21-scikit-learn.ipynb

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   "source": [
    "# 21. scikit-learn\n",
    "\n",
    "scikit-learn is the most popular Machine Learning package in Python. It implements many different types of models, regression, trees, clustering etc. as well as many useful tools for pre- and post-processing. Just like for scipy and statsmodels, we give here an extremely brief introduction to this library, rather to explain its general functioning than to present specific methods. Note that scikit-learn only offers \"classical\" methods and cannot be used e.g. for Deep Learning."
   ]
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   "source": [
    "## Linear regression\n",
    "\n",
    "As a start we will once again look at linear regression. As we have seen this method via the precedent packages, it represents a good opportunity to understand the general mechanism of the library. Let's first import the diamond data:"
   ]
  },
  {
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   "source": [
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "diams = pd.read_csv('https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/Ecdat/Diamond.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Now we can import the scikit-learn module implementing linear models with:"
   ]
  },
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   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The module offers a very [extensive list](https://scikit-learn.org/stable/modules/classes.html#classical-linear-regressors) of regression models for almost any situation including e.g. outlier, feature selection etc. Here we first use a simple linear regressor. We first instantiate it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "93f4da29-b252-4c86-86d5-8277fbb623af",
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   "source": [
    "model = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f04d6d7-d76a-47b3-a6be-ed74915c2af7",
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   "source": [
    "And like in statsmodels we can now ```fit``` our data. For this we have again to pass our indpendent and dependent variables as Numpy arrays (one row per element in the dataset, one column per feature). Here we only use again price and carat. As we could pass multiple features (not just carat), the ```fit``` function expects a 2D array for X:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8ce890b8-c9cb-4f78-8a31-bc1384553e40",
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    {
     "data": {
      "text/plain": [
       "(308, 1)"
      ]
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     "execution_count": 4,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = diams.carat.values\n",
    "X = X[:,np.newaxis]\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c1b681e0-db3f-41d7-8e29-21e53aec6d46",
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   "outputs": [],
   "source": [
    "res = model.fit(X=X, y=diams.price)"
   ]
  },
  {
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   "source": [
    "Also here ```res``` is an object that contains all the necessary information about our fit. For example we can recover the intercept and fit coefficient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d0a1b57a-9cbb-4615-a9af-2043c293420b",
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    {
     "data": {
      "text/plain": [
       "-2298.3576018938074"
      ]
     },
     "execution_count": 6,
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     "output_type": "execute_result"
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   ],
   "source": [
    "res.intercept_"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "id": "883755c8-68d2-4d86-a2e7-600dc03b9a51",
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    {
     "data": {
      "text/plain": [
       "array([11598.88401288])"
      ]
     },
     "execution_count": 7,
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     "output_type": "execute_result"
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   ],
   "source": [
    "res.coef_"
   ]
  },
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   "source": [
    "We can also use the ```predict``` function on new values for the price. We use it here to display the fit:"
   ]
  },
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   "execution_count": 8,
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    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diams.carat, diams.price, \"b.\", label=\"data\")\n",
    "plt.plot(np.linspace(0.1,1.25,10), res.predict(np.linspace(0.1,1.25,10)[:,np.newaxis]), \"r-\", label=\"OLS\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcbb3a97-c1a7-465a-915a-b948bbe934b8",
   "metadata": {},
   "source": [
    "As before, we can consider a more complex models by adding higher terms (quadratic etc.). We could do it \"manually\" by adding those features to ```X``` but scikit-learn offers some help for this. We can use the ```PolynomialFeatures``` class for that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d442d306-3bc9-4d05-9edb-3fddb7abd443",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "X_2 = poly.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1e65be6f-18b8-4bed-a727-f0214a3c5069",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(308, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e52f799b-3ec1-4f38-b69d-23f2b3c76ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.    , 0.3   , 0.09  ],\n",
