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<!DOCTYPE html>
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<title>adapt.metrics.linear_discrepancy — adapt 0.1.0 documentation</title>
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<p class="caption" role="heading"><span class="caption-text">Tutorials</span></p>
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<p class="caption" role="heading"><span class="caption-text">API Documentation</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../contents.html#adapt-feature-based">Feature-based</a><ul>
<li class="toctree-l2"><a class="reference internal" href="adapt.feature_based.PRED.html">PRED</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.feature_based.CORAL.html">CORAL</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.KMM.html">KMM</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.ULSIF.html">ULSIF</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.RULSIF.html">RULSIF</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.IWC.html">IWC</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.BalancedWeighting.html">BalancedWeighting</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.TrAdaBoost.html">TrAdaBoost</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.TrAdaBoostR2.html">TrAdaBoostR2</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.TwoStageTrAdaBoostR2.html">TwoStageTrAdaBoostR2</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.instance_based.WANN.html">WANN</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="../contents.html#adapt-parameter-based">Parameter-based</a><ul>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.LinInt.html">LinInt</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.RegularTransferLR.html">RegularTransferLR</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.RegularTransferLC.html">RegularTransferLC</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.RegularTransferNN.html">RegularTransferNN</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.RegularTransferGP.html">RegularTransferGP</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.parameter_based.FineTuning.html">FineTuning</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../contents.html#adapt-metrics">Metrics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.make_uda_scorer.html">make_uda_scorer</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.cov_distance.html">cov_distance</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.neg_j_score.html">neg_j_score</a></li>
<li class="toctree-l2"><a class="reference internal" href="#">linear_discrepancy</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.normalized_linear_discrepancy.html">normalized_linear_discrepancy</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.frechet_distance.html">frechet_distance</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.normalized_frechet_distance.html">normalized_frechet_distance</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.metrics.domain_classifier.html">domain_classifier</a></li>
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</ul>
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<li class="toctree-l1"><a class="reference internal" href="../contents.html#adapt-utils">Utility Functions</a><ul>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.UpdateLambda.html">UpdateLambda</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.utils.get_default_task.html">get_default_task</a></li>
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<li class="toctree-l2"><a class="reference internal" href="adapt.utils.make_classification_da.html">make_classification_da</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.make_regression_da.html">make_regression_da</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.check_sample_weight.html">check_sample_weight</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.set_random_seed.html">set_random_seed</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.check_fitted_estimator.html">check_fitted_estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="adapt.utils.check_fitted_network.html">check_fitted_network</a></li>
</ul>
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</ul>
<p class="caption" role="heading"><span class="caption-text">Synthetic Examples</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../examples/Classification.html">Classification</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Classification.html#Experimental-Setup">Experimental Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Classification.html#Src-Only">Src Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Classification.html#DANN">DANN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Classification.html#Instance-Based">Instance Based</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Two_moons.html">Two Moons</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#Network">Network</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#Source-Only">Source Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#DANN">DANN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#ADDA">ADDA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#DeepCORAL">DeepCORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#CORAL">CORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#MCD">MCD</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#MDD">MDD</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#WDGRL">WDGRL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Two_moons.html#CDAN">CDAN</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="../examples/Rotation.html">Rotation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Rotation.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Rotation.html#Source-Only">Source Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Rotation.html#CORAL">CORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Rotation.html#DANN">DANN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Rotation.html#ADDA">ADDA</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Regression.html">Toy Regression</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#Experimental-Setup">Experimental Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#TGT-Only">TGT Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#Src-Only">Src Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#All">All</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#CORAL">CORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#TrAdaBoostR2">TrAdaBoostR2</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Regression.html#RegularTransferNN">RegularTransferNN</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/sample_bias.html">Sample Bias 1D</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias.html#KMM">KMM</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias.html#KLIEP">KLIEP</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/sample_bias_2d.html">Sample Bias 2D</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias_2d.