5.bias_vs_variance/ex5.bias_vs_variance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 偏差和方差"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此Notebook是配合Andrew Ng \\\"Machine Leanring\\\"中[打造实用的机器学习系统](https://github.com/loveunk/machine-learning-deep-learning-notes/blob/master/machine-learning/advice-for-appying-and-system-design.md)部分学习使用。\n",
    "\n",
    "测试用Python版本为3.6\n",
    "* 机器学习路径：https://github.com/loveunk/machine-learning-deep-learning-notes/\n",
    "* 内容正文综合参考网络资源，使用中如果有疑问请联络：https://www.kaikai.ai"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import scipy.optimize as opt\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data():\n",
    "    \"\"\"\n",
    "    说明：d['X'] shape = (12, 1)，使用 np.ravel 把它们 flattern 为 vector\n",
    "    \"\"\"\n",
    "    d = sio.loadmat('ex5data1.mat')\n",
    "    return map(np.ravel, [d['X'], d['y'], d['Xval'], d['yval'], d['Xtest'], d['ytest']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y, Xval, yval, Xtest, ytest = load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame({'water_level':X, 'flow':y})\n",
    "\n",
    "sns.lmplot('water_level', 'flow', data=df, fit_reg=False, height=7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Xval, Xtest = [np.insert(x.reshape(x.shape[0], 1), 0, np.ones(x.shape[0]), axis=1) for x in (X, Xval, Xtest)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 代价函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "代价函数公式：\n",
    "$$J(\\theta)=\\frac{1}{2m}\\sum_{i=1}^m\\left(h_{\\theta}(x^{(i)})-y^{(i)}\\right)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(theta, X, y):\n",
    "    \"\"\"\n",
    "    X: R(m*n), m records, n features\n",
    "    y: R(m)\n",
    "    theta : R(n), linear regression parameters\n",
    "    \"\"\"\n",
    "    m = X.shape[0]\n",
    "\n",
    "    inner = X @ theta - y  # R(m*1)\n",
    "\n",
    "    square_sum = inner.T @ inner\n",
    "    cost = square_sum / (2 * m)\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "303.9515255535976"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.ones(X.shape[1])\n",
    "cost(theta, X, y)\n",
    "\n",
    "# 输出值约为 303.951"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 正则化代价函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正则化代价函数公式：\n",
    "$$J(\\theta)=\\frac{1}{2m}\\left(\\sum_{i=1}^m\\left(h_{\\theta}(x^{(i)})-y^{(i)}\\right)^2\\right) + \\dfrac{\\lambda}{2m}\\left(\\sum_{j=1}^n \\theta_j^2\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularized_cost(theta, X, y, l=1):\n",
    "    \"\"\"\n",
    "    X: R(m*n), m records, n features\n",
    "    y: R(m)\n",
    "    theta : R(n), linear regression parameters\n",
    "    l: lambda constant for regularization\n",
    "    \"\"\"\n",
    "    m = X.shape[0]\n",
    "\n",
    "    inner = X @ theta - y  # R(m*1)\n",
    "    \n",
    "    cost = (inner.T @ inner) / (2 * m) \n",
    "\n",
    "    regularized_term = np.sum(theta[1:]**2) * l / (2 * m)\n",
    "\n",
    "    return cost + regularized_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "303.9931922202643"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.ones(X.shape[1])\n",
    "regularized_cost(theta, X, y)\n",
    "\n",
    "# 输出值约为 303.993"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 梯度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "梯度下降公式：\n",
    "$$\\theta_j := \\theta_j - \\alpha \\dfrac {\\partial }{\\partial \\theta _{j}} J(\\theta)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(theta, X, y):\n",
    "    m = X.shape[0]\n",
    "\n",
    "    inner = X.T @ (X @ theta - y)  # (m,n).T @ (m, 1) -> (n, 1)\n",
    "\n",
    "    return inner / m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-15.30301567, 598.16741084])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient(theta, X, y)\n",
    "\n",
    "# 输出值约为 array([-15.30301567, 598.16741084])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 正则化梯度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正则化梯度公式：\n",
    "$$\n",
    "\\begin{align*}\n",
    "&\\dfrac {\\partial J(\\theta)}{\\partial \\theta _{0}} = \\dfrac{1}{m} \\sum_{i=1}^m \\left(h_\\theta(x^{(i)}) - y^{(i)}\\right)x_j^{(i)} & \\text{for } j=0 \\\\\n",
