05_python_learning.ipynb

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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Scikit-learn\" data-toc-modified-id=\"Scikit-learn-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Scikit-learn</a></span><ul class=\"toc-item\"><li><span><a href=\"#Transforming-the-outcome/target\" data-toc-modified-id=\"Transforming-the-outcome/target-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Transforming the outcome/target</a></span></li><li><span><a href=\"#Transforming-the-predictors\" data-toc-modified-id=\"Transforming-the-predictors-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Transforming the predictors</a></span></li></ul></li><li><span><a href=\"#The-methods\" data-toc-modified-id=\"The-methods-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>The methods</a></span><ul class=\"toc-item\"><li><span><a href=\"#A-quick-example\" data-toc-modified-id=\"A-quick-example-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>A quick example</a></span></li></ul></li><li><span><a href=\"#A-data-analytic-example\" data-toc-modified-id=\"A-data-analytic-example-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>A data analytic example</a></span><ul class=\"toc-item\"><li><span><a href=\"#Visualizing-a-decision-tree\" data-toc-modified-id=\"Visualizing-a-decision-tree-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Visualizing a decision tree</a></span></li><li><span><a href=\"#Cross-validation\" data-toc-modified-id=\"Cross-validation-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Cross-validation</a></span></li><li><span><a href=\"#Improving-models-through-cross-validation\" data-toc-modified-id=\"Improving-models-through-cross-validation-3.3\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>Improving models through cross-validation</a></span></li><li><span><a href=\"#Feature-selection\" data-toc-modified-id=\"Feature-selection-3.4\"><span class=\"toc-item-num\">3.4&nbsp;&nbsp;</span>Feature selection</a></span></li></ul></li><li><span><a href=\"#Logistic-regression\" data-toc-modified-id=\"Logistic-regression-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Logistic regression</a></span></li><li><span><a href=\"#Unsupervised-learning\" data-toc-modified-id=\"Unsupervised-learning-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Unsupervised learning</a></span></li></ul></div>"
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    "# Machine Learning using Python\n",
    "\n",
    "## Scikit-learn\n",
    "\n",
    "Scikit-learn (`sklearn`) is the main Python package for machine learning. It is a widely-used and well-regarded package. However, there are a couple of challenges to using it given the usual `pandas`-based data munging pipeline. \n",
    "\n",
    "1. `sklearn` requires that all inputs be numeric, and in fact, `numpy` arrays.\n",
    "1. `sklearn` requires that all categorical variables by replaced by 0/1 dummy variables\n",
    "1. `sklearn` requires us to separate the predictors from the outcome. We need to have one `X` matrix for the predictors and one `y` vector for the outcome.\n",
    "\n",
    "The big issue, of course, is the first point. Given we used `pandas` precisely because we wanted to be able to keep heterogenous data. We have to be able to convert non-numeric data to numeric. `pandas` does help us out with this problem. \n",
    "\n",
    "1. First of all, we know that all `pandas` Series and DataFrame objects can be converted to `numpy` arrays using the `values` or `to_numpy` functions. \n",
    "1. Second, we can easily extract a single variable from the data set using either the usual extracton methods or the \n",
    "`pop` function. \n",
    "1. Third, `pandas` gives us a way to convert all categorical values to numeric dummy variables using the `get_dummies` function. This is actually a more desirable solution than what you will see in cyberspace, which is to use the \n",
    "`OneHotEncoder` function from `sklearn`. \n",
    "    + This is generally fine since many machine learning models look for interactions internally and don't need them to be overtly specified. The main exceptions to this are linear and logistic regression. For those, we can use the formula methods described in the Statistical Modeling module to generate the appropriately transformed design matrix.\n",
    "    + If the outcome variable is not numeric, we can `LabelEncoder` function from the `sklearn.preprocessing` submodule to convert it. \n",
    "\n",
    "I just threw a bunch of jargon at you. Let's see what this means.\n",
    "\n",
    "### Transforming the outcome/target"
   ]
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    "name": "05-python-learning-1"
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       "<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",
