aparrish/text-prediction-with-linear-regression.ipynb

## text-prediction-with-linear-regression.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Text prediction with linear regression\n",
    "\n",
    "It's not very effective..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "pd.set_option('max_rows', 25)\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in some sonnets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "text = open(\"sonnets.txt\").read()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function maps an incoming character to a value from zero to 26 (inclusive). If the character is an alphanumeric, it maps the character's value to 1-26 (A-Z); any other character is a zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def chr2val(ch):\n",
    "    ch = ch.lower()\n",
    "    if ch.isalpha():\n",
    "        return 1 + (ord(ch) - ord('a'))\n",
    "    else:\n",
    "        return 0\n",
    "chr2val(\"z\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inverse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'h'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def val2chr(v):\n",
    "    v = int(round(v))\n",
    "    if v == 0:\n",
    "        return ' '\n",
    "    else:\n",
    "        return chr(ord('a') + v - 1)\n",
    "val2chr(7.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll make a simple list of all the bigrams in the text, represented as integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bigrams = [(chr2val(a), chr2val(b)) for a, b in zip(text.lower()[:-1], text.lower()[1:])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and then load them into a DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(bigrams, columns=[\"a\", \"b\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>18</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94721</th>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94722</th>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94723</th>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94724</th>\n",
       "      <td>15</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94725</th>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94726</th>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94727</th>\n",
       "      <td>12</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94728</th>\n",
       "      <td>15</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94729</th>\n",
       "      <td>22</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94730</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94731</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94732</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>94733 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        a   b\n",
       "0       0   6\n",
       "1       6  18\n",
       "2      18  15\n",
       "3      15  13\n",
       "4      13   0\n",
       "5       0   6\n",
       "6       6   1\n",
       "7       1   9\n",
       "8       9  18\n",
       "9      18   5\n",
       "10      5  19\n",
       "11     19  20\n",
       "...    ..  ..\n",
       "94721  19   0\n",
       "94722   0  14\n",
       "94723  14  15\n",
       "94724  15  20\n",
       "94725  20   0\n",
       "94726   0  12\n",
       "94727  12  15\n",
       "94728  15  22\n",
       "94729  22   5\n",
       "94730   5   0\n",
       "94731   0   0\n",
       "94732   0   0\n",
       "\n",
       "[94733 rows x 2 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the data look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x116454400>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wcRxTxnZ9Xeo8jMdmjG0zgEBYih0eb2xsTOscpFsFUC3VJPPqtVAMIIDxZCwg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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117a8a128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind=\"scatter\", x=\"a\", y=\"b\", alpha=0.002)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a value in the first column, we should be able to predict the value in the second column. What algorithm will we use? Why not linear regression?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = LinearRegression()\n",
    "ols.fit(df[\"a\"].values.reshape(-1, 1), df[\"b\"].values.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x117a63f60>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RhIl2TOnbbY2p4zARm9G3TQD8YSm22V40GtU6BplmAVSXapK59VwoA+DHRDLm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\nXRXv2OkEFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117a63e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind=\"scatter\", x=\"a\", y=\"b\", alpha=0.002)\n",
    "plt.plot(df[\"a\"].values, ols.predict(df[\"a\"].values.reshape(-1, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the character `a`, the linear regression predicts that the next character will be..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'j'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val2chr(ols.predict(chr2val(\"a\"))[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `j`. Good enough for me! Let's chain the predictions together and see what comes out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "jiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "ejiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "bjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "fjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "jiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "whjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "liiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "ajiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "jiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "oiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "cjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "thiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "vhjiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n",
      "kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n"
     ]
    }
   ],
   "source": [
    "for i in range(14):\n",
    "    output = [np.array([[np.random.uniform()*27]])]\n",
    "    for i in range(60):\n",
    "        nextv = ols.predict(output[-1])\n",
    "        output.append(nextv)\n",
    "    print(''.join([val2chr(i[0][0]) for i in output]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "😚👌 perfect"
   ]
  }
 ],
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