06.04-Feature-Engineering.ipynb

{
 "cells": [
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "---\n",
    "---\n",
    "# Feature Engineering\n",
    "\n",
    "---\n",
    "---\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) | [Contents](Index.ipynb) | [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "numerical data in a tidy, ``[n_samples, n_features]`` format VS. Real world. \n",
    "\n",
    "**Feature engineering** taking whatever information you have about your problem and turning it into numbers that you can use to build your ``feature matrix``.\n",
    "\n",
    "In this section, we will cover a few common examples of feature engineering tasks: \n",
    "- features for representing *categorical data*, \n",
    "- features for representing *text*, and \n",
    "- features for representing *images*.\n",
    "- *derived features* for increasing model complexity\n",
    "- *imputation* of missing data.\n",
    "\n",
    "Often this process is known as *vectorization*\n",
    "- as it involves converting arbitrary data into well-behaved vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Categorical Features\n",
    "\n",
    "One common type of non-numerical data is *categorical* data.\n",
    "\n",
    "Housing prices, \n",
    "- \"price\" and \"rooms\"\n",
    "- \"neighborhood\" information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:47:42.438325Z",
     "start_time": "2023-07-01T07:47:42.435177Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "data = [\n",
    "    {'price': 850000, 'rooms': 4, 'neighborhood': 'Queen Anne'},\n",
    "    {'price': 700000, 'rooms': 3, 'neighborhood': 'Fremont'},\n",
    "    {'price': 650000, 'rooms': 3, 'neighborhood': 'Wallingford'},\n",
    "    {'price': 600000, 'rooms': 2, 'neighborhood': 'Fremont'}\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "You might be tempted to encode this data with a straightforward numerical mapping:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:27.779127Z",
     "start_time": "2020-05-18T14:03:27.776656Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "{'Queen Anne': 1, 'Fremont': 2, 'Wallingford': 3};\n",
    "# It turns out that this is not generally a useful approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "A fundamental assumption: numerical features reflect algebraic quantities.\n",
    "\n",
    "- *Queen Anne < Fremont < Wallingford*\n",
    "- *Wallingford - Queen Anne = Fremont*\n",
    "\n",
    "It does not make much sense.\n",
    "\n",
    "**One-hot encoding** (Dummy coding) effectively creates extra columns indicating the presence or absence of a category with a value of 1 or 0, respectively.\n",
    "- When your data comes as a list of dictionaries\n",
    "    - Scikit-Learn's ``DictVectorizer`` will do this for you:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:28.404603Z",
     "start_time": "2020-05-18T14:03:27.780783Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[     0,      1,      0, 850000,      4],\n",
       "       [     1,      0,      0, 700000,      3],\n",
       "       [     0,      0,      1, 650000,      3],\n",
       "       [     1,      0,      0, 600000,      2]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_extraction import DictVectorizer\n",
    "vec = DictVectorizer(sparse=False, dtype=int )\n",
    "vec.fit_transform(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Notice\n",
    "- the 'neighborhood' column has been expanded into **three** separate columns (why not four?)\n",
    "- representing the three neighborhood labels, and that each row has a 1 in the column associated with its neighborhood.\n",
    "\n",
    "To see the meaning of each column, you can inspect the feature names:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:28.410602Z",