       "       [1.    , 0.3   , 0.09  ],\n",
       "       [1.    , 0.3   , 0.09  ],\n",
       "       [1.    , 0.3   , 0.09  ],\n",
       "       [1.    , 0.31  , 0.0961]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_2[0:5,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6877853-411d-4eea-9977-8ba20aa1e46f",
   "metadata": {},
   "source": [
    "We see now that we have turned our single parameter into three (including the intercept). We can now again fit and display. Note that here again the ```predict``` input should also be passed through the ```fit_transform``` function to match the dimensions of the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "34973e4d-4979-409b-91fc-ddf312a67986",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = model.fit(X=X_2, y=diams.price)\n",
    "\n",
    "plt.plot(diams.carat, diams.price, \"b.\", label=\"data\")\n",
    "plt.plot(np.linspace(0.1,1.25,20), res.predict(poly.fit_transform(np.linspace(0.1,1.25,20)[:,np.newaxis])), \"r-\", label=\"OLS\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8452a08-4d98-4a40-89d8-25060e799770",
   "metadata": {},
   "source": [
    "### SGD\n",
    "\n",
    "We show now one alternative model for linear regression, just to highlight the fact the despite using very different algorithms, they are used almost in the same way in scikit-learn. We use here Stochastic Gradient Descent, which can be useful for large high-dimensional datasets where OLS would be very slow. Let's define our regressor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01350e37-c36e-4f3d-bbd7-24b2ca41734e",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = linear_model.SGDRegressor()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4efc7528-64dd-4118-a6df-68ae044c4f52",
   "metadata": {},
   "source": [
    "And now we use it just like done above. As you can see, the **only** thing that changes is the model definition. All the rest, with the ```fit``` and ```predict``` methods remains unchanged! This makes it very easy to explore many models to find the best one for your problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a98946d0-4cd4-4ca2-8cda-2c08d65463ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = model.fit(X=X_2, y=diams.price)\n",
    "\n",
    "plt.plot(diams.carat, diams.price, \"b.\", label=\"data\")\n",
    "plt.plot(np.linspace(0.1,1.25,20), res.predict(poly.fit_transform(np.linspace(0.1,1.25,20)[:,np.newaxis])), \"r-\", label=\"OLS\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25894ae8-102e-4e58-802a-ee845a1fcbff",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "A big strength of scikit-learn is its vast collection of classification methods. In contrast to regression where a continuous value is predicted from a set of features, classification attempts to assign data to *discrete* categories. \n",
    "\n",
    "For example we can split the diamonds into \"expensive\" and \"cheap\" categories and then try to classify them using the carat:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "01baa8b9-57bb-4891-963d-e35b2b25182a",
   "metadata": {},
   "outputs": [],
   "source": [
    "diams['price_cat'] = diams.price.apply(lambda x: 1 if x > 4000 else 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d222a20b-afa5-4861-95dd-96cd6d8545cc",
   "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>carat</th>\n",
       "      <th>colour</th>\n",
       "      <th>clarity</th>\n",
       "      <th>certification</th>\n",
       "      <th>price</th>\n",
       "      <th>price_cat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.30</td>\n",
       "      <td>D</td>\n",
       "      <td>VS2</td>\n",
       "      <td>GIA</td>\n",
       "      <td>1302</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.30</td>\n",
       "      <td>E</td>\n",
       "      <td>VS1</td>\n",
       "      <td>GIA</td>\n",
       "      <td>1510</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.30</td>\n",
       "      <td>G</td>\n",
       "      <td>VVS1</td>\n",
       "      <td>GIA</td>\n",
       "      <td>1510</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.30</td>\n",
       "      <td>G</td>\n",
       "      <td>VS1</td>\n",
       "      <td>GIA</td>\n",
       "      <td>1260</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.31</td>\n",
       "      <td>D</td>\n",
       "      <td>VS1</td>\n",
       "      <td>GIA</td>\n",
       "      <td>1641</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat colour clarity certification  price  price_cat\n",
       "1   0.30      D     VS2           GIA   1302          0\n",
       "2   0.30      E     VS1           GIA   1510          0\n",
       "3   0.30      G    VVS1           GIA   1510          0\n",
       "4   0.30      G     VS1           GIA   1260          0\n",
       "5   0.31      D     VS1           GIA   1641          0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diams.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d801208-7097-45ef-98fd-85a1a4181765",
