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<h1>Module <a href="type_Gpr_cov_se_fat.html">Gpr_cov_se_fat</a></h1>
<pre><span class="keyword">module</span> Gpr_cov_se_fat: <code class="code">sig</code> <a href="Gpr_cov_se_fat.html">..</a> <code class="code">end</code></pre><div class="info module top">
<h6 id="6_Featurerichfatsquaredexponentialcovariance">Feature-rich ("fat") squared exponential covariance</h6><br>
</div>
<hr width="100%">
<br>
The covariance is defined as:
<p>
<code class="code">k(x, y) = sf^2 * exp(-1/2 * |(Q_i*P*(x-y))|^2)</code>
<p>
where <code class="code">sf^2</code> is the amplitude, <code class="code">P</code> a general <code class="code">d*D</code> dimensionality reduction
matrix (<code class="code">d << D</code>), and <code class="code">Q_i</code> is a <code class="code">d*d</code> diagonal matrix containing all
multiscales for inducing input number <code class="code">i</code>.
<p>
Note that multiscales must not get smaller than <code class="code">0.5</code> in this framework,
because the overall length scale is considered to be equal to <code class="code">1</code>, which
imposes this mathematical constraint for positive-definiteness. There is no
need for a variable global length scale, because the dimensionality
reduction matrix already generalizes this feature anyway. Hence an
unconstrained multiscale parameter <code class="code">q</code> is stored as <code class="code">log(q - 0.5)</code>.
<p>
If <code class="code">x</code> and <code class="code">y</code> are the same inducing input, then and only then extra noise
(a different noise level for each inducing input) will be added for
heteroskedasticity.
<p>
Dimensionality reduction, heteroskedasticity, and multiscales are optional
features and can be easily turned off by setting the parameters to <code class="code">None</code>.<br>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Params.html">Params</a>: <code class="code">sig</code> <a href="Gpr_cov_se_fat.Params.html">..</a> <code class="code">end</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Eval.html">Eval</a>: <code class="type">Eval</code><code class="type">
with type Kernel.params = Params.t</code><code class="type">
with type Inducing.t = mat</code><code class="type">
with type Input.t = vec</code><code class="type">
with type Inputs.t = mat</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Proj_hyper.html">Proj_hyper</a>: <code class="code">sig</code> <a href="Gpr_cov_se_fat.Proj_hyper.html">..</a> <code class="code">end</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Dim_hyper.html">Dim_hyper</a>: <code class="code">sig</code> <a href="Gpr_cov_se_fat.Dim_hyper.html">..</a> <code class="code">end</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Inducing_hyper.html">Inducing_hyper</a>: <code class="code">sig</code> <a href="Gpr_cov_se_fat.Inducing_hyper.html">..</a> <code class="code">end</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Hyper_repr.html">Hyper_repr</a>: <code class="code">sig</code> <a href="Gpr_cov_se_fat.Hyper_repr.html">..</a> <code class="code">end</code></pre>
<pre><span class="keyword">module</span> <a href="Gpr_cov_se_fat.Deriv.html">Deriv</a>: <code class="type">Deriv</code><code class="type">
with module Eval = Eval</code><code class="type">
with type Hyper.t = Hyper_repr.t</code></pre></body></html>
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