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<section id="sde-calibration-package">
<h1>sde_calibration Package<a class="headerlink" href="#sde-calibration-package" title="Permalink to this headline"></a></h1>
<section id="id1">
<h2><code class="xref py py-mod docutils literal notranslate"><span class="pre">sde_calibration</span></code> Package<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h2>
<span class="target" id="module-sde_calibration.__init__"></span><p>SDE calibration module. It provides an interface for several different methods
that are used to infer the drift and diffusion coefficient of a diffusion process.
The stochastic process is modelled by an SDE of the following form</p>
<div class="math notranslate nohighlight">
\[\mathrm{d}X_t = b(X_t) \mathrm{d}t + \sigma(X_t) \mathrm{d}W_t \ ,\]</div>
<p>where <span class="math notranslate nohighlight">\(X \in \mathbb{R}\)</span>, <span class="math notranslate nohighlight">\(W \in \mathbb{R}\)</span> is a standard Wiener
process, <span class="math notranslate nohighlight">\(b \colon \mathbb{R} \to \mathbb{R}\)</span> is the drift coefficient,
and <span class="math notranslate nohighlight">\(\sigma \colon \mathbb{R} \to \mathbb{R}\)</span> is the diffusion coefficient.
The task of calibrating the SDE involves estimating the drift and diffusion
coefficient from an observed trajectory of the process <span class="math notranslate nohighlight">\(X_t\)</span>.
Note that the drift coefficient of the SDE is the same of the corresponding
diffusion process. In contrast, the diffusion coefficient of the SDE <span class="math notranslate nohighlight">\(\sigma\)</span>
and the corresponding diffusion process <span class="math notranslate nohighlight">\(\Sigma\)</span> are related as follows:</p>
<div class="math notranslate nohighlight">
\[\Sigma(x) = \sigma^2(x) \ .\]</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p>For more information on SDEs and diffusion processes, c.f.</p>
<ul class="simple">
<li><p><a class="reference external" href="https://link.springer.com/book/10.1007/978-0-387-75839-8">Simulation and Inference for Stochastic Differential Equations</a></p></li>
<li><p><a class="reference external" href="https://link.springer.com/book/10.1007/978-1-4939-1323-7">Stochastic Processes and Applications – Diffusion Processes, the Fokker-Planck
and Langevin Equations</a></p></li>
</ul>
</div>
</section>
<section id="module-sde_calibration.estimators">
<span id="estimators-module"></span><h2><code class="xref py py-mod docutils literal notranslate"><span class="pre">estimators</span></code> Module<a class="headerlink" href="#module-sde_calibration.estimators" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="sde_calibration.estimators.Estimator">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sde_calibration.estimators.</span></span><span class="sig-name descname"><span class="pre">Estimator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logger</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">preprocessor_arguments</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.Estimator" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">abc.ABC</span></code></p>
<p>Abstract base class for any kind of estimator that is used. It defines the
basic functionalities like data handling, preprocessing, and logging.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>data</strong> (<em>pd.DataFrame</em>) – The time series data that should be used for the estimation.
