.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/07_plot_a2de_xor_slice.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_07_plot_a2de_xor_slice.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_07_plot_a2de_xor_slice.py:


=====================================================
Analytic View: 2D Slice of the 3D XOR Problem
=====================================================

While 3D visualizations show the global structure, taking a **2D slice**
(fixing one feature) allows for a precise analysis of the decision boundary.

Here we fix $z = 1.0$.
In the 3D XOR problem $(x \oplus y \oplus z)$, if $z$ is positive (True),
the logic simplifies to a standard 2D XOR between $x$ and $y$:
$(x \oplus y \oplus 1) 
ightarrow 
eg(x \oplus y)$ (XNOR behavior).

**What to look for:**

1.  **A0DE (NB):** Blurry background, no structure. Accuracy ~0.5 (Random).
2.  **A1DE (AODE):** Might show vertical or horizontal stripes, but fails
    to capture the checkerboard. Accuracy ~0.5 (Random).
3.  **A2DE (n=2):** Shows a distinct "Checkerboard" pattern with
    sharp boundaries. Accuracy ~0.965 (Solved).

.. GENERATED FROM PYTHON SOURCE LINES 22-113



.. image-sg:: /auto_examples/images/sphx_glr_07_plot_a2de_xor_slice_001.png
   :alt: Decision Boundary Analysis at Slice Z=1.0, A0DE (Naive Bayes) Global Accuracy: 0.542, A1DE (AODE) Global Accuracy: 0.527, A2DE (n=2) Global Accuracy: 0.965
   :srcset: /auto_examples/images/sphx_glr_07_plot_a2de_xor_slice_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Training models...






|

.. 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.metrics import accuracy_score

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

    # --- 1. Generate 3D XOR Dataset ---
    np.random.seed(42)
    n_samples = 2000
    X = np.random.randn(n_samples, 3)
    # Logic: Product of signs > 0 -> Class 1
    y = (np.sign(X[:, 0]) * np.sign(X[:, 1]) * np.sign(X[:, 2]) > 0).astype(int)

    # --- 2. Fit Models ---
    print("Training models...")
    models = [MixedNB(), AnDE(n_dependence=1, n_bins=4), AnDE(n_dependence=2, n_bins=4)]
    names = ["A0DE (Naive Bayes)", "A1DE (AODE)", "A2DE (n=2)"]

    for model in models:
        model.fit(X, y)

    # --- 3. Visualization Setup ---
    fig, axes = plt.subplots(1, 3, figsize=(18, 6), sharey=True)

    # Grid for Z=1 slice
    h = 0.05
    limit = 3
    xx, yy = np.meshgrid(np.arange(-limit, limit, h), np.arange(-limit, limit, h))
    grid_flat = np.c_[xx.ravel(), yy.ravel()]
    # Construct query points (x, y, 1.0)
    X_test_slice = np.hstack([grid_flat, np.ones((len(grid_flat), 1))])

    for ax, model, name in zip(axes, models, names):
        # Global Accuracy
        acc = accuracy_score(y, model.predict(X))

        # Probabilities on the slice
        probs = model.predict_proba(X_test_slice)[:, 1]
        Z_probs = probs.reshape(xx.shape)

        # A. Plot Probability Background (Diverging Colormap)
        # RdBu_r: Red (Class 0) <--> White (0.5) <--> Blue (Class 1)
        # This clearly shows confidence and the decision boundary
        cf = ax.pcolormesh(
            xx, yy, Z_probs, cmap="RdBu_r", vmin=0, vmax=1, shading="auto", alpha=0.9
        )

        # B. Add Contour Line for Decision Boundary
        ax.contour(
            xx, yy, Z_probs, levels=[0.5], colors="black", linewidths=2, linestyles="--"
        )

        # C. Overlay Data Points (Only those near the slice Z=1)
        # We take a slice z in [0.5, 1.5] to represent the volume being projected
        mask_slice = (X[:, 2] > 0.5) & (X[:, 2] < 1.5)

        # Plot Class 0 (Red dots) vs Class 1 (Blue dots) to match colormap
        ax.scatter(
            X[mask_slice & (y == 0), 0],
            X[mask_slice & (y == 0), 1],
            c="darkred",
            edgecolors="w",
            s=30,
            label="Class 0",
        )
        ax.scatter(
            X[mask_slice & (y == 1), 0],
            X[mask_slice & (y == 1), 1],
            c="navy",
            edgecolors="w",
            s=30,
            label="Class 1",
        )

        ax.set_title(f"{name}\nGlobal Accuracy: {acc:.3f}")
        ax.set_xlabel("Feature 0 (X)")

        # Quadrant reference lines
        ax.axvline(0, color="k", linestyle=":", alpha=0.3)
        ax.axhline(0, color="k", linestyle=":", alpha=0.3)

    axes[0].set_ylabel("Feature 1 (Y)")
    fig.suptitle("Decision Boundary Analysis at Slice Z=1.0", 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 0.395 seconds)


.. _sphx_glr_download_auto_examples_07_plot_a2de_xor_slice.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 07_plot_a2de_xor_slice.ipynb <07_plot_a2de_xor_slice.ipynb>`

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

      :download:`Download Python source code: 07_plot_a2de_xor_slice.py <07_plot_a2de_xor_slice.py>`

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

      :download:`Download zipped: 07_plot_a2de_xor_slice.zip <07_plot_a2de_xor_slice.zip>`


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_