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

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

.. _sphx_glr_auto_examples_plot_gaussian_model_selection.py:


Using AIC and BIC for Model Selection
-------------------------------------

This example will demonstrate how the Akaike Information Criterion (AIC) and
Bayesian Information Criterion (BIC) values may be used to select the number
of components for a model.

1) We train models with varying numbers of ``n_components``.
2) For each ``n_components`` we train multiple models with different random
   initializations; the best model is kept.
3) Now we plot the values of the AIC and BIC for each n_components.
   A clear minimum is detected for the model with ``n_components=4``.
   We also see that using the log-likelihood of the training data is not
   suitable for model selection, as it is always increasing.

.. GENERATED FROM PYTHON SOURCE LINES 17-24

.. code-block:: Python

    import numpy as np
    import matplotlib.pyplot as plt
    from sklearn.utils import check_random_state

    from hmmlearn.hmm import GaussianHMM

    rs = check_random_state(546)







.. GENERATED FROM PYTHON SOURCE LINES 25-26

Our model to generate sample data from:

.. GENERATED FROM PYTHON SOURCE LINES 26-39

.. code-block:: Python

    model = GaussianHMM(4, init_params="")
    model.n_features = 4
    model.startprob_ = np.array([1/4., 1/4., 1/4., 1/4.])
    model.transmat_ = np.array([[0.3, 0.4, 0.2, 0.1],
                                [0.1, 0.2, 0.3, 0.4],
                                [0.5, 0.2, 0.1, 0.2],
                                [0.25, 0.25, 0.25, 0.25]])
    model.means_ = np.array([[-2.5], [0], [2.5], [5.]])
    model.covars_ = np.sqrt([[0.25], [0.25], [0.25], [0.25]])

    X, _ = model.sample(1000, random_state=rs)
    lengths = [X.shape[0]]








.. GENERATED FROM PYTHON SOURCE LINES 40-44

Search over various n_components and examine the
AIC, BIC, and the LL of the data. Train a few different
models with different random initializations, saving the one
with the best LL.

.. GENERATED FROM PYTHON SOURCE LINES 44-62

.. code-block:: Python

    aic = []
    bic = []
    lls = []
    ns = [2, 3, 4, 5, 6]
    for n in ns:
        best_ll = None
        best_model = None
        for i in range(10):
            h = GaussianHMM(n, n_iter=200, tol=1e-4, random_state=rs)
            h.fit(X)
            score = h.score(X)
            if not best_ll or best_ll < best_ll:
                best_ll = score
                best_model = h
        aic.append(best_model.aic(X))
        bic.append(best_model.bic(X))
        lls.append(best_model.score(X))








.. GENERATED FROM PYTHON SOURCE LINES 63-65

Visualize our results: a clear minimum is seen for 4 components
which matches our expectation.

.. GENERATED FROM PYTHON SOURCE LINES 65-79

.. code-block:: Python

    fig, ax = plt.subplots()
    ln1 = ax.plot(ns, aic, label="AIC", color="blue", marker="o")
    ln2 = ax.plot(ns, bic, label="BIC", color="green", marker="o")
    ax2 = ax.twinx()
    ln3 = ax2.plot(ns, lls, label="LL", color="orange", marker="o")

    ax.legend(handles=ax.lines + ax2.lines)
    ax.set_title("Using AIC/BIC for Model Selection")
    ax.set_ylabel("Criterion Value (lower is better)")
    ax2.set_ylabel("LL (higher is better)")
    ax.set_xlabel("Number of HMM Components")
    fig.tight_layout()

    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_gaussian_model_selection_001.png
   :alt: Using AIC/BIC for Model Selection
   :srcset: /auto_examples/images/sphx_glr_plot_gaussian_model_selection_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 12.218 seconds)


.. _sphx_glr_download_auto_examples_plot_gaussian_model_selection.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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