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      "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,
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "iris = sm.datasets.get_rdataset('iris').data\n",
    "iris.head()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Let's hit the first issue first. We need to separate out the outcome (the variable we want to predict) from the predictors (in this case the sepal and petal measurements). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "name": "05-python-learning-2"
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   "outputs": [],
   "source": [
    "y = iris['Species']\n",
    "X = iris.drop('Species', axis = 1) # drops column, makes a copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to do this is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "name": "05-python-learning-3"
   },
   "outputs": [],
   "source": [
    "y = iris.pop('Species')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you look at this, `iris` now only has 4 columns. So we could just use `iris` after the `pop` application, as the predictor set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We still have to update `y` to become numeric. This is where the `sklearn` functions start to be handy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "name": "05-python-learning-4"
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       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder\n",
    "le = LabelEncoder()\n",
    "y = le.fit_transform(y)\n",
    "y"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's talk about this code, since it's very typical of the way the `sklearn`\n",
    "code works. First, we import a method (`LabelEncoder`) from the appropriate\n",
    "`sklearn` module. The second line, `le = LabelEncoder()` works to \"turn on\" the\n",
    "method. This is like taking a power tool off the shelf and plugging it in to a\n",
    "socket. It's now ready to work. The third line does the actual work.  The\n",
    "`fit_transform` function transforms the data you input into it based on the\n",
    "method it is then attached to.\n",
    "\n",
    "> Let's make a quick analogy. You can plug in both a power washer and a\n",
    "jackhammer to get them ready to go. You can then apply each of them to your\n",
    "driveway. They \"transform\" the driveway in different ways depending on which\n",
    "tool is used. The washer would \"transform\" the driveway by cleaning it, while\n",
    "the jackhammer would transform the driveway by breaking it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's an interesting invisible quirk to the code, though. The object `le` also got transformed during this \n",
    "process. There were pieces added to it during the `fit_transform` process. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "name": "05-python-learning-5"
   },
   "outputs": [],
   "source": [
    "le = LabelEncoder()\n",
    "d1 = dir(le)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "name": "05-python-learning-6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'classes_'}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = le.fit_transform( pd.read_csv('data/iris.csv')['species'])\n",
    "d2 = dir(le)\n",
    "set(d2).difference(set(d1)) # set of things in d2 but not in d1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that there is a new component added, called `classes_`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "name": "05-python-learning-7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype=object)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "le.classes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the original labels aren't destroyed; they are being stored. This can be useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "name": "05-python-learning-8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'versicolor', 'virginica', 'setosa'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "le.inverse_transform([0,1,1,2,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can transform back from the numeric to the labels. Keep this in hand, since it will prove useful after\n",
    "we have done some predictions using a ML model, which will give numeric predictions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming the predictors\n",
    "\n",
    "Let's look at a second example. The `diamonds` dataset has several categorical variables that would need to be transformed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "name": "05-python-learning-9"
   },
   "outputs": [],
   "source": [
    "diamonds = pd.read_csv('data/diamonds.csv.gz')\n",
    "\n",
    "y = diamonds.pop('price').values\n",
    "X = pd.get_dummies(diamonds)\n",
    "\n",
    "# Alternatively\n",
    "# import patsy\n",
    "# f = '~ np.log(carat) + clarity + depth + cut * color'\n",
