notebooks/05.02-Introducing-Scikit-Learn.ipynb

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    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
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   "source": [
    "<!--NAVIGATION-->\n",
    "< [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Introducing Scikit-Learn"
   ]
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    "There are several Python libraries which provide solid implementations of a range of machine learning algorithms.\n",
    "One of the best known is [Scikit-Learn](http://scikit-learn.org), a package that provides efficient versions of a large number of common algorithms.\n",
    "Scikit-Learn is characterized by a clean, uniform, and streamlined API, as well as by very useful and complete online documentation.\n",
    "A benefit of this uniformity is that once you understand the basic use and syntax of Scikit-Learn for one type of model, switching to a new model or algorithm is very straightforward.\n",
    "\n",
    "This section provides an overview of the Scikit-Learn API; a solid understanding of these API elements will form the foundation for understanding the deeper practical discussion of machine learning algorithms and approaches in the following chapters.\n",
    "\n",
    "We will start by covering *data representation* in Scikit-Learn, followed by covering the *Estimator* API, and finally go through a more interesting example of using these tools for exploring a set of images of hand-written digits."
   ]
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   "source": [
    "## Data Representation in Scikit-Learn"
   ]
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   "source": [
    "Machine learning is about creating models from data: for that reason, we'll start by discussing how data can be represented in order to be understood by the computer.\n",
    "The best way to think about data within Scikit-Learn is in terms of tables of data."
   ]
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    "### Data as table\n",
    "\n",
    "A basic table is a two-dimensional grid of data, in which the rows represent individual elements of the dataset, and the columns represent quantities related to each of these elements.\n",
    "For example, consider the [Iris dataset](https://en.wikipedia.org/wiki/Iris_flower_data_set), famously analyzed by Ronald Fisher in 1936.\n",
    "We can download this dataset in the form of a Pandas ``DataFrame`` using the [seaborn](http://seaborn.pydata.org/) library:"
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
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     "output_type": "execute_result"
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   ],
   "source": [
    "import seaborn as sns\n",
    "iris = sns.load_dataset('iris')\n",
    "iris.head()"
   ]
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    "Here each row of the data refers to a single observed flower, and the number of rows is the total number of flowers in the dataset.\n",
    "In general, we will refer to the rows of the matrix as *samples*, and the number of rows as ``n_samples``.\n",
    "\n",
    "Likewise, each column of the data refers to a particular quantitative piece of information that describes each sample.\n",
    "In general, we will refer to the columns of the matrix as *features*, and the number of columns as ``n_features``."
   ]
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    "#### Features matrix\n",
    "\n",
    "This table layout makes clear that the information can be thought of as a two-dimensional numerical array or matrix, which we will call the *features matrix*.\n",
    "By convention, this features matrix is often stored in a variable named ``X``.\n",
    "The features matrix is assumed to be two-dimensional, with shape ``[n_samples, n_features]``, and is most often contained in a NumPy array or a Pandas ``DataFrame``, though some Scikit-Learn models also accept SciPy sparse matrices.\n",
    "\n",
    "The samples (i.e., rows) always refer to the individual objects described by the dataset.\n",
    "For example, the sample might be a flower, a person, a document, an image, a sound file, a video, an astronomical object, or anything else you can describe with a set of quantitative measurements.\n",
    "\n",
    "The features (i.e., columns) always refer to the distinct observations that describe each sample in a quantitative manner.\n",
    "Features are generally real-valued, but may be Boolean or discrete-valued in some cases."
