14 迴歸法預測函數.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14 迴歸法預測函數\n",
    "\n",
    "我們認真的來做一下數據分析!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 線性迴歸"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 做一條直線\n",
    "\n",
    "我們來一條線, 比如說\n",
    "\n",
    "$$f(x) = 1.2x + 0.8$$\n",
    "\n",
    "準備好個 50 個點"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 5, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = 1.2*x + 0.8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "畫出圖形來。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f41759ae898>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mri5bRHKCgvs8zn3uY5HNP1L19Ufh4O/80aItHavez95cEa55ddkiklP0zMnz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\niJ9RcIuI+Jn/B5B1RabyuRYGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41759ae630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "plt.plot(x, 1.2*x+0.8, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 加入 noise 項, 看來更真實\n",
    "\n",
    "大概的想法就是, 我們真實世界的問題, 化成函數, 我們假設背後有個美好的函數。但相信我們很少看到真實世界的資料那麼漂亮。在統計上, 我們就是假設\n",
    "\n",
    "$$f(x) + \\varepsilon(x)$$\n",
    "\n",
    "也就是都有個 noise 項。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = 1.2*x + 0.8 + 0.6*np.random.randn(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4172e48c18>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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STFeXOedmA7OTNYjaZtXrysqrfU5N3xcRSXehqJysbVbdpkV2tc+p6fsiIuku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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4172e48be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "plt.plot(x, 1.2*x + 0.8, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 做線性迴歸找出那條線"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "做線性迴歸有很多套件, 但我們這裡用 `sklearn.svm` 裡的 `SVR` 來做各種迴歸。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "svr_lin = SVR(kernel='linear', C=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = x.reshape(len(x),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma='auto',\n",
       "  kernel='linear', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr_lin.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y = svr_lin.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f41634a52e8>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EJI5QBbeZnWhmS8xsqZkVp7ueoJnZk2a2yswWpLuWVDCzPc3sHTNbZGYLzey6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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41634a5dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, Y, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 標準函數訓練及測試\n",
    "\n",
    "#### 分訓練資料、測試資料\n",
    "\n",
    "一般我們想要看算出來的逼近函數在預測上是不是可靠, 會把一些資料留給「測試」, 就是不讓電腦在計算時「看到」這些測試資料。等函數學成了以後, 再來測試準不準確。這是我們可以用\n",
    "\n",
    "    sklearn.cross_validation\n",
    "    \n",
    "裡的\n",
    "\n",
    "    train_test_split\n",
    "    \n",
    "來亂數選一定百分比的資料來用。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "把原來的 `x`, `y` 中的 80% 給 training data, 20% 給 testing data。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我們在「訓練」這個函數時只有以下這些資料。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10cf41710>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YUCONQunbqvtwsXUBV155Ze8Vw5UVllQ/hgE1yiiUvh2FPsDFK/+9+c1vHaqssKT6Mgyo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\nI4Wi21EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cef2198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 用訓練資料來 fit 函數\n",
    "\n",
    "記得現在我們只用 80% 的資料去訓練。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma='auto',\n",
       "  kernel='linear', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr_lin = SVR(kernel='linear', C=1e3)\n",
    "X_train = x_train.reshape(len(x_train),1)\n",
    "svr_lin.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y_train = svr_lin.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4163278198>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lbCytN+Mi/XZgFgxtd0IbaBKCuwm6J7dr/sxJam9rlUlqb2vV/JmTUlnjrfRbwPi21vD9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\nA0DGENwAkDEENwBkDMENABnz/zOUAJBhQNnJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41632780b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train)\n",
    "plt.plot(x_train, Y_train, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 用測試資料試試我們預測準不準"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_test = x_test.reshape(len(x_test),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y_test = svr_lin.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mse = np.sum((Y_test-y_test)**2) / len(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39921372448740139"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f4163208a90>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4do6ImJI01e5DbE9nXfmq31T52iWuv8rXX+Vrl/K7/ixDJT+T9Pu2P277Ykl3SvpxtwsB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4163208e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_test, y_test)\n",
    "plt.scatter(x_test, Y_test, c='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. 不是線性的目標函數\n",
    "\n",
    "這裡我們用個非線性的函數來生假數據:\n",
    "\n",
    "$$f(x) = \\sin(3.2x) + 0.8x$$\n",
    "\n",
    "一樣準備加上一些 noise。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 生成假資料"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 5, 50)\n",
    "y = np.sin(3.2*x) + 0.8*x + 0.3*np.random.randn(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f41630a4cc0>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eCg5Ut/Mvty0jf2iH20zctyEPk1L8Zl/17AUXwOo7rKTEhEmHgxCzQBL3KPsr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\nigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41631a0898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 準備生這個函數"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "svr_rbf = SVR(kernel='rbf', C=1e3, gamma=0.3)\n",
    "svr_lin = SVR(kernel='linear', C=1e3)\n",
    "svr_poly = SVR(kernel='poly', C=1e3, degree=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = x_train.reshape(len(x_train), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=1000.0, cache_size=200, coef0=0.0, degree=4, epsilon=0.1, gamma='auto',\n",
       "  kernel='poly', max_iter=-1, shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svr_rbf.fit(X_train,y_train)\n",
    "svr_lin.fit(X_train,y_train)\n",
    "svr_poly.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 看看訓練成果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = x.reshape(len(x),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y_rbf = svr_rbf.predict(X)\n",
    "Y_lin = svr_lin.predict(X)\n",
    "Y_poly = svr_poly.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4162c3bd68>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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D8z9gSKch7ruZuRoOZDUsn1QUOi6GUqD7ED18MnEDz4D4NAiWxq2tJQldCJwv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\nhPATktCFEMJP/H9Z2WwxQbLevQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4162cc4908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "\n",
    "plt.plot(x, Y_rbf, label='rbf')\n",
    "plt.plot(x, Y_lin, label='linear')\n",
    "plt.plot(x, Y_poly, label='polynomial')\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}