    "# X = patsy.dmatrix(f, data=diamonds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "name": "05-python-learning-10"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.frame.DataFrame"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "name": "05-python-learning-11"
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     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 53940 entries, 0 to 53939\n",
      "Data columns (total 26 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   carat          53940 non-null  float64\n",
      " 1   depth          53940 non-null  float64\n",
      " 2   table          53940 non-null  float64\n",
      " 3   x              53940 non-null  float64\n",
      " 4   y              53940 non-null  float64\n",
      " 5   z              53940 non-null  float64\n",
      " 6   cut_Fair       53940 non-null  uint8  \n",
      " 7   cut_Good       53940 non-null  uint8  \n",
      " 8   cut_Ideal      53940 non-null  uint8  \n",
      " 9   cut_Premium    53940 non-null  uint8  \n",
      " 10  cut_Very Good  53940 non-null  uint8  \n",
      " 11  color_D        53940 non-null  uint8  \n",
      " 12  color_E        53940 non-null  uint8  \n",
      " 13  color_F        53940 non-null  uint8  \n",
      " 14  color_G        53940 non-null  uint8  \n",
      " 15  color_H        53940 non-null  uint8  \n",
      " 16  color_I        53940 non-null  uint8  \n",
      " 17  color_J        53940 non-null  uint8  \n",
      " 18  clarity_I1     53940 non-null  uint8  \n",
      " 19  clarity_IF     53940 non-null  uint8  \n",
      " 20  clarity_SI1    53940 non-null  uint8  \n",
      " 21  clarity_SI2    53940 non-null  uint8  \n",
      " 22  clarity_VS1    53940 non-null  uint8  \n",
      " 23  clarity_VS2    53940 non-null  uint8  \n",
      " 24  clarity_VVS1   53940 non-null  uint8  \n",
      " 25  clarity_VVS2   53940 non-null  uint8  \n",
      "dtypes: float64(6), uint8(20)\n",
      "memory usage: 3.5 MB\n"
     ]
    }
   ],
   "source": [
    "X.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So everything is now numeric!!. Let's take a peek inside."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "name": "05-python-learning-12"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['carat', 'depth', 'table', 'x', 'y', 'z', 'cut_Fair', 'cut_Good',\n",
       "       'cut_Ideal', 'cut_Premium', 'cut_Very Good', 'color_D', 'color_E',\n",
       "       'color_F', 'color_G', 'color_H', 'color_I', 'color_J', 'clarity_I1',\n",
       "       'clarity_IF', 'clarity_SI1', 'clarity_SI2', 'clarity_VS1',\n",
       "       'clarity_VS2', 'clarity_VVS1', 'clarity_VVS2'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, it looks like the continuous variables remain intact, but the categorical variables got exploded out. Each\n",
    "variable name has a level with it, which represents the particular level it is representing. Each of these \n",
    "variables, called dummy variables, are numerical 0/1 variables. For example, `color_F` is 1 for those diamonds which have color F, and 0 otherwise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "lines_to_next_cell": 0,
    "name": "05-python-learning-13"
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>color</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
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       "      <th>color_F</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6775</td>\n",
       "      <td>9797</td>\n",
       "      <td>0</td>\n",
       "      <td>11292</td>\n",
       "      <td>8304</td>\n",
       "      <td>5422</td>\n",
       "      <td>2808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9542</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "color       D     E     F      G     H     I     J\n",
       "color_F                                           \n",
       "0        6775  9797     0  11292  8304  5422  2808\n",
       "1           0     0  9542      0     0     0     0"
      ]
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   "source": [
    "pd.crosstab(X['color_F'], diamonds['color'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The methods\n",
    "\n",
    "We will first look at supervised learning methods. \n",
    "\n",
    "| ML method               | Code to call it                                              |\n",
    "| ----------------------- | ------------------------------------------------------------ |\n",
    "| Decision Tree           | `sklearn.tree.DecisionTreeClassifier`, `sklearn.tree.DecisionTreeRegressor` |\n",
    "| Random Forest           | `sklearn.ensemble.RandomForestClassifier`, `sklearn.ensemble.RandomForestRegressor` |\n",
    "| Linear Regression       | `sklearn.linear_model.LinearRegression`                      |\n",