   ]
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    "#### Target array\n",
    "\n",
    "In addition to the feature matrix ``X``, we also generally work with a *label* or *target* array, which by convention we will usually call ``y``.\n",
    "The target array is usually one dimensional, with length ``n_samples``, and is generally contained in a NumPy array or Pandas ``Series``.\n",
    "The target array may have continuous numerical values, or discrete classes/labels.\n",
    "While some Scikit-Learn estimators do handle multiple target values in the form of a two-dimensional, ``[n_samples, n_targets]`` target array, we will primarily be working with the common case of a one-dimensional target array.\n",
    "\n",
    "Often one point of confusion is how the target array differs from the other features columns. The distinguishing feature of the target array is that it is usually the quantity we want to *predict from the data*: in statistical terms, it is the dependent variable.\n",
    "For example, in the preceding data we may wish to construct a model that can predict the species of flower based on the other measurements; in this case, the ``species`` column would be considered the target array.\n",
    "\n",
    "With this target array in mind, we can use Seaborn (see [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb)) to conveniently visualize the data:"
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1ICc4Ty+XT+7pp2qjJejc1eV0Y3d24+r28OQbR4lSyFidMnxDL0NOWnQqn5gO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3/+E4B169axaNGiVucvLS1l4cKFrFq1iiuuuKJFedpTTOZEdoXvf7PV0ehaSUUt2YU1JMXqCQkM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1170288d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns; sns.set()\n",
    "sns.pairplot(iris, hue='species', size=1.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "For use in Scikit-Learn, we will extract the features matrix and target array from the ``DataFrame``, which we can do using some of the Pandas ``DataFrame`` operations discussed in the [Chapter 3](03.00-Introduction-to-Pandas.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_iris = iris.drop('species', axis=1)\n",
    "X_iris.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_iris = iris['species']\n",
    "y_iris.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To summarize, the expected layout of features and target values is visualized in the following diagram:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](figures/05.02-samples-features.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Features-and-Labels-Grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With this data properly formatted, we can move on to consider the *estimator* API of Scikit-Learn:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Scikit-Learn's Estimator API"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The Scikit-Learn API is designed with the following guiding principles in mind, as outlined in the [Scikit-Learn API paper](http://arxiv.org/abs/1309.0238):\n",
    "\n",
    "- *Consistency*: All objects share a common interface drawn from a limited set of methods, with consistent documentation.\n",
    "\n",
    "- *Inspection*: All specified parameter values are exposed as public attributes.\n",
    "\n",
    "- *Limited object hierarchy*: Only algorithms are represented by Python classes; datasets are represented\n",
    "  in standard formats (NumPy arrays, Pandas ``DataFrame``s, SciPy sparse matrices) and parameter\n",
    "  names use standard Python strings.\n",
    "\n",
    "- *Composition*: Many machine learning tasks can be expressed as sequences of more fundamental algorithms,\n",
    "  and Scikit-Learn makes use of this wherever possible.\n",
    "\n",
    "- *Sensible defaults*: When models require user-specified parameters, the library defines an appropriate default value.\n",
    "\n",
    "In practice, these principles make Scikit-Learn very easy to use, once the basic principles are understood.\n",
    "Every machine learning algorithm in Scikit-Learn is implemented via the Estimator API, which provides a consistent interface for a wide range of machine learning applications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Basics of the API\n",
    "\n",
    "Most commonly, the steps in using the Scikit-Learn estimator API are as follows\n",
    "(we will step through a handful of detailed examples in the sections that follow).\n",
    "\n",
    "1. Choose a class of model by importing the appropriate estimator class from Scikit-Learn.\n",
    "2. Choose model hyperparameters by instantiating this class with desired values.\n",
    "3. Arrange data into a features matrix and target vector following the discussion above.\n",
    "4. Fit the model to your data by calling the ``fit()`` method of the model instance.\n",
    "5. Apply the Model to new data:\n",
    "   - For supervised learning, often we predict labels for unknown data using the ``predict()`` method.\n",
    "   - For unsupervised learning, we often transform or infer properties of the data using the ``transform()`` or ``predict()`` method.\n",
    "\n",
    "We will now step through several simple examples of applying supervised and unsupervised learning methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Supervised learning example: Simple linear regression\n",
    "\n",
    "As an example of this process, let's consider a simple linear regression—that is, the common case of fitting a line to $(x, y)$ data.\n",
