update kernel tutorial

2026-05-05 09:42:39 +02:00 · 2015-07-19 14:30:27 -07:00 · 2015-07-19 14:30:27 -07:00 · 1d7712ecc8
commit 1d7712ecc8
parent 3a150198e8
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+++ b/doc/_build/html/GPy.mappings.html
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+            
+  <div class="section" id="gpy-mappings-package">
+<h1>GPy.mappings package<a class="headerlink" href="#gpy-mappings-package" title="Permalink to this headline">¶</a></h1>
+<div class="section" id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h2>
+</div>
+<div class="section" id="module-GPy.mappings.additive">
+<span id="gpy-mappings-additive-module"></span><h2>GPy.mappings.additive module<a class="headerlink" href="#module-GPy.mappings.additive" title="Permalink to this headline">¶</a></h2>
+<dl class="class">
+<dt id="GPy.mappings.additive.Additive">
+<em class="property">class </em><code class="descclassname">GPy.mappings.additive.</code><code class="descname">Additive</code><span class="sig-paren">(</span><em>mapping1</em>, <em>mapping2</em>, <em>tensor=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/additive.html#Additive"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.additive.Additive" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="GPy.core.html#GPy.core.mapping.Mapping" title="GPy.core.mapping.Mapping"><code class="xref py py-class docutils literal"><span class="pre">GPy.core.mapping.Mapping</span></code></a></p>
+<p>Mapping based on adding two existing mappings together.</p>
+<div class="math">
+<p><img src="_images/math/2984fd9b4b48bc7212f5b97e2ffabbc4060cb544.png" alt="f(\mathbf{x}*) = f_1(\mathbf{x}*) + f_2(\mathbf(x)*)"/></p>
+</div><table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
+<li><strong>mapping1</strong> (<em>GPy.mappings.Mapping</em>) &#8211; first mapping to add together.</li>
+<li><strong>mapping2</strong> (<em>GPy.mappings.Mapping</em>) &#8211; second mapping to add together.</li>
+<li><strong>tensor</strong> (<em>bool</em>) &#8211; whether or not to use the tensor product of input spaces</li>
+</ul>
+</td>
+</tr>
+</tbody>
+</table>
+<dl class="method">
+<dt id="GPy.mappings.additive.Additive.df_dX">
+<code class="descname">df_dX</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/additive.html#Additive.df_dX"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.additive.Additive.df_dX" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.additive.Additive.df_dtheta">
+<code class="descname">df_dtheta</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/additive.html#Additive.df_dtheta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.additive.Additive.df_dtheta" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.additive.Additive.f">
+<code class="descname">f</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/additive.html#Additive.f"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.additive.Additive.f" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.additive.Additive.randomize">
+<code class="descname">randomize</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/additive.html#Additive.randomize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.additive.Additive.randomize" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</div>
+<div class="section" id="module-GPy.mappings.kernel">
+<span id="gpy-mappings-kernel-module"></span><h2>GPy.mappings.kernel module<a class="headerlink" href="#module-GPy.mappings.kernel" title="Permalink to this headline">¶</a></h2>
+<dl class="class">
+<dt id="GPy.mappings.kernel.Kernel">
+<em class="property">class </em><code class="descclassname">GPy.mappings.kernel.</code><code class="descname">Kernel</code><span class="sig-paren">(</span><em>X</em>, <em>output_dim=1</em>, <em>kernel=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/kernel.html#Kernel"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.kernel.Kernel" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="GPy.core.html#GPy.core.mapping.Mapping" title="GPy.core.mapping.Mapping"><code class="xref py py-class docutils literal"><span class="pre">GPy.core.mapping.Mapping</span></code></a></p>
+<p>Mapping based on a kernel/covariance function.</p>
+<div class="math">
+<p><img src="_images/math/67a3ca8b772a75e4d54fe3e40f9e567f00b66f2f.png" alt="f(\mathbf{x}*) = \mathbf{A}\mathbf{k}(\mathbf{X}, \mathbf{x}^*) + \mathbf{b}"/></p>
+</div><table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
+<li><strong>X</strong> (<em>ndarray</em>) &#8211; input observations containing <img class="math" src="_images/math/7a9b78bdb36f2fbd5ca087212e58fc74dde40e86.png" alt="\mathbf{X}"/></li>
+<li><strong>output_dim</strong> (<em>int</em>) &#8211; dimension of output.</li>
+<li><strong>kernel</strong> (<em>GPy.kern.kern</em>) &#8211; a GPy kernel, defaults to GPy.kern.RBF</li>
+</ul>
+</td>
+</tr>
+</tbody>
+</table>
+<dl class="method">
+<dt id="GPy.mappings.kernel.Kernel.df_dX">
+<code class="descname">df_dX</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/kernel.html#Kernel.df_dX"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.kernel.Kernel.df_dX" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.kernel.Kernel.df_dtheta">
+<code class="descname">df_dtheta</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/kernel.html#Kernel.df_dtheta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.kernel.Kernel.df_dtheta" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.kernel.Kernel.f">
+<code class="descname">f</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/kernel.html#Kernel.f"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.kernel.Kernel.f" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.kernel.Kernel.randomize">
+<code class="descname">randomize</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/kernel.html#Kernel.randomize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.kernel.Kernel.randomize" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</div>
+<div class="section" id="module-GPy.mappings.linear">
+<span id="gpy-mappings-linear-module"></span><h2>GPy.mappings.linear module<a class="headerlink" href="#module-GPy.mappings.linear" title="Permalink to this headline">¶</a></h2>
+<dl class="class">
+<dt id="GPy.mappings.linear.Linear">
