30. Regularization and Ridge Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "oriented-destruction",
   "metadata": {},
   "source": [
    "# Regularization and Ridge Regression\n",
    "### Bias Variance Trade off\n",
    "\n",
    "###### Bias\n",
    "\n",
    "prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair.\n",
    "\n",
    "###### Variance\n",
    "\n",
    "the fact or quality of being different, divergent, or inconsistent.\n",
    "\n",
    "##### Errors\n",
    "\n",
    "模型误差 = 偏差（Bias） + 方差（Variance） + 不可避免的误差"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pressing-representation",
   "metadata": {},
   "source": [
    "解决高方差的通常手段\n",
    "\n",
    "1）降低模型复杂度\n",
    "如多项式回归中，可通过较小 degree 来降低模型复杂度；\n",
    " \n",
    "\n",
    "2）减少数据维度；降噪\n",
    "方差过大的大部分原因是模型学习的过多的噪音；\n",
    " \n",
    "\n",
    "3）增加样本数\n",
    "也就是增大训练数据的规模：有时候算法具有高的方差，是因为模型太过复杂，模型中的参数非常多，而训练模型的样本数不足以支撑计算出这么多复杂的参数。（如：神经网络和深度学习）\n",
    "使用深度学习的一个非常重要的条件就是数据样本的规模必须足够的大，这样才能发挥深度学习算法的效用，其中的原因就是深度学习算法的模型太过复杂，模型中的参数非常多，而训练模型的样本数不足以支撑计算出这么多复杂的参数。否则的话，使用深度学习的算法在一个小样本上得到的结果，还不如使用简单的模型得到的结果。\n",
    "　　　　\n",
    "\n",
    "4）使用验证集\n",
    "在评测算法模型指标时需要使用 验证数据集（Validation），因为如果只使用 train_test_split 的方法得到的模型很有可能出现过拟合测试数据集的情况。\n",
    "　　　　\n",
    "\n",
    "5）模型的正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bound-treaty",
   "metadata": {},
   "source": [
    "## Refularization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "otherwise-vacuum",
   "metadata": {},
   "source": [
    "$$ J(\\theta)= argmin \\ MSE(y, \\hat y; \\theta) $$\n",
    "\n",
    "$After \\  Regularization:$\n",
    "\n",
    "$$J(\\theta)= argmin \\ MSE(y, \\hat y; \\theta)+\\frac{\\alpha}{2}\\sum _{i = 1}^n \\beta_i^2$$\n",
    "\n",
    "### Ridge Regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "behavioral-tennessee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "statewide-trick",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "x = np.random.uniform(-3.0, 3.0, size=100)\n",
    "X = x.reshape(-1, 1)\n",
    "y = 0.5 * x + 3. + np.random.normal(0, 1, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "mechanical-entry",
   "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.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "searching-disclosure",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "affecting-blake",
   "metadata": {},
   "outputs": [],
   "source": [
    "def PolynomialRegression(degree):\n",
    "    return Pipeline([\n",
    "        ('poly', PolynomialFeatures(degree=degree)),\n",
    "        ('std_scaler', StandardScaler()),\n",
    "        ('lin_reg', LinearRegression())\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "mechanical-remark",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "np.random.seed(666)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "knowing-diagram",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "167.9401085999025"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "poly_reg = PolynomialRegression(degree=20)\n",
    "poly_reg.fit(X_train, y_train)\n",
    "\n",
    "y_poly_predict = poly_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y_poly_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "certain-ukraine",
   "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": [
    "X_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "y_plot = poly_reg.predict(X_plot)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(X_plot[:, 0], poly_reg.predict(X_plot), color='r')\n",
    "plt.axis([-3, 3, 0, 6])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eleven-cancellation",
   "metadata": {},
   "source": [
    "Packaging plot code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "united-project",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_model(model):\n",
    "    X_plot = np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "    y_plot = model.predict(X_plot)\n",
    "\n",
    "    plt.scatter(x, y)\n",
    "    plt.plot(X_plot[:, 0], model.predict(X_plot), color='r')\n",
    "    plt.axis([-3, 3, 0, 6])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ethical-vietnam",
   "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_model(poly_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vocational-manchester",
   "metadata": {},
   "source": [
    "### Using Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "south-static",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def RidgeRegression(degree, alpha):\n",
    "    return Pipeline([\n",
    "        ('poly', PolynomialFeatures(degree=degree)),\n",
    "        ('std_scaler', StandardScaler()),\n",
    "        ('ridge_reg', Ridge(alpha=alpha))\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "basic-iceland",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3233492754136291"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge1_reg = RidgeRegression(20, 0.0001)\n",
    "ridge1_reg.fit(X_train, y_train)\n",
    "\n",
    "y1_predict = ridge1_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y1_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "violent-gothic",
   "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_model(ridge1_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "elder-settle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1888759304218461"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2_reg = RidgeRegression(20, 1)\n",
    "ridge2_reg.fit(X_train, y_train)\n",
    "\n",
    "y2_predict = ridge2_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y2_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "chronic-advertiser",
   "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_model(ridge2_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "relative-absence",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3196456113086197"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge3_reg = RidgeRegression(20, 100)\n",
    "ridge3_reg.fit(X_train, y_train)\n",
    "\n",
    "y3_predict = ridge3_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y3_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "different-metadata",
   "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_model(ridge3_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "suburban-benjamin",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8404103153255003"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge4_reg = RidgeRegression(20, 1000000)\n",
    "ridge4_reg.fit(X_train, y_train)\n",
    "\n",
    "y4_predict = ridge4_reg.predict(X_test)\n",
    "mean_squared_error(y_test, y4_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "present-theory",
   "metadata": {
    "scrolled": true
   },
   "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_model(ridge4_reg)"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}