     "start_time": "2020-05-18T14:03:28.406493Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['neighborhood=Fremont',\n",
       " 'neighborhood=Queen Anne',\n",
       " 'neighborhood=Wallingford',\n",
       " 'price',\n",
       " 'rooms']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec.get_feature_names()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "There is one clear disadvantage of this approach: \n",
    "- if your category has many possible values, this can *greatly* increase the size of your dataset.\n",
    "    - However, because the encoded data contains mostly zeros, a sparse output can be a very efficient solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:28.418939Z",
     "start_time": "2020-05-18T14:03:28.412935Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x5 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 12 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec = DictVectorizer(sparse=True, dtype=int)\n",
    "vec.fit_transform(data) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Many (though not yet all) of the Scikit-Learn estimators accept such sparse inputs when fitting and evaluating models. \n",
    "\n",
    "two additional tools that Scikit-Learn includes to support this type of encoding:\n",
    "- ``sklearn.preprocessing.OneHotEncoder``\n",
    "- ``sklearn.feature_extraction.FeatureHasher`` "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also using the function of ``get_dummies`` in pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:47:49.981353Z",
     "start_time": "2023-07-01T07:47:49.964817Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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>price</th>\n",
       "      <th>rooms</th>\n",
       "      <th>neighborhood</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>850000</td>\n",
       "      <td>4</td>\n",
       "      <td>Queen Anne</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>700000</td>\n",
       "      <td>3</td>\n",
       "      <td>Fremont</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>650000</td>\n",
       "      <td>3</td>\n",
       "      <td>Wallingford</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>600000</td>\n",
       "      <td>2</td>\n",
       "      <td>Fremont</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    price  rooms neighborhood\n",
       "0  850000      4   Queen Anne\n",
       "1  700000      3      Fremont\n",
       "2  650000      3  Wallingford\n",
       "3  600000      2      Fremont"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.DataFrame(data)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:47:59.536469Z",
     "start_time": "2023-07-01T07:47:59.518786Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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>price</th>\n",
       "      <th>rooms</th>\n",
       "      <th>neighborhood_Fremont</th>\n",
       "      <th>neighborhood_Queen Anne</th>\n",
       "      <th>neighborhood_Wallingford</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>850000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>700000</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>650000</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>600000</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    price  rooms  neighborhood_Fremont  neighborhood_Queen Anne  \\\n",
       "0  850000      4                     0                        1   \n",
       "1  700000      3                     1                        0   \n",
       "2  650000      3                     0                        0   \n",
       "3  600000      2                     1                        0   \n",