    "We will use the following simple data for our regression example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DyYFtu+R9+7dvn6FLl77YSrR9+6OW67HyWl6332u0P7jtD3LbpeF/GLEcyG+99Zb+9a9/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11acab828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "rng = np.random.RandomState(42)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 1 + rng.randn(50)\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With this data in place, we can use the recipe outlined earlier. Let's walk through the process: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 1. Choose a class of model\n",
    "\n",
    "In Scikit-Learn, every class of model is represented by a Python class.\n",
    "So, for example, if we would like to compute a simple linear regression model, we can import the linear regression class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Note that other more general linear regression models exist as well; you can read more about them in the [``sklearn.linear_model`` module documentation](http://Scikit-Learn.org/stable/modules/linear_model.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 2. Choose model hyperparameters\n",
    "\n",
    "An important point is that *a class of model is not the same as an instance of a model*.\n",
    "\n",
    "Once we have decided on our model class, there are still some options open to us.\n",
    "Depending on the model class we are working with, we might need to answer one or more questions like the following:\n",
    "\n",
    "- Would we like to fit for the offset (i.e., *y*-intercept)?\n",
    "- Would we like the model to be normalized?\n",
    "- Would we like to preprocess our features to add model flexibility?\n",
    "- What degree of regularization would we like to use in our model?\n",
    "- How many model components would we like to use?\n",
    "\n",
    "These are examples of the important choices that must be made *once the model class is selected*.\n",
    "These choices are often represented as *hyperparameters*, or parameters that must be set before the model is fit to data.\n",
    "In Scikit-Learn, hyperparameters are chosen by passing values at model instantiation.\n",
    "We will explore how you can quantitatively motivate the choice of hyperparameters in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb).\n",
    "\n",
    "For our linear regression example, we can instantiate the ``LinearRegression`` class and specify that we would like to fit the intercept using the ``fit_intercept`` hyperparameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression(fit_intercept=True)\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Keep in mind that when the model is instantiated, the only action is the storing of these hyperparameter values.\n",
    "In particular, we have not yet applied the model to any data: the Scikit-Learn API makes very clear the distinction between *choice of model* and *application of model to data*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 3. Arrange data into a features matrix and target vector\n",
    "\n",
    "Previously we detailed the Scikit-Learn data representation, which requires a two-dimensional features matrix and a one-dimensional target array.\n",
    "Here our target variable ``y`` is already in the correct form (a length-``n_samples`` array), but we need to massage the data ``x`` to make it a matrix of size ``[n_samples, n_features]``.\n",
    "In this case, this amounts to a simple reshaping of the one-dimensional array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = x[:, np.newaxis]\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 4. Fit the model to your data\n",
    "\n",
    "Now it is time to apply our model to data.\n",
    "This can be done with the ``fit()`` method of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This ``fit()`` command causes a number of model-dependent internal computations to take place, and the results of these computations are stored in model-specific attributes that the user can explore.\n",
    "In Scikit-Learn, by convention all model parameters that were learned during the ``fit()`` process have trailing underscores; for example in this linear model, we have the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.9776566])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.90331072553111635"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "These two parameters represent the slope and intercept of the simple linear fit to the data.\n",
    "Comparing to the data definition, we see that they are very close to the input slope of 2 and intercept of -1.\n",
    "\n",
    "One question that frequently comes up regards the uncertainty in such internal model parameters.\n",
    "In general, Scikit-Learn does not provide tools to draw conclusions from internal model parameters themselves: interpreting model parameters is much more a *statistical modeling* question than a *machine learning* question.\n",
    "Machine learning rather focuses on what the model *predicts*.\n",
    "If you would like to dive into the meaning of fit parameters within the model, other tools are available, including the [Statsmodels Python package](http://statsmodels.sourceforge.net/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### 5. Predict labels for unknown data\n",
    "\n",
    "Once the model is trained, the main task of supervised machine learning is to evaluate it based on what it says about new data that was not part of the training set.\n",
    "In Scikit-Learn, this can be done using the ``predict()`` method.\n",
    "For the sake of this example, our \"new data\" will be a grid of *x* values, and we will ask what *y* values the model predicts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "xfit = np.linspace(-1, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "As before, we need to coerce these *x* values into a ``[n_samples, n_features]`` features matrix, after which we can feed it to the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Xfit = xfit[:, np.newaxis]\n",