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias_2d.html#Estimator">Estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias_2d.html#Source-Only">Source Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias_2d.html#KMM">KMM</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/sample_bias_2d.html#KLIEP">KLIEP</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Multi_fidelity.html">Multi-Fidelity</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Multi_fidelity.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Multi_fidelity.html#Network">Network</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Multi_fidelity.html#Low-fidelity-only">Low fidelity only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Multi_fidelity.html#High-fidelity-only">High fidelity only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Multi_fidelity.html#RegularTransferNN">RegularTransferNN</a></li>
</ul>
</li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Real Examples</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../examples/Sample_bias_example.html">Sample Bias</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Sample_bias_example.html#Sample-Bias-on-the-diabetes-dataset">Diabetes Dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Sample_bias_example.html#Applying-Transfer-Learning-for-correcting-sample-bias">Sample bias correction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Sample_bias_example.html#Hidden-bias-and-features-importance-estimation">Features importance</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Flowers_example.html">Fine-Tuning</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Flowers_example.html#Training-a-model-from-scratch">Train from Scratch</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Flowers_example.html#Model-based-Transfer">Model-based Transfer</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Office_example.html">Deep Domain Adaptation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Office_example.html#Dataset-Preprocessing">Dataset Preprocessing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Office_example.html#Fit-without-adaptation">Fit without adaptation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Office_example.html#Fit-with-adaptation">Fit with adaptation</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/tradaboost_experiments.html">TrAdaBoost Experiments</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/tradaboost_experiments.html#Mushrooms">Mushrooms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/tradaboost_experiments.html#20-NewsGroup">20-NewsGroup</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../examples/Heart_Failure.html">Heart Failure</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#Setup">Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#Network">Network</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#Source-Only">Source Only</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#DANN">DANN</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#ADDA">ADDA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#DeepCORAL">DeepCORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#CORAL">CORAL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../examples/Heart_Failure.html#MCD">MCD</a></li>
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<section id="adapt-metrics-linear-discrepancy">
<h1><a class="reference internal" href="../contents.html#adapt-metrics"><span class="std std-ref">adapt.metrics</span></a>.linear_discrepancy<a class="headerlink" href="#adapt-metrics-linear-discrepancy" title="Permalink to this headline"></a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="adapt.metrics.linear_discrepancy">
<span class="sig-prename descclassname"><span class="pre">adapt.metrics.</span></span><span class="sig-name descname"><span class="pre">linear_discrepancy</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Xs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Xt</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">power_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_iter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">20</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/antoinedemathelin/adapt/tree/master/adapt/metrics.py"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#adapt.metrics.linear_discrepancy" title="Permalink to this definition"></a></dt>
<dd><p>Compute the linear discrepancy
between Xs and Xt.</p>
<div class="math notranslate nohighlight">
\[\Delta = \max_{u \in \mathbb{R}^p} u^T (X_S^T X_S - X_T^T X_T) u\]</div>
<p>Where:</p>
<ul class="simple">
<li><p><span class="math notranslate nohighlight">\(p\)</span> is the number of features of Xs and Xt.</p></li>
</ul>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>Xs</strong><span class="classifier">array</span></dt><dd><p>Source array</p>
</dd>
<dt><strong>Xt</strong><span class="classifier">array</span></dt><dd><p>Target array</p>
</dd>
<dt><strong>power_method</strong><span class="classifier">bool (default=False)</span></dt><dd><p>Weither to use the power method
approximation or not.</p>
</dd>
<dt><strong>n_iter</strong><span class="classifier">int (default=20)</span></dt><dd><p>Number of iteration for power method</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>score</strong><span class="classifier">float</span></dt><dd></dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="adapt.metrics.normalized_linear_discrepancy.html#adapt.metrics.normalized_linear_discrepancy" title="adapt.metrics.normalized_linear_discrepancy"><code class="xref py py-obj docutils literal notranslate"><span class="pre">normalized_linear_discrepancy</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="adapt.metrics.frechet_distance.html#adapt.metrics.frechet_distance" title="adapt.metrics.frechet_distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">frechet_distance</span></code></a></dt><dd></dd>
<dt><a class="reference internal" href="adapt.metrics.normalized_frechet_distance.html#adapt.metrics.normalized_frechet_distance" title="adapt.metrics.normalized_frechet_distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">normalized_frechet_distance</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r24197d27a4d6-1"><span class="brackets">1</span></dt>
<dd><p><a class="reference external" href="https://arxiv.org/pdf/0902.3430.pdf">[1]</a> Y. Mansour, M. Mohri, and A. Rostamizadeh. “Domain adaptation: Learning bounds and algorithms”. In COLT, 2009.</p>
</dd>
</dl>
</dd></dl>
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