   "metadata": {},
   "source": [
    "We obtain now a plot that can definitely not be modelled via simple linear regression. The goal is to estimate where the boundary is between cheap and expensive:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "177f0ab8-95ae-4903-88af-ad1e3c0fe808",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVwg0AALAVy+Hm+PHjLVEHAACAX1gON3Fxcbrjjju0efPmlqgHAADgtFgON2vWrFFxcbEuv/xy9evXT4899pgOHz7cErUBAABYZjncXHPNNXrjjTd0+PBh/c///I/WrFmjXr166eqrr9abb76pysrKlqgTAADAFIdhGMbpDvLcc8/p/vvvV3l5uWJjY5Wenq558+YpIiLCHzX6VUlJiWJiYlRcXKzo6OhAlwMAAEyw8vfb2dydFBQUaNWqVXr55ZeVl5enG2+8UZMnT9bhw4f12GOP6YMPPtCGDRuaOzwAAECzWA43b775pl5++WX94x//0HnnnaepU6fqF7/4hTp27OjuM2jQIA0ePNifdQIAAJhiOdxMmjRJt9xyi7Zs2aKhQ4f67NOnTx/Nnz//tIsDAACwytI9N5WVlVq+fLl+9rOf6ayzzmrJuloM99wAAND+WPn7belpKafTqfvuu09lZWWnVSAAAEBLsfwo+LBhw5STk9MStQAAAJw2y/fc3H333br33nt18OBBJScnKzIy0uP7AwcO9FtxAAAAVll+5Wb8+PHKzc3VjBkzlJqa6n4yqrlPSC1ZskS9e/eWy+VScnKyNm3a1Gj/srIyzZ8/X7169VJYWJh+9KMfaeXKlZb3CwAA7MnyKze5ubl+2/natWs1c+ZMLVmyRKmpqVq2bJnGjh2rXbt26eyzz/a5zU033aRvvvlGL730khITE3XkyBFWRQYAAG5+WaG4uYYNG6YhQ4Zo6dKl7rb+/ftr3LhxyszM9Or/zjvv6Oabb9a+ffvUuXNnU/soKyvzuAG6pKRECQkJPC0FAEA70mJPS9Xau3evpk+frjFjxuiKK67QjBkztHfvXktjlJeXKzs7W2lpaR7taWlp2rp1q89t3n77baWkpOiJJ55Qjx491K9fP9133306efJkg/vJzMxUTEyM+yshIcFSnQAAoH2xHG5qVyb+6KOPNHDgQCUlJenDDz/UgAEDlJWVZXqcwsJCVVVVKS4uzqM9Li5OBQUFPrfZt2+fNm/erC+++ELr1q3TM888o9dff11Tp05tcD8ZGRkqLi52fx04cMB0jQAAoP2xfM/NvHnzNGvWLD322GNe7XPnztUVV1xhaTyHw+Hxb8MwvNpqVVdXy+FwaPXq1YqJiZEkLV68WDfeeKNeeOEFhYeHe20TFhamsLAwSzUBAID2y/IrN7t379bkyZO92u+44w7t2rXL9DixsbEKDg72epXmyJEjXq/m1Orevbt69OjhDjZSzT06hmHo4MGDpvcNAADsy3K46dq1q3bs2OHVvmPHDnXr1s30OKGhoUpOTvZ6KysrK0sjRozwuU1qaqoOHz6sY8eOudu+/PJLBQUFqWfPnqb3DQAA7Mvy21J33nmnfvnLX2rfvn0aMWKEHA6HNm/erMcff1z33nuvpbFmz56t2267TSkpKRo+fLiWL1+uvLw8paenS6q5X+bQoUNatWqVJOnWW2/Vb37zG02aNEmLFi1SYWGh7r//ft1xxx0+35ICAABnHsvhZsGCBYqKitJTTz2ljIwMSVJ8fLwWLlyoGTNmWBpr/PjxKioq0kMPPaT8/HwlJSVp/fr16tWrlyQpPz9feXl57v4dOnRQVlaWpk+frpSUFHXp0kU33XSTHn74YauHAQAAbOq01rkpLS2VJEVFRfmtoJbGp4IDAND+WPn7bfmVm7raU6gBAABnBsvhZvDgwT4f1XY4HHK5XEpMTNTEiRM1evRovxQIAABgheWnpX7yk59o3759ioyM1OjRo3XppZeqQ4cO2rt3r4YOHar8/HyNGTNGf/3rX1uiXgAAgEZZfuWmsLBQ9957rxYsWODR/vDDD+vrr7/Whg0b9OCDD+o3v/mNrrvuOr8VCgAAYIblG4pjYmKUnZ2txMREj/Y9e/YoOTlZxcXF+ve//62hQ4e6bzhuS7ihGACA9qdFPzjT5XL5/GDLrVu3yuVySar5mAQ+8gAAAASC5belpk+frvT0dGVnZ2vo0KFyOBz66KOP9OKLL+pXv/qVpJoP1xw8eLDfiwUAAGhKs9a5Wb16tZ5//nn95z//kST9+Mc/1vTp03XrrbdKkk6ePOl+eqqt4W0pAADaHyt/v09rEb/2iHADAED706L33EjS0aNH3W9Dffvtt5KkTz75RIcOHWrOcAAAAH5j+Z6bzz77TGPGjFFMTIz279+vKVOmqHPnzlq3bp2+/vpr94dcAgAABILlV25mz56tiRMn6quvvvK4p2bs2LF6//33/VocAACAVZbDzccff6y77rrLq71Hjx4qKCjwS1EAAADN1ax1bkpKSrza//Of/6hr165+KQoAAKC5LIeb6667Tg899JAqKiok1XxgZl5enubNm6cbbrjB7wUCAABYYTnc/Pa3v9V///tfdevWTSdPntQll1yixMRERUVF6ZFHHmmJGgEAAEyz/LRUdHS0Nm/erHfffVeffPKJqqurNWTIEI0ZM6Yl6gMAALDE8iJ+q1at0vjx470+O6q8vFyvvfaaJkyY4NcC/Y1F/AAAaH9adIXi4OBg5efnq1u3bh7tRUVF6tatm6qqqqxX3IoINwAAtD8tukKxYRhyOBxe7QcPHlRMTIzV4QAAAPzK9D03gwcPlsPhkMPh0OWXXy6n84dNq6qqlJubq5/85CctUiQAAIBZpsPNuHHjJEk7duzQlVdeqQ4dOri/FxoaqnPOOYdHwQEAQMCZDjcPPvigJOmcc87R+PHjPT56AQAAoK2w/Cj47bff3hJ1AAAA+IXlcFNVVaWnn35af/7zn5WXl6fy8nKP73/77bd+Kw4AAMAqy09LLVq0SIsXL9ZNN92k4uJizZ49Wz/72c8UFBSkhQsXtkCJAAAA5lkON6tXr9aKFSt03333yel06pZbbtGLL76oBx54QB988EFL1AgAAGCa5XBTUFCg888/X5LUoUMHFRcXS5Kuvvpq/e1vf/NvdQAAABZZDjc9e/ZUfn6+JCkxMVEbNmyQJH388cdeH8kAAADQ2iyHm+uvv17//Oc/JUn33HOPFixYoL59+2rChAm64447/F4gAACAFZY/W6q+Dz/8UFu2bFFiYqKuvfZaf9XVYvhsKQAA2h8rf78tPwpe37BhwzRs2LDTHQYAAMAvLL8tlZmZqZUrV3q1r1y5Uo8//rhfigIAAGguy+Fm2bJlOvfcc73aBwwYoN///vd+KQoAAKC5mvUoePfu3b3au3bt6n6KCgAAIFAsh5uEhARt2bLFq33Lli2Kj4/3S1EAAADNZfmG4ilTpmjmzJmqqKjQZZddJkn65z//qTlz5ujee+/1e4EAAABWWA43c+bM0bfffqu7777b/aGZLpdLc+fOVUZGht8LBAAAsKLZ69wcO3ZMu3fvVnh4uPr27dtuVidmnRsAANqfVlnnpkOHDho6dGhzNwcAAGgRlm8oBgAAaMsINwAAwFYINwAAwFYINwAAwFaaFW7++Mc/KjU1VfHx8fr6668lSc8884z++te/+rU4AAAAqyyHm6VLl2r27Nm66qqrdPToUVVVVUmSOnbsqGeeecbf9QEAAFhiOdw899xzWrFihebPn6/g4GB3e0pKij7//HO/FgcAAGCV5XCTm5urwYMHe7WHhYXp+PHjfikKAACguSyHm969e2vHjh1e7X//+9913nnn+aMmAACAZrO8QvH999+vqVOn6tSpUzIMQx999JHWrFmjzMxMvfjiiy1RIwAAgGmWw82kSZNUWVmpOXPm6MSJE7r11lvVo0cP/e53v9PNN9/cEjUCAACY1uwPzpSkwsJCVVdXq1u3bv6sqUXxwZkAALQ/LfrBmbm5uaqsrFTfvn0VGxvrbv/qq68UEhKic845x3LBAAAA/mL5huKJEydq69atXu0ffvihJk6c6I+aAAAAms1yuMnJyVFqaqpX+0UXXeTzKSoAAIDWZDncOBwOlZaWerUXFxe7VysGAAAIFMvhZtSoUcrMzPQIMlVVVcrMzNTIkSMtF7BkyRL17t1bLpdLycnJ2rRpk6nttmzZIqfTqUGDBlneJwAAsC/LNxQ/8cQTuvjii/XjH/9Yo0aNkiRt2rRJJSUlevfddy2NtXbtWs2cOVNLlixRamqqli1bprFjx2rXrl06++yzG9yuuLhYEyZM0OWXX65vvvnG6iEAAAAba9aj4IcPH9bzzz+vTz/9VOHh4Ro4cKCmTZumzp07Wxpn2LBhGjJkiJYuXepu69+/v8aNG6fMzMwGt7v55pvVt29fBQcH66233rJ0rw+PggMA0P606KPgkhQfH69HH320WcXVKi8vV3Z2tubNm+fRnpaW5vNprFovv/yy9u7dq1dffVUPP/xwk/spKytTWVmZ+98lJSXNLxoAALR5psLNZ599pqSkJAUFBemzzz5rtO/AgQNN7biwsFBVVVWKi4vzaI+Li1NBQYHPbb766ivNmzdPmzZtktNpLpdlZmZq0aJFpvoCAID2z1RCGDRokAoKCtStWzcNGjRIDodDvt7Ncjgclp+YcjgcHv82DMOrTaq5afnWW2/VokWL1K9fP9PjZ2RkaPbs2e5/l5SUKCEhwVKNAACg/TAVbnJzc9W1a1f3f/tDbGysgoODvV6lOXLkiNerOZJUWlqq7du3KycnR9OmTZMkVVdXyzAMOZ1ObdiwQZdddpnXdmFhYQoLC/NLzQAAoO0zFW569eolSaqoqNDChQu1YMEC9enT57R2HBoaquTkZGVlZen66693t2dlZem6667z6h8dHa3PP//co23JkiV699139frrr6t3796nVQ8AALAHSzcUh4SEaN26dVqwYIFfdj579mzddtttSklJ0fDhw7V8+XLl5eUpPT1dUs1bSocOHdKqVasUFBSkpKQkj+27desml8vl1Q4AAM5clp+Wuv766/XWW2953MfSXOPHj1dRUZEeeugh5efnKykpSevXr3e/UpSfn6+8vLzT3g8AADhzWF7n5pFHHtFvf/tbXX755UpOTlZkZKTH92fMmOHXAv2NdW4AAGh/rPz9thxuGru3xeFwaN++fVaGa3WEGwAA2p8WXcTPX09LAQAAtATLH5xZl2EYPte7AQAACJRmhZuXXnpJSUlJcrlc7qeVXnzxRX/XBgAAYJnlt6UWLFigp59+WtOnT9fw4cMlSdu2bdOsWbO0f/9+U5/3BAAA0FIs31AcGxur5557TrfccotH+5o1azR9+nQVFhb6tUB/44ZiAADaHyt/vy2/LVVVVaWUlBSv9uTkZFVWVlodDgAAwK8sh5tf/OIXWrp0qVf78uXL9fOf/9wvRQEAADSX5XtupJobijds2KCLLrpIkvTBBx/owIEDmjBhgsfKxYsXL/ZPlQAAACZZDjdffPGFhgwZIknau3evJKlr167q2rWrvvjiC3c/h8PhpxIBAADMsxxu/vWvf7VEHQAAAH5xWov4AQAAtDWEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCsBDzdLlixR79695XK5lJycrE2bNjXY980339QVV1yhrl27Kjo6WsOHD9c//vGPVqwWAAC0dQENN2vXrtXMmTM1f/585eTkaNSoURo7dqzy8vJ89n///fd1xRVXaP369crOztbo0aN1zTXXKCcnp5UrBwAAbZXDMAwjUDsfNmyYhgwZoqVLl7rb+vfvr3HjxikzM9PUGAMGDND48eP1wAMPmOpfUlKimJgYFRcXKzo6ull1AwCA1mXl73fAXrkpLy9Xdna20tLSPNrT0tK0detWU2NUV1ertLRUnTt3brBPWVmZSkpKPL4AAIB9BSzcFBYWqqqqSnFxcR7tcXFxKigoMDXGU089pePHj+umm25qsE9mZqZiYmLcXwkJCadVNwAAaNsCfkOxw+Hw+LdhGF5tvqxZs0YLFy7U2rVr1a1btwb7ZWRkqLi42P114MCB064ZAAC0Xc5A7Tg2NlbBwcFer9IcOXLE69Wc+tauXavJkyfrL3/5i8aMGdNo37CwMIWFhZ12vQAAoH0I2Cs3oaGhSk5OVlZWlkd7VlaWRowY0eB2a9as0cSJE/WnP/1JP/3pT1u6TAAA0M4E7JUbSZo9e7Zuu+02paSkaPjw4Vq+fLny8vKUnp4uqeYtpUOHDmnVqlWSaoLNhAkT9Lvf/U4XXXSR+1Wf8PBwxcTEBOw4AABA2xHQcDN+/HgVFRXpoYceUn5+vpKSkrR+/Xr16tVLkpSfn++x5s2yZctUWVmpqVOnaurUqe7222+/Xa+88kprlw8AANqggK5zEwiscwMAQPvTLta5AQAAaAmEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCuEGwAAYCvOQBewZMkSPfnkk8rPz9eAAQP0zDPPaNSoUQ3237hxo2bPnq2dO3cqPj5ec+bMUXp6eitW7NvB706o9FSlSk5WKCY8RF1cTpVJHm0dXU5VSSqp09bJ5VRlvbZol1ORYU4VHitXyakKdQoPUYgzyKNPTHiIIkKD3X2iw0MUGxmqY2WVTY4f43IqKDhI3x0vV8mpSkWHO9U5IlRhziCv8U5VVnv06xIRqrKqao/jivn+uOq2RbmcCnI4dPRkhUpOVqhjZIgiQ50efTqFh6jCMJocq4PLqbDgIBXVq6Na8qitU0So4qJdpubr8NGTKv6+tpjwEHUMD1G15NEWHR6i+I7hHtsVnyj3OkcxEaFe4/vqJ8lUW/1z3tBx1b/molw1P871r6XqOuezU2SIIurNQweXU1F1rrfaOkrLKpucm2iXU4aPfQbXu746RYTK5eP6Ol5e5XHOG7qufZ2n+ufd7Dn3NV+nw+w1AaD1BDTcrF27VjNnztSSJUuUmpqqZcuWaezYsdq1a5fOPvtsr/65ubm66qqrdOedd+rVV1/Vli1bdPfdd6tr16664YYbAnAENb4uOq5frftcW/YUSZLGnBurX1+dpPlv/dDWr1sHLZ+Q0mRbRGiwXro9RUv+tUeb9hQpoVO4Vk2+UHPe+KzBPlbGj+0Qqtd+eZEebGK8mn7D9eDbX7j7DewRrWdvGeIxXkKncP1x8oWa/9YXDY4XERqsZ28ZrJe35Narw3N8d21v73S3SdLIxC5aeO0A/eKlD1V4rLzRfo9ef77O7hJpab581VI73iPXn69e3493+OhJzX3jM236qtDd5+K+sXrshoEeIah+v4jQYK2cOFQvvLtHm/aYafvKPQ8NHVf9YzAzh7EdQrV6ykWaW2fu657fm5d/oMJj5T7n2ex8+arjh30k6ebl21R4rPz762ZYo9d+Q+fJ13k3c84bmq/TYfaaANC6HIZhGIHa+bBhwzRkyBAtXbrU3da/f3+NGzdOmZmZXv3nzp2rt99+W7t373a3paen69NPP9W2bdtM7bOkpEQxMTEqLi5WdHT0aR/Dwe9OeP2x2HT/pZpX5w+PJGXNvlgL6/0x9tU27bJE5eR95257e1qqHn/n3432sTL+S7enaGWdkNHQeL76vXffJR4hxmx9Zsf31VZrZGIXTUrtrcl/2N5kv6duGtTgKziHj57U/a9/amm/T9x4gSJDgzVtTY7HH7FaF/eN1XO3DFZMRKiKT5R79fN1/GbbfB2Xr2vOzDk2e359zbPZ+WrqGGr3Yfa6bmy82vMuydQ5r7/d6b664muu/b0PAD+w8vc7YPfclJeXKzs7W2lpaR7taWlp2rp1q89ttm3b5tX/yiuv1Pbt21VRUeFzm7KyMpWUlHh8+VPpqUqvX6DHyqu82iqrDFNtgxM6erQ5g4Oa7GNl/G7RYabG89XvZEW1V5uZ+syO76ut1uY9ReoWHWaq33fHy31+T6p528nqfotPVqjwWLnPP2KS9P5XhSo8VrNPX/18Hb/ZNl/H5euaM3OOzZ5fX/Nsdr6aOobafZi9rhsbr/a8mz3n9bc7XWavCQCtL2DhprCwUFVVVYqLi/Noj4uLU0FBgc9tCgoKfPavrKxUYaHvXzKZmZmKiYlxfyUkJPjnAL5XctI7VJ1OW1lltce/S030sTL+sVNVpsbz1c/XeGbqMzu+rzZf32+qX8mpyoa/Z/Kc1FV6qkIlp3yH57p9avZtbr7MttVVe1xmrhvJ+7jMnl+z58jsteRrG7PXdVPjNTQ3ZrY7XWavCQCtL+BPSzkcDo9/G4bh1dZUf1/ttTIyMlRcXOz+OnDgwGlW7Ck6PMSvbWFOzymJMtHHyvgdXMGmxvPVz9d4ZuozO76vNl/fb6pftKvhW8nMnpO6olwhinZ5b1e/T82+zc2X2ba6ao/LzHUjeR+X2fNr9hyZvZZ8bWP2um5qvIbmxsx2p8vsNQGg9QUs3MTGxio4ONjrVZojR454vTpT66yzzvLZ3+l0qkuXLj63CQsLU3R0tMeXP0W5nBqZ6LnvDqHBXm3OYIeptpwDR5Vap62yqrrJPlbGP1JSZmo8X/3CQ4K82szUZ3Z8X221RiZ20ZGSMlP9OkU2fJ9DTHiI5f3GhIcotkOoLu4b67PPxX1jFduhZp+++vk6frNtvo7L1zVn5hybPb++5tnsfDV1DLX7MHtdNzZe7Xk3e87rb3e6zF4TAFpfwMJNaGiokpOTlZWV5dGelZWlESNG+Nxm+PDhXv03bNiglJQUhYQE5v+SenaK0CPXn+/xi3rR//tCD4/zbJv66iem2lZuztW00Yka9f0vzamrP9FvxiU12sfK+HPf+EwLrx3Q5Hg1/Tz3O2NNjvc+Vn+ih5uob+XmXE1K7e2jjqQma5N+eNJm7hufNdnv0evPb/Rx8PiO4V7z5auW2vEeuf58xXcMV0xEqB67YaDXH7OL+8bq8RsGum8c9dVv5eZcTb+sr8f5bbQt0XMf9Y/L1zVnZg7nvvGZFlzd9Pn1Nc9m58tXHb72UXPdNH0Mvs6T5HnezZ7z+tudLrPXBIDWF9CnpdauXavbbrtNv//97zV8+HAtX75cK1as0M6dO9WrVy9lZGTo0KFDWrVqlaSaR8GTkpJ011136c4779S2bduUnp6uNWvWmH4U3N9PS9WqXXOk9FSFolwhiq2zzk1tW6c669zUtnWusw5NbVtMnXVuSk9VqGOddW5q+3Sssx6Ie58dfljnprHxO9Zf58blVOfIH9a5qTuex5orLqe6RP6wzk3d8arqHWt0nXVuSk/VrGESGeb06NO5zjo3jY0VVX+dm+/r8FjnxuVUp0jr69y456bOOjfueWhknZu656ixdW7q9pNkqq3+OW/ouOpfc9F11rmpey3VrnNTeqpCMRE/rDdU9/xG1bneauuoXeemsbmJqbPOTd224HrXV6fIH9a5qbuP2nVumrqufZ2nhta5sbrd6TJ7TQA4PVb+fgc03Eg1i/g98cQTys/PV1JSkp5++mldfPHFkqSJEydq//79eu+999z9N27cqFmzZrkX8Zs7d66lRfxaKtwAAICW067CTWsj3AAA0P60i3VuAAAAWgLhBgAA2ArhBgAA2ArhBgAA2ArhBgAA2ArhBgAA2ArhBgAA2ArhBgAA2ArhBgAA2Ioz0AW0ttoFmUtKSgJcCQAAMKv277aZD1Y448JNaWmpJCkhISHAlQAAAKtKS0sVExPTaJ8z7rOlqqurdfjwYUVFRcnhcASkhpKSEiUkJOjAgQN8vlUAMQ9tA/PQNjAPbQPz0DDDMFRaWqr4+HgFBTV+V80Z98pNUFCQevbsGegyJEnR0dFcvG0A89A2MA9tA/PQNjAPvjX1ik0tbigGAAC2QrgBAAC2QrgJgLCwMD344IMKCwsLdClnNOahbWAe2gbmoW1gHvzjjLuhGAAA2Buv3AAAAFsh3AAAAFsh3AAAAFsh3AAAAFsh3LSQJUuWqHfv3nK5XEpOTtamTZsa7Pvmm2/qiiuuUNeuXRUdHa3hw4frH//4RytWa19W5qGuLVu2yOl0atCgQS1b4BnC6jyUlZVp/vz56tWrl8LCwvSjH/1IK1eubKVq7cvqPKxevVoXXHCBIiIi1L17d02aNElFRUWtVK39vP/++7rmmmsUHx8vh8Oht956q8ltNm7cqOTkZLlcLvXp00e///3vW75QOzDgd6+99poREhJirFixwti1a5dxzz33GJGRkcbXX3/ts/8999xjPP7448ZHH31kfPnll0ZGRoYREhJifPLJJ61cub1YnYdaR48eNfr06WOkpaUZF1xwQesUa2PNmYdrr73WGDZsmJGVlWXk5uYaH374obFly5ZWrNp+rM7Dpk2bjKCgION3v/udsW/fPmPTpk3GgAEDjHHjxrVy5faxfv16Y/78+cYbb7xhSDLWrVvXaP99+/YZERERxj333GPs2rXLWLFihRESEmK8/vrrrVNwO0a4aQEXXnihkZ6e7tF27rnnGvPmzTM9xnnnnWcsWrTI36WdUZo7D+PHjzd+/etfGw8++CDhxg+szsPf//53IyYmxigqKmqN8s4YVufhySefNPr06ePR9uyzzxo9e/ZssRrPJGbCzZw5c4xzzz3Xo+2uu+4yLrroohaszB54W8rPysvLlZ2drbS0NI/2tLQ0bd261dQY1dXVKi0tVefOnVuixDNCc+fh5Zdf1t69e/Xggw+2dIlnhObMw9tvv62UlBQ98cQT6tGjh/r166f77rtPJ0+ebI2Sbak58zBixAgdPHhQ69evl2EY+uabb/T666/rpz/9aWuUDEnbtm3zmrMrr7xS27dvV0VFRYCqah/OuA/ObGmFhYWqqqpSXFycR3tcXJwKCgpMjfHUU0/p+PHjuummm1qixDNCc+bhq6++0rx587Rp0yY5nfxo+ENz5mHfvn3avHmzXC6X1q1bp8LCQt1999369ttvue+mmZozDyNGjNDq1as1fvx4nTp1SpWVlbr22mv13HPPtUbJkFRQUOBzziorK1VYWKju3bsHqLK2j1duWojD4fD4t2EYXm2+rFmzRgsXLtTatWvVrVu3lirvjGF2HqqqqnTrrbdq0aJF6tevX2uVd8aw8vNQXV0th8Oh1atX68ILL9RVV12lxYsX65VXXuHVm9NkZR527dqlGTNm6IEHHlB2drbeeecd5ebmKj09vTVKxfd8zZmvdnjif0/9LDY2VsHBwV7/N3TkyBGvBF7f2rVrNXnyZP3lL3/RmDFjWrJM27M6D6Wlpdq+fbtycnI0bdo0STV/ZA3DkNPp1IYNG3TZZZe1Su120pyfh+7du6tHjx6KiYlxt/Xv31+GYejgwYPq27dvi9ZsR82Zh8zMTKWmpur++++XJA0cOFCRkZEaNWqUHn74YV41aAVnnXWWzzlzOp3q0qVLgKpqH3jlxs9CQ0OVnJysrKwsj/asrCyNGDGiwe3WrFmjiRMn6k9/+hPvafuB1XmIjo7W559/rh07dri/0tPT9eMf/1g7duzQsGHDWqt0W2nOz0NqaqoOHz6sY8eOudu+/PJLBQUFqWfPni1ar101Zx5OnDihoCDPPxHBwcGSfnj1AC1r+PDhXnO2YcMGpaSkKCQkJEBVtRMBu5XZxmofuXzppZeMXbt2GTNnzjQiIyON/fv3G4ZhGPPmzTNuu+02d/8//elPhtPpNF544QUjPz/f/XX06NFAHYItWJ2H+nhayj+szkNpaanRs2dP48YbbzR27txpbNy40ejbt68xZcqUQB2CLVidh5dfftlwOp3GkiVLjL179xqbN282UlJSjAsvvDBQh9DulZaWGjk5OUZOTo4hyVi8eLGRk5Pjfhy//hzUPgo+a9YsY9euXcZLL73Eo+AmEW5ayAsvvGD06tXLCA0NNYYMGWJs3LjR/b3bb7/duOSSS9z/vuSSSwxJXl+333576xduM1bmoT7Cjf9YnYfdu3cbY8aMMcLDw42ePXsas2fPNk6cONHKVduP1Xl49tlnjfPOO88IDw83unfvbvz85z83Dh482MpV28e//vWvRn/X+5qD9957zxg8eLARGhpqnHPOOcbSpUtbv/B2yGEYvL4IAADsg3tuAACArRBuAACArRBuAACArRBuAACArRBuAACArRBuAACArRBuAACArRBuAACArRBuAACArRBuAJzx9u/fL4fDoR07dgS6FAB+QLgBYFsVFRWBLgFAABBuALQp1dXVevzxx5WYmKiwsDCdffbZeuSRRyRJc+fOVb9+/RQREaE+ffpowYIFHgFm4cKFGjRokFauXKk+ffooLCxMhmHonXfe0ciRI9WxY0d16dJFV199tfbu3evernfv3pKkwYMHy+Fw6NJLL23VYwbgX85AFwAAdWVkZGjFihV6+umnNXLkSOXn5+vf//63JCkqKkqvvPKK4uPj9fnnn+vOO+9UVFSU5syZ495+z549+vOf/6w33nhDwcHBkqTjx49r9uzZOv/883X8+HE98MADuv7667Vjxw4FBQXpo48+0oUXXqj/+7//04ABAxQaGhqQYwfgH3wqOIA2o7S0VF27dtXzzz+vKVOmNNn/ySef1Nq1a7V9+3ZJNa/cPProozp06JC6du3a4Hb//e9/1a1bN33++edKSkrS/v371bt3b+Xk5GjQoEH+OhwAAcLbUgDajN27d6usrEyXX365z++//vrrGjlypM466yx16NBBCxYsUF5enkefXr16eQWbvXv36tZbb1WfPn0UHR3tfhuq/rYA7IFwA6DNCA8Pb/B7H3zwgW6++WaNHTtW//u//6ucnBzNnz9f5eXlHv0iIyO9tr3mmmtUVFSkFStW6MMPP9SHH34oSV7bArAH7rkB0Gb07dtX4eHh+uc//+n1ttSWLVvUq1cvzZ8/39329ddfNzlmUVGRdu/erWXLlmnUqFGSpM2bN3v0qb3Hpqqq6nQPAUAbQLgB0Ga4XC7NnTtXc+bMUWhoqFJTU/Xf//5XO3fuVGJiovLy8vTaa69p6NCh+tvf/qZ169Y1OWanTp3UpUsXLV++XN27d1deXp7mzZvn0adbt24KDw/XO++8o549e8rlcikmJqalDhNAC+NtKQBtyoIFC3TvvffqgQceUP/+/TV+/HgdOXJE1113nWbNmqVp06Zp0KBB2rp1qxYsWNDkeEFBQXrttdeUnZ2tpKQkzZo1S08++aRHH6fTqWeffVbLli1TfHy8rrvuupY6PACtgKelAACArfDKDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsBXCDQAAsJX/D/Q71HAA0aenAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data = {'carat': diams.carat, 'price category': diams.price_cat},\n",
    "                x='carat', y='price category');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c6ec9c3-0cb3-4a09-b0f1-cc74477e627d",
   "metadata": {},
   "source": [
    "To find this boundary we can use logistic regression, which fits a sigmoid to the data. Again this is available from the ```linear_model``` module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0f795e9d-c0ff-4526-ab8d-a4e478a93d38",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "684c86d1-5878-4195-81f4-d6f42158ff1d",
   "metadata": {},
   "source": [
    "We feed the fit method exactly as before: we need an ```X``` array (or dataframe) of features and a ```y``` vector of targets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1ae1f1b7-189a-4d86-8d5d-852d11a6dabd",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression()\n",
    "model.fit(X=diams[['carat']], y=diams.price_cat)\n",
    "\n",
    "pred = model.predict(pd.DataFrame({'carat': np.arange(0,1,0.1)}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5c95e8a3-3cb0-4332-9653-1da8b235aaa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data = {'carat': diams.carat, 'price category': diams.price_cat},\n",
    "                x='carat', y='price category', label='data');\n",
    "sns.lineplot(x=np.arange(0,1,0.1), y=pred, label='logistic reg', color='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cf4bbde-9194-4ea4-bd7a-636d81420472",
   "metadata": {},
   "source": [
    "Another large class of methods are tree based: you use all the features and by answering binary questions about them of the type \"is feature large than a threshold\" you can create a question-tree that in the end answers in which category a certain item falls. For example we can now try to use both the carat and the color to predict price. Here we have however one problem: these methods work only with numerical variable but the color is categorical. So we have to turn that variable into numbers, but we can't just assign numbers: if we do, suddenly a given color has a large or small value that doesn't make any sense but will impact the classification. The common solution is to use *one hot encoding* in this case: we create one new column for each colour and fill it with zeros and ones. Ones will only appear on those lines where the colour is actually appearing. Both Pandas and scikit-learn offer tools for that. In scikit-learn we use the ```OneHotEncoder``` from the ```preprocessing``` module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "04386589-c832-4d29-a5cd-9d0b7192fe6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e9a9c188-15d7-4663-9956-e1b22496a58a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encoder = preprocessing.OneHotEncoder(sparse_output=False)\n",