    "| Logistic Regression     | `sklearn.linear_model.LogisticRegression`                    |\n",
    "| Support Vector Machines | `sklearn.svm.LinearSVC`, `sklearn.svm.LinearSVR`             |\n",
    "|                         |                                                              |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general method that the code will follow is :\n",
    "\n",
    "```\n",
    "from sklearn.... import Machine\n",
    "machine = Machine(*parameters*)\n",
    "machine.fit(X, y)\n",
    "```\n",
    "\n",
    "### A quick example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "name": "05-python-learning-14"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "lm = LinearRegression()\n",
    "dt = DecisionTreeRegressor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets manufacture some data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "lines_to_next_cell": 2,
    "name": "05-python-learning-15"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 436.375x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 10, 200)\n",
    "y = 2 + 3*x - 5*(x**2)\n",
    "d = pd.DataFrame({'x': x})\n",
    "\n",
    "lm.fit(d,y)\n",
    "dt.fit(d, y)\n",
    "\n",
    "p1 = lm.predict(d)\n",
    "p2 = dt.predict(d)\n",
    "\n",
    "d['y'] = y\n",
    "d['lm'] = p1\n",
    "d['dt'] = p2\n",
    "\n",
    "D = pd.melt(d, id_vars = 'x')\n",
    "\n",
    "sns.relplot(data=D, x = 'x', y = 'value', hue = 'variable')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A data analytic example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "name": "05-python-learning-16"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 53940 entries, 0 to 53939\n",
      "Data columns (total 10 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   carat    53940 non-null  float64\n",
      " 1   cut      53940 non-null  object \n",
      " 2   color    53940 non-null  object \n",
      " 3   clarity  53940 non-null  object \n",
      " 4   depth    53940 non-null  float64\n",
      " 5   table    53940 non-null  float64\n",
      " 6   price    53940 non-null  int64  \n",
      " 7   x        53940 non-null  float64\n",
      " 8   y        53940 non-null  float64\n",
      " 9   z        53940 non-null  float64\n",
      "dtypes: float64(6), int64(1), object(3)\n",
      "memory usage: 4.1+ MB\n"
     ]
    }
   ],
   "source": [
    "diamonds = pd.read_csv('data/diamonds.csv.gz')\n",
    "diamonds.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, lets separate out the outcome (price) and the predictors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "name": "05-python-learning-17"
   },
   "outputs": [],
   "source": [
    "y = diamonds.pop('price')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For many machine learning problems, it is useful to scale the numeric predictors so that they have mean 0 and \n",
    "variance 1. First we need to separate out the categorical and numeric variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "name": "05-python-learning-18"
   },
   "outputs": [],
   "source": [
    "d1 = diamonds.select_dtypes(include = 'number')\n",
    "d2 = diamonds.select_dtypes(exclude = 'number')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's scale the columns of `d1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "name": "05-python-learning-19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.19816781, -0.17409151, -1.09967199, -1.58783745, -1.53619556,\n",
       "        -1.57112919],\n",
       "       [-1.24036129, -1.36073849,  1.58552871, -1.64132529, -1.65877419,\n",
       "        -1.74117497],\n",
       "       [-1.19816781, -3.38501862,  3.37566251, -1.49869105, -1.45739502,\n",
       "        -1.74117497],\n",
       "       ...,\n",
       "       [-0.20662095,  0.73334442,  1.13799526, -0.06343409, -0.04774083,\n",
       "         0.03013526],\n",
       "       [ 0.13092691, -0.52310533,  0.24292836,  0.37338325,  0.33750627,\n",
       "         0.28520393],\n",
       "       [-0.10113725,  0.31452784, -1.09967199,  0.08811478,  0.11861587,\n",
       "         0.14349912]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import scale\n",
    "\n",
    "bl = scale(d1)\n",
    "bl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Woops!! We get a `numpy` array, not a `DataFrame`!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "name": "05-python-learning-20"
   },
   "outputs": [],
   "source": [
    "bl = pd.DataFrame(scale(d1))\n",
    "bl.columns = list(d1.columns)\n",
    "d1 = bl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's recode the categorical variables into dummy variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "name": "05-python-learning-21"
   },
   "outputs": [],
   "source": [
    "d2 = pd.get_dummies(d2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and put them back together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "name": "05-python-learning-22"
