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class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="bayesian-ridge-regression"> <span id="example-linear-model-plot-bayesian-ridge-py"></span><h1>Bayesian Ridge Regression<a class="headerlink" href="#bayesian-ridge-regression" title="Permalink to this headline">ΒΆ</a></h1> <p>Computes a Bayesian Ridge Regression on a synthetic dataset</p> <img alt="auto_examples/linear_model/images/plot_bayesian_ridge.png" class="align-center" src="auto_examples/linear_model/images/plot_bayesian_ridge.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_bayesian_ridge.py"><tt class="xref download docutils literal"><span class="pre">plot_bayesian_ridge.py</span></tt></a></p> <div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">__doc__</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">pylab</span> <span class="kn">as</span> <span class="nn">pl</span> <span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span> <span class="kn">from</span> <span class="nn">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">BayesianRidge</span> <span class="c">################################################################################</span> <span class="c"># Generating simulated data with Gaussian weigthts</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">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">100</span> <span class="n">X</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">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span><span class="p">)</span> <span class="c"># Create gaussian data</span> <span class="c"># Create weigts with a precision lambda_ of 4.</span> <span class="n">lambda_</span> <span class="o">=</span> <span class="mf">4.</span> <span class="n">w</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">n_features</span><span class="p">)</span> <span class="c"># Only keep 10 weights of interest</span> <span class="n">relevant_features</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">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n_features</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">relevant_features</span><span class="p">:</span> <span class="n">w</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">loc</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mf">1.</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">lambda_</span><span class="p">))</span> <span class="c"># Create noite with a precision alpha of 50.</span> <span class="n">alpha_</span> <span class="o">=</span> <span class="mf">50.</span> <span class="n">noise</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">loc</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mf">1.</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">alpha_</span><span class="p">),</span> <span class="n">size</span> <span class="o">=</span> <span class="n">n_samples</span><span class="p">)</span> <span class="c"># Create the target</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">w</span><span class="p">)</span> <span class="o">+</span> <span class="n">noise</span> <span class="c">################################################################################</span> <span class="c"># Fit the Bayesian Ridge Regression</span> <span class="n">clf</span> <span class="o">=</span> <span class="n">BayesianRidge</span><span class="p">(</span><span class="n">compute_score</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span> <span class="n">clf</span><span class="o">.</span><span class="n">fit</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="c">################################################################################</span> <span class="c"># Plot true weights, estimated weights and histogram of the weights</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span> <span class="n">axe</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">axes</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.6</span><span class="p">,</span><span class="mf">0.8</span><span class="p">,</span><span class="mf">0.325</span><span class="p">])</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s">"Bayesian Ridge - Weights of the model"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="s">'b-'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"Estimate"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="s">'g-'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"Ground truth"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">"Features"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">"Values of the weights"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s">"upper right"</span><span class="p">)</span> <span class="n">axe</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">axes</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.45</span><span class="p">,</span><span class="mf">0.325</span><span class="p">])</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s">"Histogram of the weights"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">n_features</span><span class="p">,</span> <span class="n">log</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">[</span><span class="n">relevant_features</span><span class="p">],</span><span class="mi">5</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="nb">len</span><span class="p">(</span><span class="n">relevant_features</span><span class="p">)),</span><span class="s">'ro'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"Relevant features"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">"Features"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">"Values of the weights"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s">"lower left"</span><span class="p">)</span> <span class="n">axe</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">axes</span><span class="p">([</span><span class="mf">0.65</span><span class="p">,</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.3</span><span class="p">,</span><span class="mf">0.325</span><span class="p">])</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s">"Objective function"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">scores_</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">"Score"</span><span class="p">)</span> <span class="n">axe</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">"Iterations"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </pre></div> </div> </div> </div> </div> </div> <div class="clearer"></div> </div> </div> <div class="footer"> <p style="text-align: center">This documentation is relative to scikits.learn version 0.6.0<p> © 2010, scikits.learn developers (BSD Lincense). 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