       "\n",
       "   neighborhood_Wallingford  \n",
       "0                         0  \n",
       "1                         0  \n",
       "2                         1  \n",
       "3                         0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.get_dummies(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Text Features\n",
    "\n",
    "Another common need in feature engineering is to convert text to a set of representative numerical values.\n",
    "\n",
    "Most automatic mining of social media data relies on some form of encoding the text as numbers.\n",
    "- One of the simplest methods of encoding data is by *word counts*: \n",
    "    - you take each snippet of text, count the occurrences of each word within it, and put the results in a table.\n",
    "\n",
    "For example, consider the following set of three phrases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:51:32.760883Z",
     "start_time": "2023-07-01T07:51:32.758329Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "sample = ['problem of evil',\n",
    "          'evil queen',\n",
    "          'horizon problem']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For a vectorization of this data based on word count, we could construct a column representing the word \"problem,\" the word \"evil,\" the word \"horizon,\" and so on.\n",
    "\n",
    "While doing this by hand would be possible, the tedium can be avoided by using Scikit-Learn's ``CountVectorizer``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:51:37.177307Z",
     "start_time": "2023-07-01T07:51:36.604580Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<3x5 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 7 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "\n",
    "vec = CountVectorizer()\n",
    "X = vec.fit_transform(sample)\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The result is a sparse matrix recording the number of times each word appears; \n",
    "\n",
    "it is easier to inspect if we convert this to a ``DataFrame`` with labeled columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:51:40.772100Z",
     "start_time": "2023-07-01T07:51:40.764711Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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>evil</th>\n",
       "      <th>horizon</th>\n",
       "      <th>of</th>\n",
       "      <th>problem</th>\n",
       "      <th>queen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   evil  horizon  of  problem  queen\n",
       "0     1        0   1        1      0\n",
       "1     1        0   0        0      1\n",
       "2     0        1   0        1      0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd \n",
    "pd.DataFrame(X.toarray(), columns=vec.get_feature_names())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Problem: The raw word counts put too much weight on words that appear very frequently.\n",
    "\n",
    "*term frequency-inverse document frequency* (**TF–IDF**) weights the word counts by a measure of how often they appear in the documents.\n",
    "\n",
    "The syntax for computing these features is similar to the previous example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:52:39.030659Z",
     "start_time": "2023-07-01T07:52:39.017065Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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>evil</th>\n",
       "      <th>horizon</th>\n",
       "      <th>of</th>\n",
       "      <th>problem</th>\n",
       "      <th>queen</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.517856</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.680919</td>\n",