   },
   "outputs": [],
   "source": [
    "X = pd.concat([d1,d2], axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we need to split the data into a training set and a test set. Usually we do this as an 80/20 split. \n",
    "The purpose of the test set is to see how well the model works on an \"external\" data set. We don't touch the \n",
    "test set until we're done with all our model building in the training set. We usually do the split using \n",
    "random numbers. We'll put 40,000 observations in the training set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "lines_to_next_cell": 2,
    "name": "05-python-learning-23"
   },
   "outputs": [],
   "source": [
    "ind = list(X.index)\n",
    "np.random.shuffle(ind)\n",
    "\n",
    "X_train, y_train = X.loc[ind[:40000],:], y[ind[:40000]]\n",
    "X_test, y_test = X.loc[ind[40000:],:], y[ind[40000:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is another way to do this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "name": "05-python-learning-24"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y , test_size = 0.2, random_state= 40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will fit our models to the training data. Let's use a decision tree model, a random forest model, and a linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "lines_to_next_cell": 2,
    "name": "05-python-learning-25"
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "lm = LinearRegression()\n",
    "dt = DecisionTreeRegressor()\n",
    "rf = RandomForestRegressor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will use our training data to fit the models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "lines_to_next_cell": 2,
    "name": "05-python-learning-26"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X_train, y_train)\n",
    "dt.fit(X_train, y_train)\n",
    "rf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to see how well the model fit the data. We'll use the R2 statistic to be our metric of choice to evaluate the model fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "name": "05-python-learning-27"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nLinear regression: 0.9202636015648039, \\nDecision tree: 0.9999965428396391,\\nRandom Forest: 0.9973277168190097\\n'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import  r2_score\n",
    "\n",
    "f\"\"\"\n",
    "Linear regression: {r2_score(y_train, lm.predict(X_train))}, \n",
    "Decision tree: {r2_score(y_train, dt.predict(X_train))},\n",
    "Random Forest: {r2_score(y_train, rf.predict(X_train))}\n",
    "\"\"\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is pretty amazing. However, we know that if we try and predict using the same data we used to train \n",
    "the model, we get better than expected results. One way to get a better idea about the true performance of the \n",
    "model when we will try it on external data is to do cross-validation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing a decision tree\n",
    "\n",
    "**scikit-learn** provides a decent way of visualizing a decision tree using a program called _Graphviz_, which is a dedicated graph and network visualization program."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"middle\" x=\"816.29\" y=\"-20.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 2680</text>\n",
       "<text text-anchor=\"middle\" x=\"816.29\" y=\"-6.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = 4672.047</text>\n",
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       "<title>9&#45;&gt;11</title>\n",
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       "<text text-anchor=\"middle\" x=\"970.29\" y=\"-20.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 3152</text>\n",
       "<text text-anchor=\"middle\" x=\"970.29\" y=\"-6.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = 10919.98</text>\n",
       "</g>\n",
       "<!-- 12&#45;&gt;13 -->\n",
       "<g id=\"edge13\" class=\"edge\">\n",
       "<title>12&#45;&gt;13</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M970.29,-85.94C970.29,-77.68 970.29,-68.72 970.29,-60.31\"/>\n",
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       "<g id=\"node15\" class=\"node\">\n",
       "<title>14</title>\n",
       "<path fill=\"#e58139\" stroke=\"black\" d=\"M1186.45,-50C1186.45,-50 1070.14,-50 1070.14,-50 1064.14,-50 1058.14,-44 1058.14,-38 1058.14,-38 1058.14,-12 1058.14,-12 1058.14,-6 1064.14,0 1070.14,0 1070.14,0 1186.45,0 1186.45,0 1192.45,0 1198.45,-6 1198.45,-12 1198.45,-12 1198.45,-38 1198.45,-38 1198.45,-44 1192.45,-50 1186.45,-50\"/>\n",
       "<text text-anchor=\"middle\" x=\"1128.29\" y=\"-34.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">mse = 7160525.258</text>\n",