    "encoder.fit_transform(diams[['colour']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9434b35c-d60e-4406-96ed-46163b992c5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    D\n",
       "2    E\n",
       "3    G\n",
       "4    G\n",
       "5    D\n",
       "Name: colour, dtype: object"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diams.colour.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac0104d0-0bfc-4e8a-855f-a68ea817ed82",
   "metadata": {},
   "source": [
    "Here we see how the encoding works: the first column corresponds to the colour ```D```. As the first item is D, we have a ```1``` there and zeros for all other columns. The second item has colour ```E``` which is encoded in the second column. So we have a ```1``` in the second column and zeros in all others etc.\n",
    "\n",
    "The ```get_dummies``` function in Pandas allows us to do the same operation but here we get a DataFrame as output: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "37b58b27-dd39-466e-bb85-8af017e5160c",
   "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>colour_D</th>\n",
       "      <th>colour_E</th>\n",
       "      <th>colour_F</th>\n",
       "      <th>colour_G</th>\n",
       "      <th>colour_H</th>\n",
       "      <th>colour_I</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   colour_D  colour_E  colour_F  colour_G  colour_H  colour_I\n",
       "1         1         0         0         0         0         0\n",
       "2         0         1         0         0         0         0\n",
       "3         0         0         0         1         0         0\n",
       "4         0         0         0         1         0         0\n",
       "5         1         0         0         0         0         0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "color_one_hot = pd.get_dummies(diams.colour, prefix='colour')\n",
    "color_one_hot.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21c99433-1d29-4665-8f5f-f18eeaf1b60d",
   "metadata": {},
   "source": [
    "Now we can combine the carat information with this new colour dataframe to create our variable ```X```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e9748d1b-8bc7-4773-8a4b-4a95b45b8f0c",
   "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>carat</th>\n",
       "      <th>colour_D</th>\n",
       "      <th>colour_E</th>\n",
       "      <th>colour_F</th>\n",
       "      <th>colour_G</th>\n",
       "      <th>colour_H</th>\n",
       "      <th>colour_I</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.31</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat  colour_D  colour_E  colour_F  colour_G  colour_H  colour_I\n",
       "1   0.30         1         0         0         0         0         0\n",
       "2   0.30         0         1         0         0         0         0\n",
       "3   0.30         0         0         0         1         0         0\n",
       "4   0.30         0         0         0         1         0         0\n",
       "5   0.31         1         0         0         0         0         0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = pd.concat([diams[['carat']], color_one_hot], axis=1)\n",
    "X.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4905e5b2-a6b6-401b-be7b-acce6af7a523",
   "metadata": {},
   "source": [
    "Finally, we can create a decision tree. Again, we use it by feeding an ```X``` array and ```y``` vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2853ab1c-2bbc-490f-928b-d3f62198eb73",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import tree\n",
    "\n",
    "y = diams.price_cat\n",
    "clf = tree.DecisionTreeClassifier(max_depth=3)\n",
    "clf = clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da3a30bb-21b9-4aa2-88e3-1378043189d9",
   "metadata": {},
   "source": [
    "We can visualize the decision tree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "80ba89af-5583-441c-a93c-fd4734f7ab18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,10))\n",
    "tree.plot_tree(clf, feature_names=X.columns, ax=ax);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "291b2a0e-426e-4e0a-a0fc-8c5930846c23",
   "metadata": {},
   "source": [
    "We limited the tree to three levels. We could add more and have a better classification, but the risk is to overfit. In this tree we see that the most important feature is the ```carat``` which does the first split at a value of 0.625. Then some minor improvement is added by using the colours ```E``` and ```G``` in two places."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d9f3c56-4a58-4e6e-9bdf-f065875277f3",
   "metadata": {},
   "source": [
    "## Clustering\n",
    "\n",
