05.02-Introducing-Scikit-Learn.ipynb 144 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introducing Scikit-Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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 _(et c'est français !)_.\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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Representation in Scikit-Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "iris = sns.load_dataset('iris')\n",
    "iris.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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``."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Sylvain/anaconda3/lib/python3.7/site-packages/seaborn/axisgrid.py:2065: UserWarning: The `size` parameter has been renamed to `height`; pleaes update your code.\n",
      "  warnings.warn(msg, UserWarning)\n",
      "/Users/Sylvain/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 518.85x432 with 20 Axes>"
      ]
     },
     "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": {},
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "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": {},
   "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": {},
   "source": [
    "To summarize, the expected layout of features and target values is visualized in the following diagram:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](figures/05.02-samples-features.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this data properly formatted, we can move on to consider the *estimator* API of Scikit-Learn:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit-Learn's Estimator API"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": {},
   "source": [
    "With this data in place, we can use the recipe outlined earlier. Let's walk through the process: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression(fit_intercept=True)\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9033107255311164"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": {},
   "outputs": [],
   "source": [
    "xfit = np.linspace(-1, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "outputs": [],
   "source": [
    "Xfit = xfit[:, np.newaxis]\n",
    "yfit = model.predict(Xfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "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": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X_iris, y_iris,\n",
    "                                                random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the data arranged, we can follow our recipe to predict the labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "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": {},
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9736842105263158"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(ytest, y_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# C'est tout pour aujourd'hui !\n",
    "\n",
    "Ne vous inquiétez pas si vous n'avez pas eu le temps de tout faire, ou si vous n'avez pas tout compris, c'est tout à fait normal. Rappelez-vous simplement: à quoi sert numpy ? matplotlib ? quel est le but du machine learning ? quels sont les différents problèmes ? (régression, classification, etc)\n",
    "\n",
    "Vous aurez à utiliser scikit-learn pour la suite. Retenez bien comment c'est utilisé, peut importe le modèle: la fonction `fit` puis `predict`."
   ]
  }
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