    "yfit = model.predict(Xfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Finally, let's visualize the results by plotting first the raw data, and then this model fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cLiMwwMzc6YMZN7QHgQHmS34feveuAH5sJ+rdu7LTfL/87Wd/ofZ+GHEqkP/whz/w/PPP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c4d9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Typically the efficacy of the model is evaluated by comparing its results to some known baseline, as we will see in the next example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Supervised learning example: Iris classification\n",
    "\n",
    "Let's take a look at another example of this process, using the Iris dataset we discussed earlier.\n",
    "Our question will be this: given a model trained on a portion of the Iris data, how well can we predict the remaining labels?\n",
    "\n",
    "For this task, we will use an extremely simple generative model known as Gaussian naive Bayes, which proceeds by assuming each class is drawn from an axis-aligned Gaussian distribution (see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) for more details).\n",
    "Because it is so fast and has no hyperparameters to choose, Gaussian naive Bayes is often a good model to use as a baseline classification, before exploring whether improvements can be found through more sophisticated models.\n",
    "\n",
    "We would like to evaluate the model on data it has not seen before, and so we will split the data into a *training set* and a *testing set*.\n",
    "This could be done by hand, but it is more convenient to use the ``train_test_split`` utility function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X_iris, y_iris,\n",
    "                                                random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With the data arranged, we can follow our recipe to predict the labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB # 1. choose model class\n",
    "model = GaussianNB()                       # 2. instantiate model\n",
    "model.fit(Xtrain, ytrain)                  # 3. fit model to data\n",
    "y_model = model.predict(Xtest)             # 4. predict on new data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Finally, we can use the ``accuracy_score`` utility to see the fraction of predicted labels that match their true value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97368421052631582"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(ytest, y_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With an accuracy topping 97%, we see that even this very naive classification algorithm is effective for this particular dataset!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Unsupervised learning example: Iris dimensionality\n",
    "\n",
    "As an example of an unsupervised learning problem, let's take a look at reducing the dimensionality of the Iris data so as to more easily visualize it.\n",
    "Recall that the Iris data is four dimensional: there are four features recorded for each sample.\n",
    "\n",
    "The task of dimensionality reduction is to ask whether there is a suitable lower-dimensional representation that retains the essential features of the data.\n",
    "Often dimensionality reduction is used as an aid to visualizing data: after all, it is much easier to plot data in two dimensions than in four dimensions or higher!\n",
    "\n",
    "Here we will use principal component analysis (PCA; see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), which is a fast linear dimensionality reduction technique.\n",
    "We will ask the model to return two components—that is, a two-dimensional representation of the data.\n",
    "\n",
    "Following the sequence of steps outlined earlier, we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA  # 1. Choose the model class\n",
    "model = PCA(n_components=2)            # 2. Instantiate the model with hyperparameters\n",
    "model.fit(X_iris)                      # 3. Fit to data. Notice y is not specified!\n",
    "X_2D = model.transform(X_iris)         # 4. Transform the data to two dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's plot the results. A quick way to do this is to insert the results into the original Iris ``DataFrame``, and use Seaborn's ``lmplot`` to show the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wa3u/dhBgQsq5nW53WGBDez/2Xs+af+RumKCczNxD8lZ5QW+ohFKpgNbPGyGBLTCodwiG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\n0CcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c6676d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris['PCA1'] = X_2D[:, 0]\n",
    "iris['PCA2'] = X_2D[:, 1]\n",
    "sns.lmplot(\"PCA1\", \"PCA2\", hue='species', data=iris, fit_reg=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see that in the two-dimensional representation, the species are fairly well separated, even though the PCA algorithm had no knowledge of the species labels!\n",
    "This indicates to us that a relatively straightforward classification will probably be effective on the dataset, as we saw before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Unsupervised learning: Iris clustering\n",
    "\n",
    "Let's next look at applying clustering to the Iris data.\n",
    "A clustering algorithm attempts to find distinct groups of data without reference to any labels.\n",
    "Here we will use a powerful clustering method called a Gaussian mixture model (GMM), discussed in more detail in [In Depth: Gaussian Mixture Models](05.12-Gaussian-Mixtures.ipynb).\n",
