ch06-梯度下降法/03-梯度下降法向量化(Boston房价).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 梯度下降法向量化(Boston房价)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston = datasets.load_boston()\n",
    "X = boston.data\n",
    "y = boston.target\n",
    "\n",
    "X = X[y<50.0]\n",
    "y = y[y<50.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from playML.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, seed=666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 564 µs, sys: 244 µs, total: 808 µs\n",
      "Wall time: 486 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8129794056212925"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from playML.LinearRegression import LinearRegression\n",
    "\n",
    "lin_reg1 = LinearRegression()\n",
    "%time lin_reg1.fit_normal(X_train, y_train)\n",
    "lin_reg1.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 真实数据集，利用梯度下降\n",
    "\n",
    "数据的维度相差太大！！不是一个规模\n",
    "\n",
    "默认学习率，会报错\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mgbook/.pyenv/versions/3.6.4rc1/lib/python3.6/site-packages/numpy/core/fromnumeric.py:83: RuntimeWarning: overflow encountered in reduce\n",
      "  return ufunc.reduce(obj, axis, dtype, out, **passkwargs)\n",
      "/Users/mgbook/Dropbox/XMG机器学习/ch06-梯度下降法/playML/LinearRegression.py:38: RuntimeWarning: overflow encountered in square\n",
      "  return np.sum((y - X_b.dot(theta)) ** 2) / len(y)\n",
      "/Users/mgbook/Dropbox/XMG机器学习/ch06-梯度下降法/playML/LinearRegression.py:59: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 384 ms, sys: 4.98 ms, total: 389 ms\n",
      "Wall time: 424 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from playML.LinearRegression import LinearRegression\n",
    "\n",
    "lin_reg2 = LinearRegression()\n",
    "%time lin_reg2.fit_gd(X_train, y_train)\n",
    "lin_reg2.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 361 ms, sys: 3.74 ms, total: 364 ms\n",
      "Wall time: 365 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.27586818724477224"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg3 = LinearRegression()\n",
    "%time lin_reg3.fit_gd(X_train, y_train, eta=0.000001)\n",
    "lin_reg3.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 步长太大！循环的次数太少(太多又耗时)！\n",
    "\n",
    "最主要原因，还是数据规模不一致，\n",
    "\n",
    "eta在不同维度上，或者太大，或者太小\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 34.8 s, sys: 160 ms, total: 34.9 s\n",
      "Wall time: 35.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.7542932581943915"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time lin_reg3.fit_gd(X_train, y_train, eta=0.000001, n_iters=1e6)\n",
    "lin_reg3.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数据归一化\n",
    "\n",
    "使用`梯度下降法`，搜索损失函数最小值之前，对数据需要归一化处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "standardScaler = StandardScaler()\n",
    "standardScaler.fit(X_train)\n",
    "X_train_standard = standardScaler.transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 222 ms, sys: 4.37 ms, total: 227 ms\n",
      "Wall time: 257 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg4 = LinearRegression()\n",
    "%time lin_reg4.fit_gd(X_train_standard, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8129873310487505"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test_standard = standardScaler.transform(X_test)\n",
    "lin_reg4.score(X_test_standard, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用梯度下降法的优势\n",
    "\n",
    "速度快"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 1000\n",
    "n = 5000\n",
    "\n",
    "big_X = np.random.normal(size=(m, n))\n",
    "true_theta = np.random.uniform(0.0, 100.0, size=n+1)\n",
    "# 参数 截距\n",
    "# 不能完全是线性的，添加噪音\n",
    "big_y = big_X.dot(true_theta[1:]) + true_theta[0] + np.random.normal(0., 10., size=m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12.5 s, sys: 591 ms, total: 13.1 s\n",
      "Wall time: 7.64 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "big_reg1 = LinearRegression()\n",
    "%time big_reg1.fit_normal(big_X, big_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.73 s, sys: 33.4 ms, total: 3.77 s\n",
      "Wall time: 1.93 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "big_reg2 = LinearRegression()\n",
    "%time big_reg2.fit_gd(big_X, big_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.4rc1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}