nbconvert1/tests/tutorial.rst.ref

.. _introduction:

An Introduction to machine learning with scikit-learn
=======================================================================

.. topic:: Section contents

    In this section, we introduce the `machine learning 
    <http://en.wikipedia.org/wiki/Machine_learning>`_
    vocabulary that we use through-out `scikit-learn` and give a 
    simple learning example.


Machine learning: the problem setting
---------------------------------------

In general, a learning problem considers a set of n 
`samples <http://en.wikipedia.org/wiki/Sample_(statistics)>`_ of
data and try to predict properties of unknown data. If each sample is
more than a single number, and for instance a multi-dimensional entry
(aka `multivariate <http://en.wikipedia.org/wiki/Multivariate_random_variable>`_ 
data), is it said to have several attributes,
or **features**.

We can separate learning problems in a few large categories:

 * `supervised learning <http://en.wikipedia.org/wiki/Supervised_learning>`_, 
   in which the data comes with additional attributes that we want to predict 
   (:ref:`Click here <supervised-learning>`
   to go to the Scikit-Learn supervised learning page).This problem 
   can be either:

    * `classification 
      <http://en.wikipedia.org/wiki/Classification_in_machine_learning>`_:
      samples belong to two or more classes and we
      want to learn from already labeled data how to predict the class
      of unlabeled data. An example of classification problem would
      be the digit recognition example, in which the aim is to assign
      each input vector to one of a finite number of discrete
      categories.

    * `regression <http://en.wikipedia.org/wiki/Regression_analysis>`_:
      if the desired output consists of one or more
      continuous variables, then the task is called *regression*. An
      example of a regression problem would be the prediction of the
      length of a salmon as a function of its age and weight.

 * `unsupervised learning <http://en.wikipedia.org/wiki/Unsupervised_learning>`_,
   in which the training data consists of a set of input vectors x 
   without any corresponding target values. The goal in such problems 
   may be to discover groups of similar examples within the data, where 
   it is called `clustering <http://en.wikipedia.org/wiki/Cluster_analysis>`_, 
   or to determine the distribution of data within the input space, known as 
   `density estimation <http://en.wikipedia.org/wiki/Density_estimation>`_, or 
   to project the data from a high-dimensional space down to two or thee 
   dimensions for the purpose of *visualization* 
   (:ref:`Click here <unsupervised-learning>` 
   to go to the Scikit-Learn unsupervised learning page).

.. topic:: Training set and testing set

    Machine learning is about learning some properties of a data set
    and applying them to new data. This is why a common practice in
    machine learning to evaluate an algorithm is to split the data
    at hand in two sets, one that we call a **training set** on which
    we learn data properties, and one that we call a **testing set**,
    on which we test these properties.

.. _loading_example_dataset:

Loading an example dataset
--------------------------

`scikit-learn` comes with a few standard datasets, for instance the
`iris <http://en.wikipedia.org/wiki/Iris_flower_data_set>`_ and `digits
<http://archive.ics.uci.edu/ml/datasets/Pen-Based+Recognition+of+Handwritten+Digits>`_
datasets for classification and the `boston house prices dataset
<http://archive.ics.uci.edu/ml/datasets/Housing>`_ for regression.::

  >>> from sklearn import datasets
  >>> iris = datasets.load_iris()
  >>> digits = datasets.load_digits()

A dataset is a dictionary-like object that holds all the data and some
metadata about the data. This data is stored in the ``.data`` member,
which is a ``n_samples, n_features`` array. In the case of supervised
problem, explanatory variables are stored in the ``.target`` member. More
details on the different datasets can be found in the :ref:`dedicated
section <datasets>`.

For instance, in the case of the digits dataset, ``digits.data`` gives
access to the features that can be used to classify the digits samples::

  >>> print digits.data  # doctest: +NORMALIZE_WHITESPACE
  [[  0.   0.   5. ...,   0.   0.   0.]
   [  0.   0.   0. ...,  10.   0.   0.]
   [  0.   0.   0. ...,  16.   9.   0.]
   ...,
   [  0.   0.   1. ...,   6.   0.   0.]
   [  0.   0.   2. ...,  12.   0.   0.]
   [  0.   0.  10. ...,  12.   1.   0.]]

and `digits.target` gives the ground truth for the digit dataset, that
is the number corresponding to each digit image that we are trying to
learn::

  >>> digits.target
  array([0, 1, 2, ..., 8, 9, 8])