The DataFrame needs to have the fields ‘t’ and ‘X’.</p></li>
<li><p><strong>logger</strong> (<em>logging.Logger</em><em>, </em><em>optional</em>) – <p>A logger that should be used for logging and/or displaying
intermediate resutls.</p>
<blockquote>
<div><p><a href="#id4"><span class="problematic" id="id5">|default|</span></a> <code class="code docutils literal notranslate"><span class="pre">None</span></code></p>
</div></blockquote>
</p></li>
<li><p><strong>**preprocessor_arguments</strong> – <p>Keyword arguments that are further passed
to the <a class="reference internal" href="sde_calibration.common.html#sde_calibration.common.utils.Preprocessor" title="sde_calibration.common.utils.Preprocessor"><code class="xref py py-class docutils literal notranslate"><span class="pre">preprocessor</span> <span class="pre">class</span></code></a>.</p>
</p></li>
</ul>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>None</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>TypeError</strong> – If the data provided is not of type pandas.DataFarme.</p></li>
<li><p><strong>KeyError</strong> – If the data provided has keys different from <em>t</em> and <em>X</em>.</p></li>
<li><p><strong>TypeError</strong> – If the keyword arguments provided are not valid for the
preprocessor class.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="sde_calibration.estimators.Estimator.fit">
<em class="property"><span class="pre">abstract</span> </em><span class="sig-name descname"><span class="pre">fit</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.Estimator.fit" title="Permalink to this definition"></a></dt>
<dd><p>Method that is implement by child classes is order to perform the process
of fitting the data. Every estimator is supposed to have this method.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sde_calibration.estimators.Estimator.get_num_parameters">
<em class="property"><span class="pre">abstract</span> </em><span class="sig-name descname"><span class="pre">get_num_parameters</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.Estimator.get_num_parameters" title="Permalink to this definition"></a></dt>
<dd><p>Returns the number of parameters in the model that is used by a certain
estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Number of parameters.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>int</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="sde_calibration.estimators.RegressionEstimator">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sde_calibration.estimators.</span></span><span class="sig-name descname"><span class="pre">RegressionEstimator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logger</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">preprocessor_arguments</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.RegressionEstimator" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#sde_calibration.estimators.Estimator" title="sde_calibration.estimators.Estimator"><code class="xref py py-class docutils literal notranslate"><span class="pre">sde_calibration.estimators.Estimator</span></code></a></p>
<p>Derived from the Estimator class. This class directly extracts the data
and sets up the preprocessor in the form that is required to either estimate
the drift or diffusion term.
For further information on the parameters see the the documentation
of the <a class="reference internal" href="#sde_calibration.estimators.Estimator" title="sde_calibration.estimators.Estimator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Estimator</span></code></a>.</p>
<dl class="py method">
<dt class="sig sig-object py" id="sde_calibration.estimators.RegressionEstimator.compile">
<span class="sig-name descname"><span class="pre">compile</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'drift'</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.RegressionEstimator.compile" title="Permalink to this definition"></a></dt>
<dd><p>Method used to compile the model. For every regression estimator. It is
crucial to specify whether the drift or diffusion coefficient should be
approximated before the estimator can be fit or called.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>mode</strong> (<em>str</em><em>, </em><em>optional</em>) – <p>A string giving the mode of estimation. Possible options
are:</p>
<ul>
<li><p>drift</p></li>
<li><p>diffusion</p>
<blockquote>
<div><p><a href="#id6"><span class="problematic" id="id7">|default|</span></a> <code class="code docutils literal notranslate"><span class="pre">'drift'</span></code></p>
</div></blockquote>
</li>
</ul>
</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>None</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError</strong> – If the provided string for the mode is invalid.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sde_calibration.estimators.RegressionEstimator.get_mode">
<span class="sig-name descname"><span class="pre">get_mode</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#sde_calibration.estimators.RegressionEstimator.get_mode" title="Permalink to this definition"></a></dt>
<dd><p>Interface that provides the mode that the regression estimator is currently
operating in.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p><p>Returns the current mode. Possible values are:</p>
<ul class="simple">
<li><p>drift</p></li>
<li><p>diffusion</p></li>
</ul>
</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>str</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
</section>
<section id="module-sde_calibration.exceptions">
<span id="exceptions-module"></span><h2><code class="xref py py-mod docutils literal notranslate"><span class="pre">exceptions</span></code> Module<a class="headerlink" href="#module-sde_calibration.exceptions" title="Permalink to this headline"></a></h2>