       "      <td>0.517856</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.605349</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.795961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.795961</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.605349</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       evil   horizon        of   problem     queen\n",
       "0  0.517856  0.000000  0.680919  0.517856  0.000000\n",
       "1  0.605349  0.000000  0.000000  0.000000  0.795961\n",
       "2  0.000000  0.795961  0.000000  0.605349  0.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "vec = TfidfVectorizer()\n",
    "X = vec.fit_transform(sample)\n",
    "pd.DataFrame(X.toarray(), columns=vec.get_feature_names())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For an example of using TF-IDF in a classification problem, see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Image Features\n",
    "The simplest approach is what we used for the digits data in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb): **simply using the pixel values themselves**.\n",
    "- But depending on the application, such approaches may not be optimal.\n",
    "- A comprehensive summary of feature extraction techniques for images in the [Scikit-Image project](http://scikit-image.org).\n",
    "\n",
    "For one example of using Scikit-Learn and Scikit-Image together, see [Feature Engineering: Working with Images](05.14-Image-Features.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Derived Features\n",
    "\n",
    "Another useful type of feature is one that is mathematically derived from some input features.\n",
    "\n",
    "We saw an example of this in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) when we constructed *polynomial features* from our input data.\n",
    "\n",
    "To convert a linear regression into a polynomial regression \n",
    "- not by changing the model\n",
    "- but by transforming the input!\n",
    "    - *basis function regression*, and is explored further in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb).\n",
    "\n",
    "For example, this data clearly cannot be well described by a straight line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:53:33.619522Z",
     "start_time": "2023-07-01T07:53:32.936376Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAD4CAYAAADFAawfAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAOUElEQVR4nO3dUWid93nH8d9vsrqeJimC+dBGcjbRG8GW0MgIk2IIWdpVyRoyEXqRQjvWG2+jjJYNlakXLbvKhaCk28WGSbq1NGnXpbIYIYka6ELpRT2OLa/K6mh0xaWWsvlkQ02yHlZFeXahI1fWjnzek5z3vI+s7weEj973td6HP0dfy+95j+2IEAAgr1+pegAAwPURagBIjlADQHKEGgCSI9QAkNyRMr7o0aNHY3x8vIwvDQA3pHPnzr0SEfVO+0oJ9fj4uBqNRhlfGgBuSLZ/st8+Ln0AQHKEGgCSI9QAkByhBoDkCDUAJNf1rg/bE5L+ftem90n6fEQ8WtZQAHCQLC6vaX5pVesbLY2O1DQ7PaGZybG+ff2uoY6IVUl3SpLtIUlrks70bQIAOMAWl9c0t7Ci1uaWJGlto6W5hRVJ6luse7308UFJ/x4R+97vBwCHyfzS6tVI72htbml+abVv5+g11A9L+nqnHbZP2W7YbjSbzbc/GQAcAOsbrZ62vxWFQ237HZIelPQPnfZHxOmImIqIqXq947sgAeCGMzpS62n7W9HLT9T3SzofEf/Zt7MDwAE3Oz2h2vDQNdtqw0OanZ7o2zl6+bc+PqZ9LnsAwGG184JhpXd9SJLtd0n6HUl/2LczA8ANYmZyrK9h3qtQqCPi55J+rbQpAAD74p2JAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHKEGgCSI9QAkByhBoDkCDUAJEeoASA5Qg0AyRFqAEiOUANAcoQaAJIj1ACQHKEGgOQINQAkR6gBIDlCDQDJEWoASI5QA0ByhBoAkisUatsjtp+y/ZLti7Y/UPZgAIBtRwoe9yVJz0XER22/Q9K7SpwJALBL11DbfrekuyX9gSRFxC8k/aLcsQAAO4pc+nifpKakv7W9bPsx2zftPcj2KdsN241ms9n3QQHgsCoS6iOSjkv664iYlPQ/kv5870ERcToipiJiql6v93lMADi8ioT6sqTLEXG2/flT2g43AGAAuoY6Iv5D0k9tT7Q3fVDSD0udCgBwVdG7Pv5E0hPtOz5+LOmT5Y0EANitUKgj4oKkqXJHAQB0wjsTASA5Qg0AyRFqAEiOUANAcoQaAJIj1ACQHKEGgOQINQAkR6gBIDlCDQDJEWoASI5QA0ByhBoAkiPUAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHKEGgCSI9QAkByhBoDkCDUAJHekyEG2L0l6TdKWpDciYqrMoQAAv1Qo1G2/HRGvlDYJAKAjLn0AQHJFQx2Svm37nO1TnQ6wfcp2w3aj2Wz2b