    "&\\dfrac {\\partial J(\\theta)}{\\partial \\theta _{0}} = \\left(\\dfrac{1}{m} \\sum_{i=1}^m \\left(h_\\theta(x^{(i)}) - y^{(i)}\\right)x_j^{(i)}\\right) + \\dfrac{\\lambda}{m}\\theta_j & \\text{for } j \\ge 1\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularized_gradient(theta, X, y, l=1):\n",
    "    m = X.shape[0]\n",
    "\n",
    "    regularized_term = theta.copy()  # same shape as theta\n",
    "    regularized_term[0] = 0  # don't regularize intercept theta\n",
    "\n",
    "    regularized_term = (l / m) * regularized_term\n",
    "\n",
    "    return gradient(theta, X, y) + regularized_term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-15.30301567, 598.25074417])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regularized_gradient(theta, X, y)\n",
    "\n",
    "# 输出值约为 array([ -15.30301567,  598.25074417])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 拟合数据\n",
    "> 正则化项 $\\lambda=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression_np(X, y, l=1):\n",
    "    \"\"\"linear regression\n",
    "    args:\n",
    "        X: feature matrix, (m, n+1) # with incercept x0=1\n",
    "        y: target vector, (m, )\n",
    "        l: lambda constant for regularization\n",
    "\n",
    "    return: trained parameters\n",
    "    \"\"\"\n",
    "    # init theta\n",
    "    theta = np.ones(X.shape[1])\n",
    "\n",
    "    # train it\n",
    "    res = opt.minimize(fun=regularized_cost,\n",
    "                       x0=theta,\n",
    "                       args=(X, y, l),\n",
    "                       method='TNC',\n",
    "                       jac=regularized_gradient,\n",
    "                       options={'disp': True})\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.ones(X.shape[0])\n",
    "\n",
    "final_theta = linear_regression_np(X, y, l=0).get('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "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": [
    "b = final_theta[0] # intercept\n",
    "m = final_theta[1] # slope\n",
    "\n",
    "plt.scatter(X[:,1], y, label=\"Training data\")\n",
    "plt.plot(X[:, 1], X[:, 1]*m + b, label=\"Prediction\")\n",
    "plt.legend(loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "training_cost, cv_cost = [], []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.使用训练集的子集来拟合应模型\n",
    "\n",
    "2.在计算训练代价和交叉验证代价时，没有用正则化\n",
    "\n",
    "3.记住使用相同的训练集子集来计算训练代价"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = X.shape[0]\n",
    "for i in range(1, m+1):\n",
    "    # print('i={}'.format(i))\n",
    "    res = linear_regression_np(X[:i, :], y[:i], l=0)\n",
    "    \n",
    "    # train cost\n",
    "    tc = regularized_cost(res.x, X[:i, :], y[:i], l=0)\n",
    "    \n",
    "    # cross-validation cost\n",
    "    cv = regularized_cost(res.x, Xval, yval, l=0)\n",
    "    # print('tc={}, cv={}'.format(tc, cv))\n",
    "    \n",
    "    training_cost.append(tc)\n",
    "    cv_cost.append(cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "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": [
    "plt.plot(np.arange(1, m+1), training_cost, label='training cost')\n",
    "plt.plot(np.arange(1, m+1), cv_cost, label='cross-validataion cost')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个模型拟合不太好, **欠拟合了**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 创建多项式特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_poly_data(*args, power):\n",
    "    \"\"\"\n",
    "    args: keep feeding in X, Xval, or Xtest\n",
    "        will return in the same order\n",
    "    \"\"\"\n",
    "    def prepare(x):\n",
    "        # expand feature\n",
    "        df = poly_features(x, power=power)\n",
    "\n",
    "        # normalization\n",
    "        ndarr = normalize_feature(df).values\n",
    "\n",
    "        # add intercept term\n",
    "        return np.insert(ndarr, 0, np.ones(ndarr.shape[0]), axis=1)\n",
    "\n",
    "    return [prepare(x) for x in args]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_features(x, power, as_ndarray=False):\n",
    "    data = {'f{}'.format(i): np.power(x, i) for i in range(1, power + 1)}\n",
