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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/queries/plot_tractable_inference.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_queries_plot_tractable_inference.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_queries_plot_tractable_inference.py:


============================
Tractable Marginal Inference
============================

This shows how to perform marginal inference on Sum-Product Networks.

This picks up from the :ref:`marginalizing_an_spn` tutorial.

.. GENERATED FROM PYTHON SOURCE LINES 10-32

.. code-block:: default


    from spn.structure.leaves.parametric.Parametric import Categorical
    from spn.structure.Base import Sum, Product
    from spn.structure.Base import assign_ids, rebuild_scopes_bottom_up
    from spn.algorithms.Marginalization import marginalize

    from spn.io.Graphics import draw_spn
    import matplotlib.pyplot as plt

    p0 = Product(children=[Categorical(p=[0.3, 0.7], scope=1), Categorical(p=[0.4, 0.6], scope=2)])
    p1 = Product(children=[Categorical(p=[0.5, 0.5], scope=1), Categorical(p=[0.6, 0.4], scope=2)])
    s1 = Sum(weights=[0.3, 0.7], children=[p0, p1])
    p2 = Product(children=[Categorical(p=[0.2, 0.8], scope=0), s1])
    p3 = Product(children=[Categorical(p=[0.2, 0.8], scope=0), Categorical(p=[0.3, 0.7], scope=1)])
    p4 = Product(children=[p3, Categorical(p=[0.4, 0.6], scope=2)])
    spn = Sum(weights=[0.4, 0.6], children=[p2, p4])

    assign_ids(spn)
    rebuild_scopes_bottom_up(spn)

    spn_marg = marginalize(spn, [1, 2])








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Here is an example on how to evaluate the SPNs from the
:ref:`marginalizing_an_spn` tutorial.
Since we have 3 variables, we want to create a 2D numpy array of 3 columns
and 1 row.

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.. code-block:: default


    import numpy as np
    test_data = np.array([1.0, 0.0, 1.0]).reshape(-1, 3)








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We can then compute the log-likelihood:

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.. code-block:: default


    from spn.algorithms.Inference import log_likelihood

    ll = log_likelihood(spn, test_data)
    print(ll, np.exp(ll))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[-1.90730501]] [[0.14848]]




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We can also compute the log-likelihood of the marginal SPN.
Notice we use the same ``test_data`` as input: the SPN still expects an array
with data at columns 1 and 2, but ignores column 0.

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.. code-block:: default


    llm = log_likelihood(spn_marg, test_data)
    print(llm, np.exp(llm))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[-1.68416146]] [[0.1856]]




.. GENERATED FROM PYTHON SOURCE LINES 58-61

Another alternative would be to perform **marginal inference** on the original
SPN. This can be done by setting ``np.nan`` for the feature we want to
marginalize on the fly. It does not change the structure.

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.. code-block:: default


    test_data2 = np.array([np.nan, 0.0, 1.0]).reshape(-1, 3)
    llom = log_likelihood(spn, test_data2)
    print(llom, np.exp(llom))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[-1.68416146]] [[0.1856]]




.. GENERATED FROM PYTHON SOURCE LINES 67-69

Observe that the *marginal inference solution* and the *marginal SPN solution*
are the same.

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.. code-block:: default


    print(np.array_equal(llm, llom))




.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    True





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.008 seconds)


.. _sphx_glr_download_auto_examples_queries_plot_tractable_inference.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_tractable_inference.py <plot_tractable_inference.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_tractable_inference.ipynb <plot_tractable_inference.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

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