0IAOOSKhvpkRByXdL+kT9m+e+8BEXE6IqYiYqper/d1SAA4zAqFOiLW279ekXRG0okyhwIA/FLXUNu+yfYtO48lfVjSi2UPBgDYVuSuj/dIOmN75/gnI+K5UqcCAFzVNdQR8WNJ7x/ALACADrg9DwCSI9QAkByhBoDkCDUAJEeoASA5Qg0AyRFqAEiOUANAcoQaAJIj1ACQHKEGgOQINQAkR6gBIDlCDQDJEWoASI5QA0ByhBoAkiPUAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHJHih5oe0hSQ9JaRDzQ70EWl9c0v7Sq9Y2WRkdqmp2e0MzkWL9PAwAHTuFQS/q0pIuS3t3vIRaX1zS3sKLW5pYkaW2jpbmFFUki1gAOvUKXPmwfk/QRSY+VMcT80urVSO9obW5pfmm1jNMBwIFS9Br1o5I+K+nN/Q6wfcp2w3aj2Wz2NMT6Rqun7QBwmHQNte0HJF2JiHPXOy4iTkfEVERM1ev1noYYHan1tB0ADpMiP1GflPSg7UuSviHpXttf6+cQs9MTqg0PXbOtNjyk2emJfp4GAA6krqGOiLmIOBYR45IelvSdiPh4P4eYmRzTIw/dobGRmixpbKSmRx66gxcSAUC93fVRqpnJMcIMAB30FOqIeEHSC6VMAgDoiHcmAkByhBoAkiPUAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHKEGgCSI9QAkByhBoDkCDUAJEeoASA5Qg0AyRFqAEiOUANAcoQaAJIj1ACQHKEGgOQINQAkR6gBIDlCDQDJEWoASO5ItwNsv1PSdyX9avv4pyLiC2UPBqA6i8trml9a1fpGS6MjNc1OT2hmcqzqsQ6trqGW9L+S7o2I120PS/qe7Wcj4vslzwagAovLa5pbWFFrc0uStLbR0tzCiiQR64p0vfQR215vfzrc/ohSpwJQmfml1auR3tHa3NL80mpFE6HQNWrbQ7YvSLoi6fmIONvhmFO2G7YbzWazz2MCGJT1jVZP21G+QqGOiK2IuFPSMUknbN/e4ZjTETEVEVP1er3PYwIYlNGRWk/bUb6e7vqIiA1JL0i6r4xhAFRvdnpCteGha7bVhoc0Oz1R0UToGmrbddsj7cc1SR+S9FLJcwGoyMzkmB556A6NjdRkSWMjNT3y0B28kFihInd93CrpK7aHtB32b0bE0+WOBaBKM5NjhDmRrqGOiB9ImhzALACADnhnIgAkR6gBIDlCDQDJEWoASI5QA0ByhBoAkiPUAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHKEGgCSI9QAkByhBoDkCDUAJEeoASA5Qg0AyRFqAEiOUANAcoQaAJIj1ACQHKEGgOSOdDvA9m2SvirpvZLelHQ6Ir5U9mC4vsXlNc0vrWp9o6XRkZpmpyc0MzlW9VgAStA11JLekPRnEXHe9i2Sztl+PiJ+WPJs2Mfi8prmFlbU2tySJK1ttDS3sCJJxBq4AXW99BERL0fE+fbj1yRdlEQNKjS/tHo10jtam1uaX1qtaCIAZerpGrXtcUmTks522HfKdsN2o9ls9mk8dLK+0eppO4CDrXCobd8s6VuSPhMRr+7dHxGnI2IqIqbq9Xo/Z8QeoyO1nrYDONgKhdr2sLYj/URELJQ7ErqZnZ5QbXjomm214SHNTk9UNBGAMhW568OSHpd0MSK+WP5I6GbnBUPu+gAOhyJ3fZyU9AlJK7YvtLd9LiKeKW0qdDUzOUaYgUOia6gj4nuSPIBZAAAd8M5EAEiOUANAcoQaAJIj1ACQHKEGgOQINQAkR6gBIDlCDQDJEWoASI5QA0ByhBoAkiPUAJAcoQaA5Ag1ACRHqAEgOUINAMkRagBIjlADQHKEGgCSI9QAkByhBoDkCDUAJEeoASA5Qg0AyR3pdoDtL0t6QNKViLi9/JGA/ltcXtP80qrWN1oaHalpdnpCM5NjVY8FFFLkJ+q/k3RfyXMApVlcXtPcworWNloKSWsbLc0trGhxea3q0YBCuoY6Ir4r6b8HMAtQivmlVbU2t67Z1trc0vzSakUTAb3p2zVq26dsN2w3ms1mv74s8Latb7R62g5k07dQR8TpiJiKiKl6vd6vLwu8baMjtZ62A9lw1wdueLPTE6oND12zrTY8pNnpiYomAnrT9a4P4KDbubuDuz5wUBW5Pe/rku6RdNT2ZUlfiIjHyx4M6KeZyTHCjAOra6gj4mODGAQA0BnXqAEgOUINAMkRagBIjlADQHKOiP5/Ubsp6Sdv8bcflfRKH8fpF+bqDXP1hrl6cyPO9RsR0fHdgqWE+u2w3YiIqarn2Iu5esNcvWGu3hy2ubj0AQDJEWoASC5jqE9XPcA+mKs3zNUb5urNoZor3TVqAMC1Mv5EDQDYhVADQHKVhNr2l21fsf3iPvtt+y9t/8j2D2wfTzLXPbZ/ZvtC++PzA5rrNtv/ZPui7X+1/ekOxwx8zQrONfA1s/1O2/9s+1/ac/1Fh2OqWK8ic1XyHGufe8j2su2nO+yr5HuywFxVfU9esr3SPmejw/7+rldEDPxD0t2Sjkt6cZ/9vyvpWUmWdJeks0nmukfS0xWs162Sjrcf3yLp3yT9ZtVrVnCuga9Zew1ubj8elnRW0l0J1qvIXJU8x9rn/lNJT3Y6f1XfkwXmqup78pKko9fZ39f1quQn6uj+H+b+nqSvxrbvSxqxfWuCuSoRES9HxPn249ckXZS09x9XHviaFZxr4Npr8Hr70+H2x95XzatYryJzVcL2MUkfkfTYPodU8j1ZYK6s+rpeWa9Rj0n66a7PLytBANo+0P6r67O2f2vQJ7c9LmlS2z+N7Vbpml1nLqmCNWv/dfmCpCuSno+IFOtVYC6pmufYo5I+K+nNffZX9fx6VNefS6pmvULSt22fs32qw/6+rlfWULvDtgw/eZzX9vvx3y/pryQtDvLktm+W9C1Jn4mIV/fu7vBbBrJmXeaqZM0iYisi7pR0TNIJ27fvOaSS9Sow18DXy/YDkq5ExLnrHdZhW6nrVXCuqr4nT0bEcUn3S/qU7bv37O/remUN9WVJt+36/Jik9YpmuSoiXt35q2tEPCNp2PbRQZzb9rC2Y/hERCx0OKSSNes2V5Vr1j7nhqQXJN23Z1elz7H95qpovU5KetD2JUnfkHSv7a/tOaaK9eo6V1XPr4hYb/96RdIZSSf2HNLX9coa6n+U9PvtV07vkvSziHi56qFsv9e2249PaHv9/msA57WkxyVdjIgv7nPYwNesyFxVrJntuu2R9uOapA9JemnPYVWsV9e5qliviJiLiGMRMS7pYUnfiYiP7zls4OtVZK6Knl832b5l57GkD0vae6dYX9erkv+F3B3+w1xtv7CiiPgbSc9o+1XTH0n6uaRPJpnro5L+2PYbklqSHo72S7wlOynpE5JW2tc3Jelzkn5912xVrFmRuapYs1slfcX2kLa/cb8ZEU/b/qNdc1WxXkXmquo59v8kWK8ic1WxXu+RdKb958MRSU9GxHNlrhdvIQeA5LJe+gAAtBFqAEiOUANAcoQaAJIj1ACQHKEGgOQINQAk93+yP1SHKCjRUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "y = np.array([4, 2, 1, 3, 7])\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Still, we can fit a line to the data using ``LinearRegression`` and get the optimal result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:53:37.568915Z",
