.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/06_plot_aode_xor.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_06_plot_aode_xor.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_06_plot_aode_xor.py:


=====================================================
Solving the XOR Problem: AnDE vs Naive Bayes
=====================================================

This example demonstrates the limitations of the independence assumption
in Naive Bayes and how **Averaged n-Dependence Estimators (AnDE)**
overcome them.

We use a synthetic **XOR dataset** (continuous Gaussian features).
In an XOR problem:
-   Class 0 is in quadrants 1 (+, +) and 3 (-, -).
-   Class 1 is in quadrants 2 (-, +) and 4 (+, -).

**The Challenge:**
Looking at any single feature individually, the distributions of Class 0
and Class 1 overlap perfectly (both are centered at 0). Therefore,
**MixedNB (Naive Bayes)** cannot distinguish the classes and learns a
useless decision boundary (accuracy ~50%).

**The Solution:**
**AnDE (n=1)** relaxes the independence assumption. By conditioning on one
feature (the "super-parent"), it learns that the relationship between the
other feature and the class changes depending on the parent's value.
As shown in the plot, AnDE successfully captures the XOR structure.

.. GENERATED FROM PYTHON SOURCE LINES 27-130



.. image-sg:: /auto_examples/images/sphx_glr_06_plot_aode_xor_001.png
   :alt: Impact of Higher-Order Dependencies on Classification Boundaries (XOR Problem), Naive Bayes (MixedNB) Accuracy: 0.56, AnDE (n=1, AODE) Accuracy: 0.99
   :srcset: /auto_examples/images/sphx_glr_06_plot_aode_xor_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    # Author: The scikit-bayes Developers
    # SPDX-License-Identifier: BSD-3-Clause

    import matplotlib.pyplot as plt
    import numpy as np
    from sklearn.inspection import DecisionBoundaryDisplay
    from sklearn.metrics import accuracy_score

    from skbn.ande import AnDE
    from skbn.mixed_nb import MixedNB

    # --- 1. Generate XOR Dataset (Continuous) ---
    np.random.seed(42)
    n_samples = 400

    # Generate random points
    X = np.random.randn(n_samples, 2)

    # Logic: Class 0 if signs match, Class 1 if signs differ
    y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0).astype(int)

    # --- 2. Fit Models ---

    # Model A: MixedNB (Naive Bayes, n=0)
    # Expected to fail because marginal distributions are identical for both classes.
    mnb = MixedNB()
    mnb.fit(X, y)

    # Model B: AnDE (AODE, n=1)
    # Discretizes the super-parent into 4 bins (enough to capture pos/neg split)
    # and models the child as a Gaussian conditioned on that bin.
    ande = AnDE(n_dependence=1, n_bins=4)
    ande.fit(X, y)

    models = [mnb, ande]
    titles = ["Naive Bayes (MixedNB)", "AnDE (n=1, AODE)"]

    # --- 3. Plotting ---
    fig, axes = plt.subplots(1, 2, figsize=(14, 6), sharey=True)

    for ax, model, title in zip(axes, models, titles):
        # Calculate accuracy
        acc = accuracy_score(y, model.predict(X))

        # Plot Decision Boundary - VIRIDIS
        DecisionBoundaryDisplay.from_estimator(
            model,
            X,
            response_method="predict_proba",
            plot_method="pcolormesh",
            shading="auto",
            alpha=0.8,
            ax=ax,
            vmin=0,
            vmax=1,
            cmap="viridis",
        )

        # Overlay real data points with consistent style
        # Class 0 -> Indigo Circle
        ax.scatter(
            X[y == 0, 0],
            X[y == 0, 1],
            c="indigo",
            marker="o",
            s=40,
            alpha=0.8,
            edgecolors="w",
            linewidth=0.8,
            label="Class 0",
        )

        # Class 1 -> Gold Triangle
        ax.scatter(
            X[y == 1, 0],
            X[y == 1, 1],
            c="gold",
            marker="^",
            s=40,
            alpha=0.9,
            edgecolors="k",
            linewidth=0.5,
            label="Class 1",
        )

        ax.set_title(f"{title}\nAccuracy: {acc:.2f}", fontsize=12)
        ax.set_xlabel("Feature 1")

        # Add quadrant lines for reference
        ax.axvline(0, color="white", linestyle="--", alpha=0.3)
        ax.axhline(0, color="white", linestyle="--", alpha=0.3)

    axes[0].set_ylabel("Feature 2")
    axes[0].legend(loc="lower left")

    fig.suptitle(
        "Impact of Higher-Order Dependencies on Classification Boundaries (XOR Problem)",
        fontsize=16,
    )
    plt.tight_layout()
    plt.subplots_adjust(top=0.85)
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.243 seconds)


.. _sphx_glr_download_auto_examples_06_plot_aode_xor.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 06_plot_aode_xor.ipynb <06_plot_aode_xor.ipynb>`

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

      :download:`Download Python source code: 06_plot_aode_xor.py <06_plot_aode_xor.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 06_plot_aode_xor.zip <06_plot_aode_xor.zip>`


.. only:: html

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

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