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Homer Strong 1d7712ecc8 update kernel tutorial
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<div class="section" id="list-of-implemented-kernels">
<h1>List of implemented kernels<a class="headerlink" href="#list-of-implemented-kernels" title="Permalink to this headline"></a></h1>
<p>The following table shows the implemented kernels in GPy and gives the details of the implemented function for each kernel.</p>
<table border="1" class="docutils">
<colgroup>
<col width="16%" />
<col width="9%" />
<col width="4%" />
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</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">NAME</th>
<th class="head">Dimension</th>
<th class="head">ARD</th>
<th class="head">get/set</th>
<th class="head">K</th>
<th class="head">Kdiag</th>
<th class="head">dK_dtheta</th>
<th class="head">dKdiag_dtheta</th>
<th class="head">dK_dX</th>
<th class="head">dKdiag_dX</th>
<th class="head">psi0</th>
<th class="head">psi1</th>
<th class="head">psi2</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>bias</td>
<td>n</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
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<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
</tr>
<tr class="row-odd"><td>Brownian</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td>exponential</td>
<td>n</td>
<td>yes</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>finite_dimensional</td>
<td>n</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td>linear</td>
<td>n</td>
<td>yes</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
</tr>
<tr class="row-odd"><td>Matern32</td>
<td>n</td>
<td>yes</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td>Matern52</td>
<td>n</td>
<td>yes</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>periodic_exponential</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td>periodic_Matern32</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>periodic_Matern52</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td>rational quadratic</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>rbf</td>
<td>n</td>
<td>yes</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
</tr>
<tr class="row-even"><td>spline</td>
<td>1</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>white</td>
<td>n</td>
<td>&nbsp;</td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
<td><img alt="tick" src="_images/tick.png" /></td>
</tr>
</tbody>
</table>
<p>Depending on the use, all functions may not be required</p>
<blockquote>
<div><ul class="simple">
<li><code class="docutils literal"><span class="pre">get/set,</span> <span class="pre">K,</span> <span class="pre">Kdiag</span></code>: compulsory</li>
<li><code class="docutils literal"><span class="pre">dK_dtheta</span></code>: necessary to optimize the model</li>
<li><code class="docutils literal"><span class="pre">dKdiag_dtheta</span></code>: sparse models, BGPLVM, GPs with uncertain inputs</li>
<li><code class="docutils literal"><span class="pre">dK_dX</span></code>: sparse models, GPLVM, BGPLVM, GPs with uncertain inputs</li>
<li><code class="docutils literal"><span class="pre">dKdiag_dX</span></code>: sparse models, BGPLVM, GPs with uncertain inputs</li>
<li><code class="docutils literal"><span class="pre">psi0,</span> <span class="pre">psi1,</span> <span class="pre">psi2</span></code>: BGPLVM, GPs with uncertain inputs</li>
</ul>
</div></blockquote>
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