    "    df = pd.DataFrame(data)\n",
    "\n",
    "    return df.values if as_ndarray else df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y, Xval, yval, Xtest, ytest = load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>f1</th>\n",
       "      <th>f2</th>\n",
       "      <th>f3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.936758</td>\n",
       "      <td>253.980260</td>\n",
       "      <td>-4047.621971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-29.152979</td>\n",
       "      <td>849.896197</td>\n",
       "      <td>-24777.006175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36.189549</td>\n",
       "      <td>1309.683430</td>\n",
       "      <td>47396.852168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>37.492187</td>\n",
       "      <td>1405.664111</td>\n",
       "      <td>52701.422173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-48.058829</td>\n",
       "      <td>2309.651088</td>\n",
       "      <td>-110999.127750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-8.941458</td>\n",
       "      <td>79.949670</td>\n",
       "      <td>-714.866612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15.307793</td>\n",
       "      <td>234.328523</td>\n",
       "      <td>3587.052500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-34.706266</td>\n",
       "      <td>1204.524887</td>\n",
       "      <td>-41804.560890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.389154</td>\n",
       "      <td>1.929750</td>\n",
       "      <td>2.680720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-44.383760</td>\n",
       "      <td>1969.918139</td>\n",
       "      <td>-87432.373590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>7.013502</td>\n",
       "      <td>49.189211</td>\n",
       "      <td>344.988637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>22.762749</td>\n",
       "      <td>518.142738</td>\n",
       "      <td>11794.353058</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           f1           f2             f3\n",
       "0  -15.936758   253.980260   -4047.621971\n",
       "1  -29.152979   849.896197  -24777.006175\n",
       "2   36.189549  1309.683430   47396.852168\n",
       "3   37.492187  1405.664111   52701.422173\n",
       "4  -48.058829  2309.651088 -110999.127750\n",
       "5   -8.941458    79.949670    -714.866612\n",
       "6   15.307793   234.328523    3587.052500\n",
       "7  -34.706266  1204.524887  -41804.560890\n",
       "8    1.389154     1.929750       2.680720\n",
       "9  -44.383760  1969.918139  -87432.373590\n",
       "10   7.013502    49.189211     344.988637\n",
       "11  22.762749   518.142738   11794.353058"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_features(X, power=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 准备多项式回归数据\n",
    "1. 扩展特征到 8阶,或者你需要的阶数\n",
    "2. 使用 **归一化** 来合并 $x^n$ \n",
    "3. don't forget intercept term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize_feature(df):\n",
    "    \"\"\"Applies function along input axis(default 0) of DataFrame.\"\"\"\n",
    "    return df.apply(lambda column: (column - column.mean()) / column.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -3.62140776e-01, -7.55086688e-01,\n",
       "         1.82225876e-01, -7.06189908e-01,  3.06617917e-01,\n",
       "        -5.90877673e-01,  3.44515797e-01, -5.08481165e-01],\n",
       "       [ 1.00000000e+00, -8.03204845e-01,  1.25825266e-03,\n",
       "        -2.47936991e-01, -3.27023420e-01,  9.33963187e-02,\n",
       "        -4.35817606e-01,  2.55416116e-01, -4.48912493e-01],\n",
       "       [ 1.00000000e+00,  1.37746700e+00,  5.84826715e-01,\n",
       "         1.24976856e+00,  2.45311974e-01,  9.78359696e-01,\n",
       "        -1.21556976e-02,  7.56568484e-01, -1.70352114e-01]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly, Xval_poly, Xtest_poly= prepare_poly_data(X, Xval, Xtest, power=8)\n",
    "X_poly[:3, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 画出学习曲线\n",
    "## 尝试不使用正则化 $\\lambda=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_learning_curve(X, y, Xval, yval, l=0):\n",
