.. _sphx_glr_auto_examples_approximators:

Approximators
=============

Examples demonstrating each approximator in ``shapiq`` on the same
synthetic cooperative game. All examples use a lightweight callable
game with 8 players so they execute in under a second.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Stratified SVARM for Shapley value approximation using SVARM :footciteKolpaczki.2024a.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_svarm_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_svarm`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SVARM</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Regression-based Shapley value approximation using KernelSHAP :footciteLundberg.2017.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_kernelshap_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_kernelshap`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">KernelSHAP</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Owen sampling for Shapley value approximation using OwenSamplingSV.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_owen_sampling_sv_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_owen_sampling_sv`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">OwenSamplingSV</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Unbiased Monte Carlo variant of KernelSHAP using UnbiasedKernelSHAP.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_unbiased_kernelshap_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_unbiased_kernelshap`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">UnbiasedKernelSHAP</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Stratified sampling for Shapley value approximation using StratifiedSamplingSV.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_stratified_sampling_sv_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_stratified_sampling_sv`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">StratifiedSamplingSV</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Permutation-based Shapley value approximation using PermutationSamplingSV.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_permutation_sampling_sv_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_permutation_sampling_sv`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">PermutationSamplingSV</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="k-additive SHAP approximation using kADDSHAP :footcitePelegrina.2023.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_kadd_shap_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_kadd_shap`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">kADDSHAP</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Proxy-based SPEX approximation using ProxySPEX :footciteButler.2025.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_proxyspex_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_proxyspex`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ProxySPEX</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Regression-based k-SII approximation using KernelSHAPIQ :footciteFumagalli.2024.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_kernelshapiq_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_kernelshapiq`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">KernelSHAPIQ</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Faithful Banzhaf Interaction Index via regression using RegressionFBII.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_regression_fbii_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_regression_fbii`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RegressionFBII</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Faithful Shapley Interaction Index via regression using RegressionFSII :footciteFumagalli.2023.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_regression_fsii_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_regression_fsii`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RegressionFSII</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Permutation-based SII/k-SII approximation using PermutationSamplingSII.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_permutation_sampling_sii_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_permutation_sampling_sii`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">PermutationSamplingSII</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="General Monte Carlo approximator for any-order interactions using SHAPIQ :footciteMuschalik.2024a.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_shapiq_approximator_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_shapiq_approximator`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SHAPIQ Approximator</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Permutation-based STII approximation using PermutationSamplingSTII.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_permutation_sampling_stii_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_permutation_sampling_stii`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">PermutationSamplingSTII</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Stratified Monte Carlo with coalition-size and intersection stratification using SVARMIQ :footciteKolpaczki.2024a.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_svarmiq_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_svarmiq`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SVARMIQ</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Faster variant of KernelSHAPIQ that does not converge to true SII, using InconsistentKernelSHAPIQ.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_inconsistent_kernelshapiq_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_inconsistent_kernelshapiq`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">InconsistentKernelSHAPIQ</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Proxy model-based interaction approximation using ProxySHAP.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_proxyshap_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_proxyshap`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ProxySHAP</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Sparse Explainer via Fourier transforms using SPEX :footciteKang.2025.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_spex_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_spex`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SPEX</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Proxy model-based Shapley value approximation using RegressionMSR.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_regression_msr_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_regression_msr`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RegressionMSR</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Exact computation of Shapley values and interaction indices for small games using ExactComputer.">

.. only:: html

  .. image:: /auto_examples/approximators/images/thumb/sphx_glr_plot_exact_computer_thumb.png
    :alt:

  :doc:`/auto_examples/approximators/plot_exact_computer`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ExactComputer</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/approximators/plot_svarm
   /auto_examples/approximators/plot_kernelshap
   /auto_examples/approximators/plot_owen_sampling_sv
   /auto_examples/approximators/plot_unbiased_kernelshap
   /auto_examples/approximators/plot_stratified_sampling_sv
   /auto_examples/approximators/plot_permutation_sampling_sv
   /auto_examples/approximators/plot_kadd_shap
   /auto_examples/approximators/plot_proxyspex
   /auto_examples/approximators/plot_kernelshapiq
   /auto_examples/approximators/plot_regression_fbii
   /auto_examples/approximators/plot_regression_fsii
   /auto_examples/approximators/plot_permutation_sampling_sii
   /auto_examples/approximators/plot_shapiq_approximator
   /auto_examples/approximators/plot_permutation_sampling_stii
   /auto_examples/approximators/plot_svarmiq
   /auto_examples/approximators/plot_inconsistent_kernelshapiq
   /auto_examples/approximators/plot_proxyshap
   /auto_examples/approximators/plot_spex
   /auto_examples/approximators/plot_regression_msr
   /auto_examples/approximators/plot_exact_computer