     "start_time": "2023-07-01T07:53:37.336543Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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 sklearn.linear_model import LinearRegression\n",
    "X = x[:, np.newaxis]\n",
    "model = LinearRegression().fit(X, y)\n",
    "yfit = model.predict(X)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We need a more sophisticated model to describe the relationship between $x$ and $y$.\n",
    "- One approach to this is to transform the data, \n",
    "    - adding extra columns of features to drive more flexibility in the model.\n",
    "\n",
    "For example, we can add polynomial features to the data this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-01T07:54:02.724570Z",
     "start_time": "2023-07-01T07:54:02.720060Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.   1.   1.]\n",
      " [  2.   4.   8.]\n",
      " [  3.   9.  27.]\n",
      " [  4.  16.  64.]\n",
      " [  5.  25. 125.]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly = PolynomialFeatures(degree=3, include_bias=False)\n",
    "X2 = poly.fit_transform(X)\n",
    "print(X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The derived feature matrix has one column representing $x$, and a second column representing $x^2$, and a third column representing $x^3$.\n",
    "Computing a linear regression on this expanded input gives a much closer fit to our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:29.592112Z",
     "start_time": "2020-05-18T14:03:29.453076Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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": [
    "model = LinearRegression().fit(X2, y)\n",
    "yfit = model.predict(X2)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This idea of improving a model not by changing the model, but by transforming the inputs, is fundamental to many of the more powerful machine learning methods.\n",
    "\n",
    "- We explore this idea further in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) in the context of *basis function regression*.\n",
    "\n",
    "- More generally, this is one motivational path to the powerful set of techniques known as *kernel methods*, which we will explore in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Imputation of Missing Data\n",
    "\n",
    "Another common need in feature engineering is handling of missing data.\n",
    "\n",
    "- [Handling Missing Data](03.04-Missing-Values.ipynb)\n",
    "    - ``NaN`` value is used to mark missing values.\n",
    "    \n",
    "For example, we might have a dataset that looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-21T11:27:11.477011Z",
     "start_time": "2020-05-21T11:27:11.470564Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from numpy import nan\n",
    "import numpy as np\n",
    "X = np.array([[ nan, 0,   3  ],\n",
    "              [ 3,   7,   9  ],\n",
    "              [ 3,   5,   2  ],\n",
    "              [ 4,   nan, 6  ],\n",
    "              [ 8,   8,   1  ]])\n",
    "y = np.array([14, 16, -1,  8, -5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "When applying a typical machine learning model to such data, we will need to first replace such missing data with some appropriate fill value.\n",
    "\n",
    "This is known as *imputation* of missing values\n",
    "- simple method, e.g., replacing missing values with the mean of the column\n",
    "- sophisticated method, e.g., using matrix completion or a robust model to handle such data\n",
    "    - It tends to be very application-specific, and we won't dive into them here.\n",