    "A GMM attempts to model the data as a collection of Gaussian blobs.\n",
    "\n",
    "We can fit the Gaussian mixture model as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.mixture import GMM      # 1. Choose the model class\n",
    "model = GMM(n_components=3,\n",
    "            covariance_type='full')  # 2. Instantiate the model with hyperparameters\n",
    "model.fit(X_iris)                    # 3. Fit to data. Notice y is not specified!\n",
    "y_gmm = model.predict(X_iris)        # 4. Determine cluster labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "As before, we will add the cluster label to the Iris ``DataFrame`` and use Seaborn to plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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elWKRGhdPwtSraz3m6NtLuQf2O9cd+vZq1j0G8/uD0OL3BNCAAQO0YcMGXXnl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\n6tru5al3TjBOAwPc8ZgAuum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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a932828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris['cluster'] = y_gmm\n",
    "sns.lmplot(\"PCA1\", \"PCA2\", data=iris, hue='species',\n",
    "           col='cluster', fit_reg=False);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By splitting the data by cluster number, we see exactly how well the GMM algorithm has recovered the underlying label: the *setosa* species is separated perfectly within cluster 0, while there remains a small amount of mixing between *versicolor* and *virginica*.\n",
    "This means that even without an expert to tell us the species labels of the individual flowers, the measurements of these flowers are distinct enough that we could *automatically* identify the presence of these different groups of species with a simple clustering algorithm!\n",
    "This sort of algorithm might further give experts in the field clues as to the relationship between the samples they are observing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Application: Exploring Hand-written Digits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To demonstrate these principles on a more interesting problem, let's consider one piece of the optical character recognition problem: the identification of hand-written digits.\n",
    "In the wild, this problem involves both locating and identifying characters in an image. Here we'll take a shortcut and use Scikit-Learn's set of pre-formatted digits, which is built into the library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Loading and visualizing the digits data\n",
    "\n",
    "We'll use Scikit-Learn's data access interface and take a look at this data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 8, 8)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.images.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The images data is a three-dimensional array: 1,797 samples each consisting of an 8 × 8 grid of pixels.\n",
    "Let's visualize the first hundred of these:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uXboY2qKjow1tc+fONbS5XC7L4pDGmZQwBcj9r5tA09Bkg7riUCXVSPuiSslL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11acadd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, axes = plt.subplots(10, 10, figsize=(8, 8),\n",
    "                         subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                         gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(digits.images[i], cmap='binary', interpolation='nearest')\n",
    "    ax.text(0.05, 0.05, str(digits.target[i]),\n",
    "            transform=ax.transAxes, color='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In order to work with this data within Scikit-Learn, we need a two-dimensional, ``[n_samples, n_features]`` representation.\n",
    "We can accomplish this by treating each pixel in the image as a feature: that is, by flattening out the pixel arrays so that we have a length-64 array of pixel values representing each digit.\n",
    "Additionally, we need the target array, which gives the previously determined label for each digit.\n",
    "These two quantities are built into the digits dataset under the ``data`` and ``target`` attributes, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = digits.data\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797,)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = digits.target\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see here that there are 1,797 samples and 64 features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Unsupervised learning: Dimensionality reduction\n",
    "\n",
    "We'd like to visualize our points within the 64-dimensional parameter space, but it's difficult to effectively visualize points in such a high-dimensional space.\n",
    "Instead we'll reduce the dimensions to 2, using an unsupervised method.\n",
    "Here, we'll make use of a manifold learning algorithm called *Isomap* (see [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb)), and transform the data to two dimensions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 2)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.manifold import Isomap\n",
    "iso = Isomap(n_components=2)\n",
    "iso.fit(digits.data)\n",
    "data_projected = iso.transform(digits.data)\n",
    "data_projected.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see that the projected data is now two-dimensional.\n",
