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<meta name="description" content="This example shows how to use cross_val_predict together with PredictionErrorDisplay to visualize prediction errors. We will load the diabetes dataset and create an instance of a linear regression ..." />

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<li><a class="reference internal" href="#">Plotting Cross-Validated Predictions</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-model-selection-plot-cv-predict-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="plotting-cross-validated-predictions">
<span id="sphx-glr-auto-examples-model-selection-plot-cv-predict-py"></span><h1>Plotting Cross-Validated Predictions<a class="headerlink" href="#plotting-cross-validated-predictions" title="Link to this heading">¶</a></h1>
<p>This example shows how to use
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> together with
<a class="reference internal" href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay" title="sklearn.metrics.PredictionErrorDisplay"><code class="xref py py-class docutils literal notranslate"><span class="pre">PredictionErrorDisplay</span></code></a> to visualize prediction
errors.</p>
<p>We will load the diabetes dataset and create an instance of a linear
regression model.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.load_diabetes.html#sklearn.datasets.load_diabetes" title="sklearn.datasets.load_diabetes" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_diabetes</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearRegression</span></a>

<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_diabetes.html#sklearn.datasets.load_diabetes" title="sklearn.datasets.load_diabetes" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_diabetes</span></a><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">lr</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="sklearn.linear_model.LinearRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearRegression</span></a><span class="p">()</span>
</pre></div>
</div>
<p><a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> returns an array of the
same size of <code class="docutils literal notranslate"><span class="pre">y</span></code> where each entry is a prediction obtained by cross
validation.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">cross_val_predict</span></a>

<span class="n">y_pred</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">cross_val_predict</span></a><span class="p">(</span><span class="n">lr</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
</pre></div>
</div>
<p>Since <code class="docutils literal notranslate"><span class="pre">cv=10</span></code>, it means that we trained 10 models and each model was
used to predict on one of the 10 folds. We can now use the
<a class="reference internal" href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay" title="sklearn.metrics.PredictionErrorDisplay"><code class="xref py py-class docutils literal notranslate"><span class="pre">PredictionErrorDisplay</span></code></a> to visualize the
prediction errors.</p>
<p>On the left axis, we plot the observed values <span class="math notranslate nohighlight">\(y\)</span> vs. the predicted
values <span class="math notranslate nohighlight">\(\hat{y}\)</span> given by the models. On the right axis, we plot the
residuals (i.e. the difference between the observed values and the predicted
values) vs. the predicted values.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">PredictionErrorDisplay</span>

<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
    <span class="n">y</span><span class="p">,</span>
    <span class="n">y_pred</span><span class="o">=</span><span class="n">y_pred</span><span class="p">,</span>
    <span class="n">kind</span><span class="o">=</span><span class="s2">&quot;actual_vs_predicted&quot;</span><span class="p">,</span>
    <span class="n">subsample</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
    <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
    <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Actual vs. Predicted values&quot;</span><span class="p">)</span>
<a href="../../modules/generated/sklearn.metrics.PredictionErrorDisplay.html#sklearn.metrics.PredictionErrorDisplay.from_predictions" title="sklearn.metrics.PredictionErrorDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PredictionErrorDisplay sphx-glr-backref-type-py-method"><span class="n">PredictionErrorDisplay</span><span class="o">.</span><span class="n">from_predictions</span></a><span class="p">(</span>
    <span class="n">y</span><span class="p">,</span>
    <span class="n">y_pred</span><span class="o">=</span><span class="n">y_pred</span><span class="p">,</span>
    <span class="n">kind</span><span class="o">=</span><span class="s2">&quot;residual_vs_predicted&quot;</span><span class="p">,</span>
    <span class="n">subsample</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
    <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
    <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Residuals vs. Predicted Values&quot;</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">&quot;Plotting cross-validated predictions&quot;</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_cv_predict_001.png" srcset="../../_images/sphx_glr_plot_cv_predict_001.png" alt="Plotting cross-validated predictions, Actual vs. Predicted values, Residuals vs. Predicted Values" class = "sphx-glr-single-img"/><p>It is important to note that we used
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a> for visualization
purpose only in this example.</p>
<p>It would be problematic to
quantitatively assess the model performance by computing a single
performance metric from the concatenated predictions returned by
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_predict.html#sklearn.model_selection.cross_val_predict" title="sklearn.model_selection.cross_val_predict"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_predict</span></code></a>
when the different CV folds vary by size and distributions.</p>
<p>It is recommended to compute per-fold performance metrics using:
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_score.html#sklearn.model_selection.cross_val_score" title="sklearn.model_selection.cross_val_score"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_val_score</span></code></a> or
<a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_validate.html#sklearn.model_selection.cross_validate" title="sklearn.model_selection.cross_validate"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_validate</span></code></a> instead.</p>
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