<dl class="py exception">
<dt class="sig sig-object py" id="sde_calibration.exceptions.NotCompiledError">
<em class="property"><span class="pre">exception</span> </em><span class="sig-prename descclassname"><span class="pre">sde_calibration.exceptions.</span></span><span class="sig-name descname"><span class="pre">NotCompiledError</span></span><a class="headerlink" href="#sde_calibration.exceptions.NotCompiledError" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">Exception</span></code></p>
<p>Exception that is raised if an estimator is not yet compiled. For many methods
this is crucial to compile in order to enable the training and prediction.</p>
</dd></dl>
</section>
<section id="subpackages">
<h2>Subpackages<a class="headerlink" href="#subpackages" title="Permalink to this headline"></a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="sde_calibration.classic_estimators.html">classic_estimators Package</a><ul>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.classic_estimators.html#id1"><code class="xref py py-mod docutils literal notranslate"><span class="pre">classic_estimators</span></code> Package</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.classic_estimators.html#module-sde_calibration.classic_estimators.linear_regressor"><code class="xref py py-mod docutils literal notranslate"><span class="pre">linear_regressor</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.classic_estimators.html#module-sde_calibration.classic_estimators.local_polynomial_estimator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">local_polynomial_estimator</span></code> Module</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="sde_calibration.common.html">common Package</a><ul>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.common.html#id1"><code class="xref py py-mod docutils literal notranslate"><span class="pre">common</span></code> Package</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.common.html#module-sde_calibration.common.kde"><code class="xref py py-mod docutils literal notranslate"><span class="pre">kde</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.common.html#module-sde_calibration.common.test_problems"><code class="xref py py-mod docutils literal notranslate"><span class="pre">test_problems</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.common.html#module-sde_calibration.common.utils"><code class="xref py py-mod docutils literal notranslate"><span class="pre">utils</span></code> Module</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="sde_calibration.dnn_estimators.html">dnn_estimators Package</a><ul>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#id1"><code class="xref py py-mod docutils literal notranslate"><span class="pre">dnn_estimators</span></code> Package</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.adversarial_regressor"><code class="xref py py-mod docutils literal notranslate"><span class="pre">adversarial_regressor</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.gan_losses"><code class="xref py py-mod docutils literal notranslate"><span class="pre">gan_losses</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.invariant_density_estimator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">invariant_density_estimator</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.metrics"><code class="xref py py-mod docutils literal notranslate"><span class="pre">metrics</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.mixture_density_estimator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">mixture_density_estimator</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.neural_network"><code class="xref py py-mod docutils literal notranslate"><span class="pre">neural_network</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.neural_regressor"><code class="xref py py-mod docutils literal notranslate"><span class="pre">neural_regressor</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.non_parametric_regressor"><code class="xref py py-mod docutils literal notranslate"><span class="pre">non_parametric_regressor</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.parametric_regressor"><code class="xref py py-mod docutils literal notranslate"><span class="pre">parametric_regressor</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.sde_informed_gan"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sde_informed_gan</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#module-sde_calibration.dnn_estimators.sde_informed_generator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sde_informed_generator</span></code> Module</a></li>
<li class="toctree-l2"><a class="reference internal" href="sde_calibration.dnn_estimators.html#subpackages">Subpackages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sde_calibration.dnn_estimators.layers.html">layers Package</a><ul>
<li class="toctree-l4"><a class="reference internal" href="sde_calibration.dnn_estimators.layers.html#id1"><code class="xref py py-mod docutils literal notranslate"><span class="pre">layers</span></code> Package</a></li>
<li class="toctree-l4"><a class="reference internal" href="sde_calibration.dnn_estimators.layers.html#module-sde_calibration.dnn_estimators.layers.dense_mixture"><code class="xref py py-mod docutils literal notranslate"><span class="pre">dense_mixture</span></code> Module</a></li>
<li class="toctree-l4"><a class="reference internal" href="sde_calibration.dnn_estimators.layers.html#module-sde_calibration.dnn_estimators.layers.mc_dropout"><code class="xref py py-mod docutils literal notranslate"><span class="pre">mc_dropout</span></code> Module</a></li>
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