="p">)</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="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;model selection ended: best hyper-parameters=</span><span class="si">{</span><span class="n">model</span><span class="o">.</span><span class="n">best_params_</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">best_model_</span>
<span class="c1"># evaluation in terms of MAE</span>
<span class="n">results</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">evaluation</span><span class="o">.</span><span class="n">artificial_sampling_eval</span><span class="p">(</span>
<span class="n">model</span><span class="p">,</span>
<span class="n">dataset</span><span class="o">.</span><span class="n">test</span><span class="p">,</span>
<span class="n">sample_size</span><span class="o">=</span><span class="n">qp</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s1">&#39;SAMPLE_SIZE&#39;</span><span class="p">],</span>
<span class="n">n_prevpoints</span><span class="o">=</span><span class="mi">101</span><span class="p">,</span>
<span class="n">n_repetitions</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="n">error_metric</span><span class="o">=</span><span class="s1">&#39;mae&#39;</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;MAE=</span><span class="si">{</span><span class="n">results</span><span class="si">:</span><span class="s1">.5f</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>In this example, the system outputs:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[GridSearchQ]: starting optimization with n_jobs=1
[GridSearchQ]: checking hyperparams={&#39;C&#39;: 0.0001, &#39;class_weight&#39;: &#39;balanced&#39;} got mae score 0.24987
[GridSearchQ]: checking hyperparams={&#39;C&#39;: 0.0001, &#39;class_weight&#39;: None} got mae score 0.48135
[GridSearchQ]: checking hyperparams={&#39;C&#39;: 0.001, &#39;class_weight&#39;: &#39;balanced&#39;} got mae score 0.24866
[...]
[GridSearchQ]: checking hyperparams={&#39;C&#39;: 100000.0, &#39;class_weight&#39;: None} got mae score 0.43676
[GridSearchQ]: optimization finished: best params {&#39;C&#39;: 0.1, &#39;class_weight&#39;: &#39;balanced&#39;} (score=0.19982)
[GridSearchQ]: refitting on the whole development set
model selection ended: best hyper-parameters={&#39;C&#39;: 0.1, &#39;class_weight&#39;: &#39;balanced&#39;}
1010 evaluations will be performed for each combination of hyper-parameters
[artificial sampling protocol] generating predictions: 100%|██████████| 1010/1010 [00:00&lt;00:00, 5005.54it/s]
MAE=0.20342
</pre></div>
</div>
<p>The parameter <em>val_split</em> can alternatively be used to indicate
a validation set (i.e., an instance of <em>LabelledCollection</em>) instead
of a proportion. This could be useful if one wants to have control
on the specific data split to be used across different model selection
experiments.</p>
</div>
<div class="section" id="targeting-a-classification-oriented-loss">
<h2>Targeting a Classification-oriented loss<a class="headerlink" href="#targeting-a-classification-oriented-loss" title="Permalink to this headline"></a></h2>
<p>Optimizing a model for quantification could rather be
computationally costly.
In aggregative methods, one could alternatively try to optimize
the classifier’s hyper-parameters for classification.
Although this is theoretically suboptimal, many articles in
quantification literature have opted for this strategy.</p>
<p>In QuaPy, this is achieved by simply instantiating the
classifier learner as a GridSearchCV from scikit-learn.
The following code illustrates how to do that:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">learner</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span>
<span class="n">LogisticRegression</span><span class="p">(),</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;C&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="s1">&#39;class_weight&#39;</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;balanced&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">]},</span>
<span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">PCC</span><span class="p">(</span><span class="n">learner</span><span class="p">)</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="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;model selection ended: best hyper-parameters=</span><span class="si">{</span><span class="n">model</span><span class="o">.</span><span class="n">learner</span><span class="o">.</span><span class="n">best_params_</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>In this example, the system outputs:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>model selection ended: best hyper-parameters={&#39;C&#39;: 10000.0, &#39;class_weight&#39;: None}
1010 evaluations will be performed for each combination of hyper-parameters
[artificial sampling protocol] generating predictions: 100%|██████████| 1010/1010 [00:00&lt;00:00, 5379.55it/s]
MAE=0.41734
</pre></div>
</div>
<p>Note that the MAE is worse than the one we obtained when optimizing
for quantification and, indeed, the hyper-parameters found optimal
largely differ between the two selection modalities. The
hyper-parameters C=10000 and class_weight=None have been found
to work well for the specific training prevalence of the HP dataset,
but these hyper-parameters turned out to be suboptimal when the
class prevalences of the test set differs (as is indeed tested
in scenarios of quantification).</p>
<p>This is, however, not always the case, and one could, in practice,
find examples
in which optimizing for classification ends up resulting in a better
quantifier than when optimizing for quantification.
Nonetheless, this is theoretically unlikely to happen.</p>
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<li><a class="reference internal" href="#">Model Selection</a><ul>
<li><a class="reference internal" href="#targeting-a-quantification-oriented-loss">Targeting a Quantification-oriented loss</a></li>
<li><a class="reference internal" href="#targeting-a-classification-oriented-loss">Targeting a Classification-oriented loss</a></li>
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