    "\n",
    "For a baseline imputation approach, using the mean, median, or most frequent value, Scikit-Learn provides the ``Imputer`` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-21T11:28:12.917824Z",
     "start_time": "2020-05-21T11:28:12.865274Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.5, 0. , 3. ],\n",
       "       [3. , 7. , 9. ],\n",
       "       [3. , 5. , 2. ],\n",
       "       [4. , 5. , 6. ],\n",
       "       [8. , 8. , 1. ]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.impute import SimpleImputer\n",
    "imp = SimpleImputer(strategy='mean')\n",
    "X2 = imp.fit_transform(X)\n",
    "X2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We see that in the resulting data, the two missing values have been replaced with the mean of the remaining values in the column. \n",
    "\n",
    "This imputed data can then be fed directly into, for example, a ``LinearRegression`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:29.626704Z",
     "start_time": "2020-05-18T14:03:29.621708Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13.14869292, 14.3784627 , -1.15539732, 10.96606197, -5.33782027])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression().fit(X2, y)\n",
    "model.predict(X2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Feature Pipelines\n",
    "\n",
    "With any of the preceding examples, it can quickly become tedious to do the transformations by hand, especially if you wish to string together multiple steps.\n",
    "\n",
    "For example, we might want a processing pipeline that looks something like this:\n",
    "\n",
    "1. Impute missing values using the mean\n",
    "2. Transform features to quadratic\n",
    "3. Fit a linear regression\n",
    "\n",
    "To streamline this type of processing pipeline, Scikit-Learn provides a ``Pipeline`` object, which can be used as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:29.633493Z",
     "start_time": "2020-05-18T14:03:29.628784Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "model = make_pipeline(SimpleImputer(strategy='mean'),\n",
    "                      PolynomialFeatures(degree=2),\n",
    "                      LinearRegression())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This pipeline looks and acts like a standard Scikit-Learn object, and will apply all the specified steps to any input data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-18T14:03:29.643769Z",
     "start_time": "2020-05-18T14:03:29.635205Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[14 16 -1  8 -5]\n",
      "[14. 16. -1.  8. -5.]\n"
     ]
    }
   ],
   "source": [
    "model.fit(X, y)  # X with missing values, from above\n",
    "print(y)\n",
    "print(model.predict(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "All the steps of the model are applied automatically.\n",
    "\n",
    "Notice that for the simplicity of this demonstration, we've applied the model to the data it was trained on; \n",
    "- this is why it was able to perfectly predict the result (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for further discussion of this).\n",
    "\n",
    "For some examples of Scikit-Learn pipelines in action, see the following section on naive Bayes classification, as well as [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), and [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](attachment:image.png)\n",
    "\n",
    "<!--NAVIGATION-->\n",
    "< [Hyperparameters and Model Validation](06.03-Hyperparameters-and-Model-Validation.ipynb) | [Contents](Index.ipynb) | [In Depth: Naive Bayes Classification](06.05-Naive-Bayes.ipynb) >"
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