    "The last important category of operation we can do with scikit-learn is clustering. Here the goal is to split data in multiple groups without knowing in advance the groups. For example we can try to define cluster of points in the price vs. carat plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2a9e08ee-4b16-48de-9c5a-a7047272c9c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=diams, x='carat', y='price');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d58e11e-aa41-4272-9e23-bfae4df7c895",
   "metadata": {},
   "source": [
    "We will show a simple example using k-means clustering from the ```cluster``` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6fffbff9-783d-4fc2-83d8-48446a27741e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "194da1e0-24df-4832-857a-62f75c0d74cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gw18g940/mambaforge/envs/DAVPy2023/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=3)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=3)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=3)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cls = cluster.KMeans(n_clusters=3)\n",
    "X = diams[['carat', 'price']]\n",
    "cls.fit(X=X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e88ffb59-45ca-48df-b430-162c6839a6d4",
   "metadata": {},
   "source": [
    "Now we can visualy verify the result. First we add the classification label to our table to be use it to colour points. We specify it has a categorical variable so that seaborn then uses an appropriate colour palette:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b218cd04-2312-400a-8ad8-213a0f5a2bfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/mk/632_7fgs4v374qc935pvf9v00000gn/T/ipykernel_95914/2577989311.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  X['label'] = pd.Categorical(cls.labels_)\n"
     ]
    }
   ],
   "source": [
    "X['label'] = pd.Categorical(cls.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "2fb9f2ab-9a9e-4388-aa24-795c0b006fed",
   "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>carat</th>\n",
       "      <th>price</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1302</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1510</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1510</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.30</td>\n",
       "      <td>1260</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.31</td>\n",
       "      <td>1641</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat  price label\n",
       "1   0.30   1302     0\n",
       "2   0.30   1510     0\n",
       "3   0.30   1510     0\n",
       "4   0.30   1260     0\n",
       "5   0.31   1641     0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5e9a6af7-ed26-4a33-995e-a7a222c1c121",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=X, x='carat', y='price', hue='label');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f64fe5e4-34e4-450e-8a78-e541111aea0c",
   "metadata": {},
   "source": [
    "## Other tools\n",
    "\n",
    "scikit-learn also offers many additional tools useful in ML and we only highlight a few of them here. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2627f9fd-f4b8-418d-964b-a48ed1d6f4a9",
   "metadata": {},
   "source": [
    "### Normalizing data\n",
    "\n",
    "Certain ML models require the variables to be normalized or scaled. For example in clustering, if the metric used is simply the distance between points, the feature with the largest magnitude will dominate and to avoid that, one should normalize each feature first. All normalizers can be found in the ```preprocessing``` module and are essentially used like the models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4ad9f73b-dde0-4cd2-b6d9-eba21e921594",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b8fd2150-c585-4ac1-8ecc-c4368f670947",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = diams[['carat', 'price']]\n",
    "\n",
    "scaler = preprocessing.StandardScaler()\n",
    "\n",
    "X_norm = scaler.fit_transform(X=X)\n",
    "X_norm = pd.DataFrame(X_norm, columns=X.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "85c23a51-e12d-44a5-9c86-b7ca0151b5fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gw18g940/mambaforge/envs/DAVPy2023/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "cls = cluster.KMeans(n_clusters=3)\n",
    "cls.fit(X=X_norm)\n",
    "\n",
    "X_norm['label'] = pd.Categorical(cls.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "46e006ea-e176-4ddb-bcfd-4013f64fb4e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=X_norm, x='carat', y='price', hue='label');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eacb7251-2255-4b95-a65f-752c23b9c190",
   "metadata": {},
   "source": [
    "### Metrics\n",
    "\n",
    "Another very important module contains a large choice of metrics read to use. For example instead of manually computing the mean squared error we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "2bb4aa84-4e35-4bf2-af5c-675871995c1b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "model = linear_model.LinearRegression()\n",
    "\n",
    "X=diams[['carat']]\n",
    "\n",