+<em class="property">class </em><code class="descclassname">GPy.mappings.linear.</code><code class="descname">Linear</code><span class="sig-paren">(</span><em>input_dim=1</em>, <em>output_dim=1</em>, <em>name='linear'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/linear.html#Linear"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.linear.Linear" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="GPy.core.html#GPy.core.mapping.Bijective_mapping" title="GPy.core.mapping.Bijective_mapping"><code class="xref py py-class docutils literal"><span class="pre">GPy.core.mapping.Bijective_mapping</span></code></a></p>
+<p>Mapping based on a linear model.</p>
+<div class="math">
+<p><img src="_images/math/2520c5bbd4ca1928f464fd3873b10a9b0bde8c18.png" alt="f(\mathbf{x}*) = \mathbf{W}\mathbf{x}^* + \mathbf{b}"/></p>
+</div><table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
+<li><strong>X</strong> (<em>ndarray</em>) &#8211; input observations</li>
+<li><strong>output_dim</strong> (<em>int</em>) &#8211; dimension of output.</li>
+</ul>
+</td>
+</tr>
+</tbody>
+</table>
+<dl class="method">
+<dt id="GPy.mappings.linear.Linear.dL_dX">
+<code class="descname">dL_dX</code><span class="sig-paren">(</span><em>partial</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/linear.html#Linear.dL_dX"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.linear.Linear.dL_dX" title="Permalink to this definition">¶</a></dt>
+<dd><p>The gradient of L with respect to the inputs to the mapping, where L is a function that is dependent on the output of the mapping, f.</p>
+</dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.linear.Linear.df_dtheta">
+<code class="descname">df_dtheta</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/linear.html#Linear.df_dtheta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.linear.Linear.df_dtheta" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.linear.Linear.f">
+<code class="descname">f</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/linear.html#Linear.f"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.linear.Linear.f" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.linear.Linear.g">
+<code class="descname">g</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/linear.html#Linear.g"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.linear.Linear.g" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</div>
+<div class="section" id="module-GPy.mappings.mlp">
+<span id="gpy-mappings-mlp-module"></span><h2>GPy.mappings.mlp module<a class="headerlink" href="#module-GPy.mappings.mlp" title="Permalink to this headline">¶</a></h2>
+<dl class="class">
+<dt id="GPy.mappings.mlp.MLP">
+<em class="property">class </em><code class="descclassname">GPy.mappings.mlp.</code><code class="descname">MLP</code><span class="sig-paren">(</span><em>input_dim=1</em>, <em>output_dim=1</em>, <em>hidden_dim=3</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/mlp.html#MLP"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.mlp.MLP" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="GPy.core.html#GPy.core.mapping.Mapping" title="GPy.core.mapping.Mapping"><code class="xref py py-class docutils literal"><span class="pre">GPy.core.mapping.Mapping</span></code></a></p>
+<p>Mapping based on a multi-layer perceptron neural network model.</p>
+<div class="math">
+<p><img src="_images/math/5fb1ead7a3ae880faf3e493e050ee55a0e435038.png" alt="f(\mathbf{x}*) = \mathbf{W}^0\boldsymbol{\phi}(\mathbf{W}^1\mathbf{x}+\mathbf{b}^1)^* + \mathbf{b}^0"/></p>
+</div><p>where</p>
+<div class="math">
+<p><img src="_images/math/4b19c5c53c58678e9292c8e646b72103694e99f2.png" alt="\phi(\cdot) = \text{tanh}(\cdot)"/></p>
+</div><table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
+<li><strong>X</strong> (<em>ndarray</em>) &#8211; input observations</li>
+<li><strong>output_dim</strong> (<em>int</em>) &#8211; dimension of output.</li>
+<li><strong>hidden_dim</strong> (<em>int or list of ints.</em>) &#8211; dimension of hidden layer. If it is an int, there is one hidden layer of the given dimension. If it is a list of ints there are as manny hidden layers as the length of the list, each with the given number of hidden nodes in it.</li>
+</ul>
+</td>
+</tr>
+</tbody>
+</table>
+<dl class="method">
+<dt id="GPy.mappings.mlp.MLP.df_dX">
+<code class="descname">df_dX</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/mlp.html#MLP.df_dX"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.mlp.MLP.df_dX" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.mlp.MLP.df_dtheta">
+<code class="descname">df_dtheta</code><span class="sig-paren">(</span><em>dL_df</em>, <em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/mlp.html#MLP.df_dtheta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.mlp.MLP.df_dtheta" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.mlp.MLP.f">
+<code class="descname">f</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/mlp.html#MLP.f"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.mlp.MLP.f" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="method">
+<dt id="GPy.mappings.mlp.MLP.randomize">
+<code class="descname">randomize</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/GPy/mappings/mlp.html#MLP.randomize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#GPy.mappings.mlp.MLP.randomize" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</div>
+<div class="section" id="module-GPy.mappings">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-GPy.mappings" title="Permalink to this headline">¶</a></h2>
+</div>
+</div>
+
+
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <h3><a href="index.html">Table Of Contents</a></h3>
+  <ul>
+<li><a class="reference internal" href="#">GPy.mappings package</a><ul>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-GPy.mappings.additive">GPy.mappings.additive module</a></li>
+<li><a class="reference internal" href="#module-GPy.mappings.kernel">GPy.mappings.kernel module</a></li>
+<li><a class="reference internal" href="#module-GPy.mappings.linear">GPy.mappings.linear module</a></li>
+<li><a class="reference internal" href="#module-GPy.mappings.mlp">GPy.mappings.mlp module</a></li>
+<li><a class="reference internal" href="#module-GPy.mappings">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  <h4>Previous topic</h4>
+  <p class="topless"><a href="GPy.likelihoods.html"
+                        title="previous chapter">GPy.likelihoods package</a></p>
+  <h4>Next topic</h4>
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+                        title="next chapter">GPy.models package</a></p>
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