    "    training_cost, cv_cost = [], []\n",
    "    m = X.shape[0]\n",
    "\n",
    "    for i in range(1, m + 1):\n",
    "        # regularization applies here for fitting parameters\n",
    "        res = linear_regression_np(X[:i, :], y[:i], l=l)\n",
    "\n",
    "        # remember, when you compute the cost here, you are computing\n",
    "        # non-regularized cost. Regularization is used to fit parameters only\n",
    "        tc = cost(res.x, X[:i, :], y[:i])\n",
    "        cv = cost(res.x, Xval, yval)\n",
    "\n",
    "        training_cost.append(tc)\n",
    "        cv_cost.append(cv)\n",
    "\n",
    "    plt.plot(np.arange(1, m + 1), training_cost, label='training cost')\n",
    "    plt.plot(np.arange(1, m + 1), cv_cost, label='cv cost')\n",
    "    plt.legend(loc=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "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": [
    "plot_learning_curve(X_poly, y, Xval_poly, yval, l=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你可以看到训练的代价太低了，不真实. 这是 **过拟合**了"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 尝试 $\\lambda=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "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": [
    "plot_learning_curve(X_poly, y, Xval_poly, yval, l=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "训练代价增加了些，不再是0了，也就是说减轻了**过拟合**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 尝试 $\\lambda=100$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "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": [
    "plot_learning_curve(X_poly, y, Xval_poly, yval, l=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正则化过度了，成了 **欠拟合**状态"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 找到最佳的 $\\lambda$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 尝试一系列的labmda值\n",
    "l_candidate = [0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]\n",
    "training_cost, cv_cost = [], []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "for l in l_candidate:\n",
    "    res = linear_regression_np(X_poly, y, l)\n",
    "    \n",
    "    tc = cost(res.x, X_poly, y)\n",
    "    cv = cost(res.x, Xval_poly, yval)\n",
    "    \n",
    "    training_cost.append(tc)\n",
    "    cv_cost.append(cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "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": [
    "plt.plot(l_candidate, training_cost, label='training')\n",
    "plt.plot(l_candidate, cv_cost, label='cross validation')\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlabel('lambda')\n",
    "\n",
    "plt.ylabel('cost')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用cross-validation cost找到最佳的lambda，即cross-validation cost最小时的lambda\n",
    "l_candidate[np.argmin(cv_cost)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test cost(l=0) = 10.804375286491785\n",
      "test cost(l=0.001) = 10.911365745177878\n",
      "test cost(l=0.003) = 11.265060784108712\n",
      "test cost(l=0.01) = 10.879143763702967\n",
      "test cost(l=0.03) = 10.022378551698187\n",
      "test cost(l=0.1) = 8.631776100446476\n",
      "test cost(l=0.3) = 7.3365081011786275\n",
      "test cost(l=1) = 7.466282452677015\n",
      "test cost(l=3) = 11.643940740451052\n",
      "test cost(l=10) = 27.715080273166386\n"
     ]
    }
   ],
   "source": [
    "# 使用测试数据来计算 cost\n",
    "test_cost = []\n",
    "for l in l_candidate:\n",
    "    theta = linear_regression_np(X_poly, y, l).x\n",
    "    tc = cost(theta, Xtest_poly, ytest)\n",
    "    test_cost.append(tc)\n",
    "    print('test cost(l={}) = {}'.format(l, tc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "调参后， $\\lambda = 0.3$ 是最优选择，这个时候测试代价最小。\n",
    "打印出来看看："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "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": [
    "plt.semilogx(l_candidate, test_cost, label='test')\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel('lambda')\n",
    "plt.ylabel('cost')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python (Python 3.6)",
   "language": "python",
   "name": "python36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}