altescy/sql_gd.ipynb

## sql_gd.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SQLで機械学習する\n",
    "===\n",
    "\n",
    "\n",
    "### 準備\n",
    "\n",
    "```\n",
    "$ docker run --rm -d -p3306:3306 \\\n",
    "    -e MYSQL_RANDOM_ROOT_PASSWORD='yes' \\\n",
    "    -e MYSQL_DATABASE='mysql' \\\n",
    "    -e MYSQL_USER='user' \\\n",
    "    -e MYSQL_PASSWORD='password' \\\n",
    "    mysql:8.0\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sqlalchemy.engine.result.ResultProxy at 0x7fe800801240>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymysql\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sqlalchemy import create_engine\n",
    "import warnings\n",
    "%matplotlib inline\n",
    "\n",
    "warnings.filterwarnings('ignore')\n",
    "pymysql.install_as_MySQLdb()\n",
    "\n",
    "np.random.seed(128)\n",
    "\n",
    "db_settings = {\n",
    "    \"host\": 'localhost',\n",
    "    \"database\": 'mysql',\n",
    "    \"user\": 'user',\n",
    "    \"password\": 'password',\n",
    "    \"port\":3306\n",
    "}\n",
    "\n",
    "conn = create_engine('mysql://{user}:{password}@{host}:{port}/{database}'.format(**db_settings))\n",
    "conn.execute('set @@cte_max_recursion_depth = 10000')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最急降下法\n",
    "\n",
    "$$\n",
    "\\mathrm{argmin}_{x} \\,\\, \\mathcal{f}(x), \\,\\,\\,\\,\\, \\mathrm{where} \\,\\,\\, \\mathcal{f}(x) = x^2 - 6x + 9\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial\\mathcal{f}}{\\partial x} = 2x - 6\\\\\n",
    "w \\leftarrow w - \\eta \\frac{\\partial\\mathcal{f}}{\\partial x}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>iter</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>197</td>\n",
       "      <td>2.941</td>\n",
       "      <td>0.003</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   iter      x      y\n",
       "0   197  2.941  0.003"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "query = '''\n",
    "with\n",
    "    recursive gd(iter, x, y) as (\n",
    "        select\n",
    "            0, cast(0.0 as decimal(6,3)), cast(9 as decimal(6,3))\n",
    "        union all\n",
    "        select\n",
    "            iter+1, x-0.01*(2.0*x-6.0), pow(x-0.01*(2.0*x-6.0),2)-6*(x-0.01*(2.0*x-6.0)) + 9 \n",
    "        from\n",
    "            gd\n",
    "        where\n",
    "            iter < 1000\n",
    "            and y - (pow(x-0.1*(2.0*x-6.0),2)-6*(x-0.1*(2.0*x-6.0)) + 9) > 0.001\n",
    "    )\n",
    "select * from gd order by iter desc limit 1\n",
    "'''\n",
    "\n",
    "pd.read_sql(query, conn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 線形回帰\n",
    "\n",
    "$$\n",
    "\\mathrm{argmin}_{a, b} \\,\\, \\mathcal{L}, \\,\\,\\,\\,\\, \\mathrm{where} \\,\\,\\, \\mathcal{L} = \\frac{1}{2N} \\sum_{i=1}^{N}(a+bx_i-y_i)^2\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial\\mathcal{L}}{\\partial a} = \\frac{1}{N} \\sum_{i=1}^{N}(a+bx_i-y_i)\\\\\n",
    "\\frac{\\partial\\mathcal{L}}{\\partial b} = \\frac{1}{N} \\sum_{i=1}^{N}(a+bx_i-y_i)x_i\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 30\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df['x'] = np.random.uniform(10, size=N)\n",
    "df['y'] = -3 * df['x'] + 1 + np.random.normal(scale=3.0, size=df['x'].shape)\n",
    "\n",
    "\n",
    "df.to_sql(con=conn, name='lr', index=False, if_exists='replace')\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(df['x'], df['y'], 'o')\n",
    "plt.title(\"\")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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>iter</th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0.34115</td>\n",
       "      <td>-2.84881</td>\n",
       "      <td>3.31067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   iter        a        b     loss\n",
       "0    18  0.34115 -2.84881  3.31067"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "query = '''\n",
    "\n",
    "with\n",
    "    recursive agg as (\n",
    "        select\n",
    "            sum(x) s_x,\n",
    "            sum(y) s_y,\n",
    "            sum(x*x) s_x2,\n",
    "            sum(y*y) s_y2,\n",
    "            sum(x*y) s_xy,\n",
    "            count(*) n\n",
    "        from lr\n",
    "    ),\n",
    "    gd(iter, a, b, loss) as (\n",
    "        select\n",
    "            0, cast(1.0 as decimal(10, 5)), cast(1.0 as decimal(10, 5)), cast(100.0 as decimal(10, 5))\n",
    "        from lr\n",
    "        union all\n",
    "        select\n",
    "            iter+1,\n",
    "            a-0.01*(n*a+b*s_x-s_y)/n,\n",
    "            b-0.01*(a*s_x+b*s_x2-s_xy)/n,\n",
    "            (n*pow(a-0.01*(n*a+b*s_x-s_y)/n,2)\n",
    "             +pow(b-0.01*(a*s_x+b*s_x2-s_xy),2)*s_x2\n",
    "             +s_y2\n",
    "             +2*(a-0.01*(n*a+b*s_x-s_y)/n)*(b-0.01*(a*s_x+b*s_x2-s_xy))*s_x\n",
    "             -2*(a-0.01*(n*a+b*s_x-s_y)/n)*s_y\n",
    "             -2*(b-0.01*(a*s_x+b*s_x2-s_xy))*s_xy)/(2*n)\n",
    "        from\n",
    "            gd, agg\n",
    "        where\n",
    "            iter < 5000\n",
    "            and loss > 0.1\n",
    "            and abs(\n",
    "                loss-(n*pow(a-0.01*(n*a+b*s_x-s_y)/n,2)\n",
    "                +pow(b-0.01*(a*s_x+b*s_x2-s_xy),2)*s_x2\n",
    "                +s_y2\n",
    "                +2*(a-0.01*(n*a+b*s_x-s_y)/n)*(b-0.01*(a*s_x+b*s_x2-s_xy))*s_x\n",
    "                -2*(a-0.01*(n*a+b*s_x-s_y)/n)*s_y\n",
    "                -2*(b-0.01*(a*s_x+b*s_x2-s_xy))*s_xy)/(2*n)) > 0.01\n",
    "    )\n",
    "select * from gd order by iter desc limit 1\n",
    "'''\n",
    "\n",
    "result = pd.read_sql(query, conn)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = result['a'].values[-1]\n",
    "b = result['b'].values[-1]\n",
    "x_line = np.linspace(0, 10, 100)\n",
    "y_line = a + b * x_line\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(df['x'], df['y'], 'o')\n",
    "plt.plot(x_line, y_line, label='predict')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}