       "<text text-anchor=\"middle\" x=\"1128.29\" y=\"-20.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 1770</text>\n",
       "<text text-anchor=\"middle\" x=\"1128.29\" y=\"-6.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = 14832.105</text>\n",
       "</g>\n",
       "<!-- 12&#45;&gt;14 -->\n",
       "<g id=\"edge14\" class=\"edge\">\n",
       "<title>12&#45;&gt;14</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M1024.22,-85.94C1041.58,-75.94 1060.74,-64.91 1077.84,-55.06\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"1079.65,-58.05 1086.57,-50.03 1076.16,-51.99 1079.65,-58.05\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x11f918190>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "from sklearn import tree\n",
    "\n",
    "dt = DecisionTreeRegressor(max_depth=3)\n",
    "dt.fit(X_train, y_train)\n",
    "dot_data = tree.export_graphviz(dt, out_file=None, \n",
    "                                feature_names = X_train.columns,\n",
    "                                filled=True, rounded=True)\n",
    "graph = graphviz.Source(dot_data);\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree.plot_tree(dt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross-validation\n",
    "\n",
    "In cross-validation, we split the dataset up into 5  equal parts randomly. We then train the \n",
    "model using 4 parts and predict the data on the 5th part. We do for all possible groups of 4 parts. We then \n",
    "consider the overall performance of prediction. \n",
    "\n",
    "![](graphs/CV5.png)\n",
    "\n",
    "There is nothing special about the 5 splits. If you use 5 splits, it is called 5-fold cross-validation (CV), if you use 10 splits, it is 10-fold CV. If you use all but one subject as training data, and that one subject as test data, and cycle through all the subjects, that is called leave-one-out CV (LOOCV). All these methods are widely used, but 5- and 10-fold CV are often used as a balance between effectiveness and computational efficiency. \n",
    "\n",
    "**scikit-learn** makes this pretty easy, using the `cross_val_score` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "name": "05-python-learning-28"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "cv_score = cross_val_score(dt, X_train, y_train, cv=5, scoring='r2')\n",
    "f\"CV error = {np.round(np.mean(cv_score), 3)}\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Improving models through cross-validation\n",
    "\n",
    "The cross-validation error, as we've seen, gives us a better estimate of \n",
    "how well our model predicts on new data. We can use this to tune models by tweaking their parameters to get models that reasonably will perform better. \n",
    "\n",
    "Each model that we fit has a set of parameters that govern how it proceeds\n",
    "to fit the data. These can bee seen using the `get_params` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt.get_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "le.get_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Linear regression is entirely determined by the functional form of \n",
    "the prediction equation,i.e., the \"formula\" we use. It doesn't have any parameters to tune per se. Improving a linear regression involves playing \n",
    "with the different predictors and transforming them to improve the predictions. This involve subjects called _regression diagnostics_ and \n",
    "_feature engineering_ that we will leave to Google for now. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can tune different parameters for the decision tree to try and see if\n",
    "some combination of parameters can improve predictions. One way to do this,\n",
    "since we're using a computer, is a grid search. This means that we can set out sets of values of the parameters we want to tune, and the computer will go through every combination of those values to see how the model\n",
    "performs, and will provide the \"best\" model. \n",
    "\n",
    "We would specify the values as a dictionary to the function `GridSearchCV`, which would optimize based on the cross-validation error. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "import numpy.random as rnd\n",
    "rnd.RandomState(39358)\n",
    "\n",
    "param_grid = {'max_depth': [1,3,5,7, 10], 'min_samples_leaf': [1,5,10,20],\n",
    "  'max_features' : ['auto','sqrt']}\n",
    "\n",
    "clf = GridSearchCV(dt, param_grid, scoring = 'r2', cv = 5) # Tuning dt\n",
    "clf.fit(X_train, y_train)\n",
    "\n",
    "clf.best_estimator_\n",
    "print(clf.best_score_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how does this do on the test set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 0,
    "name": "05-python-learning-29"
   },
   "outputs": [],
   "source": [
    "p = clf.best_estimator_.predict(X_test)\n",