.. topic:: Shape of the data arrays

    The data is always a 2D array, `n_samples, n_features`, although
    the original data may have had a different shape. In the case of the
    digits, each original sample is an image of shape `8, 8` and can be
    accessed using::

      >>> digits.images[0]
      array([[  0.,   0.,   5.,  13.,   9.,   1.,   0.,   0.],
             [  0.,   0.,  13.,  15.,  10.,  15.,   5.,   0.],
             [  0.,   3.,  15.,   2.,   0.,  11.,   8.,   0.],
             [  0.,   4.,  12.,   0.,   0.,   8.,   8.,   0.],
             [  0.,   5.,   8.,   0.,   0.,   9.,   8.,   0.],
             [  0.,   4.,  11.,   0.,   1.,  12.,   7.,   0.],
             [  0.,   2.,  14.,   5.,  10.,  12.,   0.,   0.],
             [  0.,   0.,   6.,  13.,  10.,   0.,   0.,   0.]])

    The :ref:`simple example on this dataset
    <example_plot_digits_classification.py>` illustrates how starting
    from the original problem one can shape the data for consumption in
    the `scikit-learn`.


Learning and Predicting
------------------------

In the case of the digits dataset, the task is to predict the value of a
hand-written digit from an image. We are given samples of each of the 10
possible classes on which we *fit* an 
`estimator <http://en.wikipedia.org/wiki/Estimator>`_ to be able to *predict*
the labels corresponding to new data.

In `scikit-learn`, an **estimator** is just a plain Python class that
implements the methods `fit(X, Y)` and `predict(T)`.

An example of estimator is the class ``sklearn.svm.SVC`` that
implements `Support Vector Classification
<http://en.wikipedia.org/wiki/Support_vector_machine>`_. The
constructor of an estimator takes as arguments the parameters of the
model, but for the time being, we will consider the estimator as a black
box::

  >>> from sklearn import svm
  >>> clf = svm.SVC(gamma=0.001, C=100.)

.. topic:: Choosing the parameters of the model

  In this example we set the value of ``gamma`` manually. It is possible
  to automatically find good values for the parameters by using tools
  such as :ref:`grid search <grid_search>` and :ref:`cross validation
  <cross_validation>`.

We call our estimator instance `clf` as it is a classifier. It now must
be fitted to the model, that is, it must `learn` from the model. This is
done by passing our training set to the ``fit`` method. As a training
set, let us use all the images of our dataset apart from the last
one::

  >>> clf.fit(digits.data[:-1], digits.target[:-1])
  SVC(C=100.0, cache_size=200, class_weight=None, coef0=0.0, degree=3,
    gamma=0.001, kernel='rbf', probability=False, scale_C=True,
    shrinking=True, tol=0.001)

Now you can predict new values, in particular, we can ask to the
classifier what is the digit of our last image in the `digits` dataset,
which we have not used to train the classifier::

  >>> clf.predict(digits.data[-1])
  array([ 8.])

The corresponding image is the following:

.. image:: ../../auto_examples/tutorial/images/plot_digits_last_image_1.png
    :target: ../../auto_examples/tutorial/plot_digits_last_image.html
    :align: center
    :scale: 50

As you can see, it is a challenging task: the images are of poor
resolution. Do you agree with the classifier?

A complete example of this classification problem is available as an
example that you can run and study:
:ref:`example_plot_digits_classification.py`.


Model persistence
-----------------

It is possible to save a model in the scikit by using Python's built-in
persistence model, namely `pickle <http://docs.python.org/library/pickle.html>`_::

  >>> from sklearn import svm
  >>> from sklearn import datasets
  >>> clf = svm.SVC()
  >>> iris = datasets.load_iris()
  >>> X, y = iris.data, iris.target
  >>> clf.fit(X, y)
  SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.25,
    kernel='rbf', probability=False, scale_C=True, shrinking=True, tol=0.001)

  >>> import pickle
  >>> s = pickle.dumps(clf)
  >>> clf2 = pickle.loads(s)
  >>> clf2.predict(X[0])
  array([ 0.])
  >>> y[0]
  0

In the specific case of the scikit, it may be more interesting to use
joblib's replacement of pickle (``joblib.dump`` & ``joblib.load``),
which is more efficient on big data, but can only pickle to the disk
and not to a string::

  >>> from sklearn.externals import joblib
  >>> joblib.dump(clf, 'filename.pkl') # doctest: +SKIP