    "Let's plot this data to see if we can learn anything from its structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J83zHi8Pt/bHzz3x+0ueGJxx9qD/RP5xEYWh1nIHkIMUcfWFyIc53kkiFOI45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MnVcyQ6SWzie3iFVzFuEzq+FPG7EYnV6sFtiHHqkV+wtd8CPlxYqNf+FUZXVze/+7v/bt5o+b1g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\npJZlWZY1Dv8fbutNhc9gqb8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11acadb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data_projected[:, 0], data_projected[:, 1], c=digits.target,\n",
    "            edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('spectral', 10))\n",
    "plt.colorbar(label='digit label', ticks=range(10))\n",
    "plt.clim(-0.5, 9.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This plot gives us some good intuition into how well various numbers are separated in the larger 64-dimensional space. For example, zeros (in black) and ones (in purple) have very little overlap in parameter space.\n",
    "Intuitively, this makes sense: a zero is empty in the middle of the image, while a one will generally have ink in the middle.\n",
    "On the other hand, there seems to be a more or less continuous spectrum between ones and fours: we can understand this by realizing that some people draw ones with \"hats\" on them, which cause them to look similar to fours.\n",
    "\n",
    "Overall, however, the different groups appear to be fairly well separated in the parameter space: this tells us that even a very straightforward supervised classification algorithm should perform suitably on this data.\n",
    "Let's give it a try."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Classification on digits\n",
    "\n",
    "Let's apply a classification algorithm to the digits.\n",
    "As with the Iris data previously, we will split the data into a training and testing set, and fit a Gaussian naive Bayes model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "model = GaussianNB()\n",
    "model.fit(Xtrain, ytrain)\n",
    "y_model = model.predict(Xtest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now that we have predicted our model, we can gauge its accuracy by comparing the true values of the test set to the predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83333333333333337"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(ytest, y_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With even this extremely simple model, we find about 80% accuracy for classification of the digits!\n",
    "However, this single number doesn't tell us *where* we've gone wrong—one nice way to do this is to use the *confusion matrix*, which we can compute with Scikit-Learn and plot with Seaborn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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a1qB4uaKMWzKSj6f1w9HJkXFLRvJak2rk8737C6i01DT2bT5A0bLP5Xr+vVQ+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\nLzLMGdy6nsSyT5eSeieVln1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oXbv2Px4/OjqaadOmAVC7du2s78lseL/99htXrlyhS5cu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f230ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "mat = confusion_matrix(ytest, y_model)\n",
    "\n",
    "sns.heatmap(mat, square=True, annot=True, cbar=False)\n",
    "plt.xlabel('predicted value')\n",
    "plt.ylabel('true value');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This shows us where the mis-labeled points tend to be: for example, a large number of twos here are mis-classified as either ones or eights.\n",
    "Another way to gain intuition into the characteristics of the model is to plot the inputs again, with their predicted labels.\n",
    "We'll use green for correct labels, and red for incorrect labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x0a8+sjs0JX/sZ+01zLr6OgBAdUM1AKCmvgbBjmBrorLAor8uQnR4NNKT0u0O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\nIiIiDZazZI8fP+7RpsqSldqlCj5Lly71aNu3b5/V0JSsVM2RsqikbDA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x121637240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(10, 10, figsize=(8, 8),\n",
    "                         subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                         gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "\n",
    "test_images = Xtest.reshape(-1, 8, 8)\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(test_images[i], cmap='binary', interpolation='nearest')\n",
    "    ax.text(0.05, 0.05, str(y_model[i]),\n",
    "            transform=ax.transAxes,\n",
    "            color='green' if (ytest[i] == y_model[i]) else 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Examining this subset of the data, we can gain insight regarding where the algorithm might be not performing optimally.\n",
    "To go beyond our 80% classification rate, we might move to a more sophisticated algorithm such as support vector machines (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)), random forests (see [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb)) or another classification approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this section we have covered the essential features of the Scikit-Learn data representation, and the estimator API.\n",
    "Regardless of the type of estimator, the same import/instantiate/fit/predict pattern holds.\n",
    "Armed with this information about the estimator API, you can explore the Scikit-Learn documentation and begin trying out various models on your data.\n",
    "\n",
    "In the next section, we will explore perhaps the most important topic in machine learning: how to select and validate your model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [What Is Machine Learning?](05.01-What-Is-Machine-Learning.ipynb) | [Contents](Index.ipynb) | [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) >"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}