    "res = model.fit(X=X, y=diams.price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "eefdeaaa-105e-412a-a23e-b2b2b72d022b",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = res.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "90923364-7b07-43dd-bb07-bd01233985f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "d0ef7e64-835d-4fea-98d3-2dc81f7144b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(308,)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "428ac757-615f-4cc8-9d90-9bd3f755df02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1240839.6897795375"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.mean_squared_error(diams.price, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf276de8-4dce-4f3a-8df9-e45d7a9e83a5",
   "metadata": {},
   "source": [
    "For classification we can use for example the accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "32fef3d0-7ece-4a46-b685-1c51a715d8e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression()\n",
    "model.fit(X=diams[['carat']], y=diams.price_cat)\n",
    "\n",
    "pred = model.predict(diams[['carat']])#pd.DataFrame({'carat': np.arange(0,1,0.1)}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "62bd6af7-6e5a-4750-a8db-345deae44909",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9642857142857143"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.accuracy_score(y_true=diams.price_cat, y_pred=pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b45adeb-d795-4b30-ace3-a38bab4e99bb",
   "metadata": {},
   "source": [
    "### Pipelines\n",
    "\n",
    "Finally we can incorporate multiple parts of our process into a single pipeline. For example if we need to first normalize and then cluster data, we can add both process into a single pipeline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "cee294d5-a5a9-420f-870a-1848eb458883",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "81ca528c-a47f-4c32-b5d7-6664908b9a99",
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe = Pipeline([('normalize', preprocessing.StandardScaler()), ('cluster', cluster.KMeans(n_clusters=3))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c93b54d0-97e4-4676-972f-43ac70ffd96d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gw18g940/mambaforge/envs/DAVPy2023/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;normalize&#x27;, StandardScaler()),\n",
       "                (&#x27;cluster&#x27;, KMeans(n_clusters=3))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;normalize&#x27;, StandardScaler()),\n",
       "                (&#x27;cluster&#x27;, KMeans(n_clusters=3))])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">StandardScaler</label><div class=\"sk-toggleable__content\"><pre>StandardScaler()</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=3)</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('normalize', StandardScaler()),\n",
       "                ('cluster', KMeans(n_clusters=3))])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "a6c19c67-8fbe-45e4-bb97-816a225cc366",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([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, 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, 0, 1, 1, 1, 1, 1, 1, 1, 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, 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, 1, 1, 1, 1, 1, 1, 1, 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, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 1, 1, 1, 1, 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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "      dtype=int32)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.named_steps['cluster'].labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "68927c9f-2ac4-4b53-a6db-c1b96e0df060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=diams, x='carat', y='price', hue=pd.Categorical(pipe.named_steps['cluster'].labels_));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd4786e2-6de7-45e1-8fe8-e1894cd69258",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "1. In the penguins dataset, do a linear regression between the ```flipper_length_mm``` and ```body_mass_g``` features and plot the result. You might run into an error: carefully read the error and try to fix the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "252da2d3-2c3a-45f6-baeb-ed4e5014aa6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "penguins = pd.read_csv('https://raw.githubusercontent.com/allisonhorst/palmerpenguins/master/inst/extdata/penguins.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f14905a6-1b50-4db9-afd1-b51427323f56",
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   "source": [
    "2. Do again a linear regression but this time add a polynomial feature (e.g. 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfe4dc3f-0015-44a8-9677-f589c2c573e1",
   "metadata": {},
   "source": [
    "3. Subselect the Gentoo species and run a logistic regression to classify penguins as male/female based on the ```body_mass_g``` feature. Use the ```liblinear``` solver option."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4052d6c-96f8-425c-bf2c-4f4a71289258",
   "metadata": {},
   "source": [
    "4. Try to cluster the ```flipper_length_mm``` vs ```bill_length_mm``` features using ```SpectralClustering``` with 3 clusters. Do the cluster first without then with applying the standard scaler to the input"
   ]
  }
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