.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/example01.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_example01.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_example01.py:

Plot Template Estimator.

===========================
Plotting Template Estimator
===========================

A simple example of using a BDE estimator.

.. GENERATED FROM PYTHON SOURCE LINES 9-17

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt
    from optax import adam

    from bde.ml.loss import GaussianNLLLoss
    from bde.ml.models import BDEEstimator, FullyConnectedModule


.. GENERATED FROM PYTHON SOURCE LINES 18-19

The following data will be used in this example

.. GENERATED FROM PYTHON SOURCE LINES 19-41

.. code-block:: Python


    n_train = 256
    x = np.random.rand(n_train * 2).astype(np.float32).reshape(-1, 1)
    x_train = np.sort(x[:n_train], axis=0)
    x_test = np.sort(x[n_train:], axis=0)
    x = np.sort(x, axis=0)


    def find_y(x, noise_level=None):
        r"""Calculate target value."""
        y = (5 * x + 1) ** 2
        y += 2
        y = y[..., 0]
        if noise_level is None:
            return y
        return y + np.random.normal(loc=0.0, scale=noise_level, size=x.shape[0])


    y_train = find_y(x_train, noise_level=2.0)
    y_test = find_y(x_test, noise_level=2.0)
    y = find_y(x)


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We'll set up the following BDE estimator to solve this regression task

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.. code-block:: Python


    est = BDEEstimator(
        model_class=FullyConnectedModule,
        model_kwargs={
            "n_output_params": 2,
            "layer_sizes": [12, 12],
            "do_final_activation": False,
        },  # No hidden layers by default
        n_chains=12,  # 1 by default
        n_samples=30,  # 1 by default
        chain_len=200,  # 1 by default
        warmup=60,  # 1 by default
        optimizer_class=adam,
        optimizer_kwargs={
            "learning_rate": 1e-3,
        },
        loss=GaussianNLLLoss(),
        batch_size=128,  # 1 by default
        epochs=60,  # 1 by default
        metrics=None,
        validation_size=None,
        seed=42,
    )

    est = est.fit(x_train, y_train)
    y_pred = est.predict(x_test)


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And examine the results

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.. code-block:: Python


    fig = plt.figure()
    plt.scatter(x_test, y_pred, c="crimson", label="Prediction")
    plt.scatter(x_test, y_test, c="green", label="True", alpha=0.2)
    plt.plot(x, y, "k", alpha=0.4, label="Trend")
    plt.title("Demonstrating value prediction")
    plt.legend()
    plt.xlabel("x")
    plt.ylabel("y")
    plt.show()


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Alternatively, the model could be used to predict the values with a
confidence interval

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.. code-block:: Python


    y_pred, low, up = [
        np.ravel(v) for v in est.predict_with_credibility_eti(x_test, 0.95)
    ]

    fig = plt.figure()
    plt.fill_between(
        np.ravel(x_test),
        y1=low,
        y2=up,
        alpha=.5,
        linewidth=0,
        facecolor="crimson",
    )
    plt.plot(x_test, y_pred, c="crimson", label="Prediction")
    plt.scatter(x_test, y_test, c="green", label="True", alpha=0.2)
    plt.plot(x, y, "k", alpha=0.4, label="Trend")
    plt.title("Demonstrating confidence interval prediction (95%)")
    plt.legend()
    plt.xlabel("x")
    plt.ylabel("y")
    plt.show()


.. _sphx_glr_download_auto_examples_example01.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: example01.ipynb <example01.ipynb>`

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

      :download:`Download Python source code: example01.py <example01.py>`

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

      :download:`Download zipped: example01.zip <example01.zip>`


.. only:: html

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

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