    "r2_score(y_test, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this predictor is doing slightly better on the test set than the training set. This is often an indicator that the model is overfitting on the data. This is probable here, given the extremely high R2 values for this model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature selection\n",
    "\n",
    "We can also use cross-validation to do recursive feature selection (or \n",
    "backwards elimination), based on a predictive score. This is different \n",
    "from usual stepwise selection methods which are based on a succession of \n",
    "hypothesis tests. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import RFECV\n",
    "\n",
    "selector = RFECV(lm, cv = 5, scoring = 'r2')\n",
    "selector = selector.fit(X_train, y_train)\n",
    "selector.support_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The support gives the set of predictors (True) that are finally selected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train.columns[selector.support_]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is indicating that the best predictive model for the linear regression includes carat, cut, color and clarity, and width of the stone.\n",
    "\n",
    "## Logistic regression\n",
    "\n",
    "We noted that logistic regression is available both through **statsmodels** and through **scikit-learn**. Let's now try to fit a \n",
    "logistic regression model using **scikit-learn**. We will use the same\n",
    "Titanic dataset we used earlier. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "titanic = sm.datasets.get_rdataset('Titanic','Stat2Data').data.dropna()\n",
    "titanic.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will model `Survived` on the age, sex and passenger class of passengers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = pd.get_dummies(titanic[['Age','Sex','PClass']], drop_first=True)\n",
    "y = titanic.Survived\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y , test_size = 0.2, random_state= 40) # 80/20 split\n",
    "\n",
    "lrm = LogisticRegression()\n",
    "lrm.fit(X_train, y_train)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a few differences that are now evident between this model and\n",
    "the model we fit using **statsmodels**. As a reminder, we fit this model again below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "titanic1 = titanic.loc[X_train.index,:]\n",
    "titanic2 = titanic.loc[X_test.index,:]\n",
    "mod_logistic = smf.glm('Survived ~ Age + Sex + PClass', data=titanic1,\n",
    "  family = sm.families.Binomial()).fit()\n",
    "mod_logistic.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the objects that are available to us from the two models using \n",
    "`dir(lrm)` and `dir(mod_logistic)`. We find that `lrm` does not give us\n",
    "any parameter estimates, p-values or summary methods. It is much leaner, and, in line with other machine learning models, emphasizes predictions. So if you want to find associations between predictors and outcome, you will have to use the **statsmodels** version. \n",
    "\n",
    "Let's compare the predictions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.clf()\n",
    "p1 = lrm.predict_proba(X_test)[:,1]\n",
    "p2 = mod_logistic.predict(titanic2)\n",
    "\n",
    "plt.plot(p1, p2, '.');\n",
    "plt.plot([0,1],[0,1], ':');\n",
    "plt.xlabel('scikit-learn');\n",
    "plt.ylabel('statsmodels');\n",
    "plt.title('Predictions');\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First note that the prediction functions work a bit differently. For `lrm` we have to explicitly ask for the probability predictions, whereas those are automatically provided for `mod_logistic`. We also find that the predictions aren't exactly the same. This is because `lrm`, by default, runs a penalized regression using the lasso criteria (L2 norm), rather than the non-penalized version that `mod_logistic` runs. We can specify no penalty for `lrm` and can see much closer agreement between the two models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "lrm = LogisticRegression(penalty='none')\n",
    "lrm.fit(X_train, y_train)\n",
    "p1 = lrm.predict_proba(X_test)[:,1]\n",
    "\n",
    "plt.clf()\n",
    "plt.plot(p1, p2, '.');\n",
    "plt.plot([0,1],[0,1], ':');\n",
    "plt.xlabel('scikit-learn');\n",
    "plt.ylabel('statsmodels');\n",
    "plt.title('Predictions');\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsupervised learning is a class of machine learning methods where we are just trying to identify patterns in the data without any labels. This is in contrast to _supervised learning_, which are the modeling methods we have discussed above. \n",
    "\n",
