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<li class="toctree-l2"><a class="reference internal" href="tutorials/1_a_representation/1_a_representation.html">Tutorial 1.a: Representing and Evaluating Uncertainty for Regression</a></li>
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<section id="quick-start">
<h1>Quick Start<a class="headerlink" href="#quick-start" title="Permalink to this headline">¶</a></h1>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span><span class="o">,</span> <span class="nn">torchuq</span>
<span class="kn">from</span> <span class="nn">torchuq.evaluate</span> <span class="kn">import</span> <span class="n">distribution</span>
<span class="kn">from</span> <span class="nn">torchuq.transform.conformal</span> <span class="kn">import</span> <span class="n">ConformalCalibrator</span>
<span class="kn">from</span> <span class="nn">torchuq.dataset</span> <span class="kn">import</span> <span class="n">create_example_regression</span>
</pre></div>
</div>
<p>In this very simple example, we create a synthetic prediction (which is
a set of Gaussian distributions), plot them, and recalibrate them with
conformal calibration.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">predictions</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">create_example_regression</span><span class="p">()</span>
</pre></div>
</div>
<p>The example predictions are intentionally incorrect (i.e. the label is
not drawn from the predictions). We will recalibrate the distribution
with a powerful recalibration algorithm called conformal calibration. It
takes as input the predictions and the labels, and learns a
recalibration map that can be applied to new data (here for illustration
purposes we apply it to the original data).</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">calibrator</span> <span class="o">=</span> <span class="n">ConformalCalibrator</span><span class="p">(</span><span class="n">input_type</span><span class="o">=</span><span class="s1">'distribution'</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'linear'</span><span class="p">)</span>
<span class="n">calibrator</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">labels</span><span class="p">)</span>
<span class="n">adjusted_predictions</span> <span class="o">=</span> <span class="n">calibrator</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
</pre></div>
</div>
<p>We can plot these distribution predictions as a sequence of density
functions, and the labels as the cross-shaped markers. As shown by the
plot, the original predictions have systematically incorrect variance
and mean, which is fixed by the recalibration algorithm.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">distribution</span><span class="o">.</span><span class="n">plot_density_sequence</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">smooth_bw</span><span class="o">=</span><span class="mi">10</span><span class="p">);</span>
<span class="n">distribution</span><span class="o">.</span><span class="n">plot_density_sequence</span><span class="p">(</span><span class="n">adjusted_predictions</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">smooth_bw</span><span class="o">=</span><span class="mi">10</span><span class="p">);</span>
</pre></div>
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