    "Most unsupervised learning methods fall broadly into a set of algorithms called _cluster analysis_. **scikit-learn** provides several clustering algorithms. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](graphs/cluster_choice.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will demonstrate the two more popular choices -- K-Means and Agglomerative clustering (also known as hierarchical clustering). We will use the classic Fisher's Iris data for this demonstration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 444.75x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.cluster import KMeans, AgglomerativeClustering\n",
    "\n",
    "iris = sm.datasets.get_rdataset('iris').data\n",
    "sns.relplot(data=iris, x = 'Sepal.Length',y = 'Sepal.Width', hue = 'Species');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The K-Means algorithm takes a pre-specified number of clusters as input, and then tries to find contiguous regions of the data to parse into clusters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters = 3)\n",
    "km.fit(iris[['Sepal.Length','Sepal.Width']]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1,\n",
       "       1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1,\n",
       "       1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2], dtype=int32)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "km.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 445.875x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris['km_labels'] = km.labels_\n",
    "iris['km_labels'] = iris.km_labels.astype('category')\n",
    "\n",
    "sns.relplot(data=iris, x = 'Sepal.Length', y = 'Sepal.Width', \n",
    "           hue = 'km_labels');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agglomerative clustering takes a different approach. It starts by coalescing individual points successively, based on a distance metric and a principle for how to coalesce groups of points (called _linkage_). The number of clusters can then be determined either visually or via different cutoffs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AgglomerativeClustering(distance_threshold=0, linkage='complete',\n",
       "                        n_clusters=None)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hc = AgglomerativeClustering(distance_threshold=0, n_clusters=None, \n",
    "                             linkage='complete')\n",
    "\n",
    "hc.fit(iris[['Sepal.Length','Sepal.Width']])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'complete'"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hc.linkage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram\n",
    "\n",
    "## The following is from https://scikit-learn.org/stable/auto_examples/cluster/plot_agglomerative_dendrogram.html\n",
    "def plot_dendrogram(model, **kwargs):\n",
    "    # Create linkage matrix and then plot the dendrogram\n",
    "\n",
    "    # create the counts of samples under each node\n",
    "    counts = np.zeros(model.children_.shape[0])\n",
    "    n_samples = len(model.labels_)\n",
    "    for i, merge in enumerate(model.children_):\n",
    "        current_count = 0\n",
    "        for child_idx in merge:\n",
    "            if child_idx < n_samples:\n",
    "                current_count += 1  # leaf node\n",
    "            else:\n",
    "                current_count += counts[child_idx - n_samples]\n",
    "        counts[i] = current_count\n",
    "\n",
    "    linkage_matrix = np.column_stack([model.children_, model.distances_,\n",
    "                                      counts]).astype(float)\n",
    "\n",
    "    # Plot the corresponding dendrogram\n",
    "    dendrogram(linkage_matrix, **kwargs)\n",
    "\n",
    "plot_dendrogram(hc, truncate_mode='level', p=3)\n",
    "plt.xlabel(\"Number of points in node (or index of point if no parenthesis).\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "hc = AgglomerativeClustering( n_clusters=3,\n",
    "                             linkage='average')\n",
    "\n",
    "hc.fit(iris[['Sepal.Length','Sepal.Width']]);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 1, 0, 1, 2, 1,\n",
       "       2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1,\n",
       "       2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hc.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 442.375x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris['hc_labels'] = pd.Series(hc.labels_).astype('category')\n",
    "\n",
    "sns.relplot(data=iris, x = 'Sepal.Length', y= 'Sepal.Width', \n",
    "           hue = 'hc_labels');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Play around with different linkage methods to see how these clusters change. "
   ]
  }
 ],
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  "jupytext": {
   "formats": "ipynb,Rmd"
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": true,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}