machinelearning/gradientDescent/04-StochasticGradientDescent/04-StochasticGradientDescent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 随机梯度下降法"
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 全量梯度下降法， 用来和下面的随机梯度做对比的"
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:12.987981Z",
     "start_time": "2024-08-25T22:47:12.566136Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:15.365958Z",
     "start_time": "2024-08-25T22:47:15.332152Z"
    }
   },
   "source": [
    "m = 100000\n",
    "\n",
    "x = np.random.normal(size=m)\n",
    "X = x.reshape(-1,1)\n",
    "y = 4.*x + 3. + np.random.normal(0, 3, size=m)"
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:17.661610Z",
     "start_time": "2024-08-25T22:47:17.485128Z"
    }
   },
   "source": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:22.650167Z",
     "start_time": "2024-08-25T22:47:22.644419Z"
    }
   },
   "source": [
    "def J(theta, X_b, y):\n",
    "    try:\n",
    "        return np.sum((y - X_b.dot(theta)) ** 2) / len(y)\n",
    "    except:\n",
    "        return float('inf')\n",
    "    \n",
    "def dJ(theta, X_b, y):\n",
    "    return X_b.T.dot(X_b.dot(theta) - y) * 2. / len(y)\n",
    "\n",
    "def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):\n",
    "\n",
    "    theta = initial_theta\n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = dJ(theta, X_b, y)\n",
    "        last_theta = theta\n",
    "        theta = theta - eta * gradient\n",
    "        if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):\n",
    "            break\n",
    "\n",
    "        cur_iter += 1\n",
    "\n",
    "    return theta"
   ],
   "outputs": [],
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:27.620210Z",
     "start_time": "2024-08-25T22:47:27.387112Z"
    }
   },
   "source": [
    "%%time\n",
    "X_b = np.hstack([np.ones((len(X), 1)), X])\n",
    "initial_theta = np.zeros(X_b.shape[1])\n",
    "eta = 0.01\n",
    "theta = gradient_descent(X_b, y, initial_theta, eta)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 275 ms, sys: 119 ms, total: 394 ms\n",
      "Wall time: 228 ms\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:30.161900Z",
     "start_time": "2024-08-25T22:47:30.155572Z"
    }
   },
   "source": [
    "theta"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.00658095, 4.00922757])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 随机梯度下降法"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-08-25T22:47:38.202779Z",
     "start_time": "2024-08-25T22:47:38.195979Z"
    }
   },
   "source": [
    "# 求随机梯队，  公式\n",
    "# X_b_i  X_b中的 第ｉ个样本 只有一行记录\n",
    "def dJ_sgd(theta, X_b_i, y_i):\n",
    "    return 2 * X_b_i.T.dot(X_b_i.dot(theta) - y_i)\n",
    "\n",
    "def sgd(X_b, y, initial_theta, n_iters):\n",
    "    # 经验值\n",
    "    t0, t1 = 5, 50\n",
    "    # 学习率 随着迭代次数（时间） ，慢慢变小。 \n",
    "    def learning_rate(t):\n",
    "        return t0 / (t + t1)\n",
    "\n",
    "    theta = initial_theta\n",
    "    for cur_iter in range(n_iters):\n",
    "        rand_i = np.random.randint(len(X_b))\n",
    "        gradient = dJ_sgd(theta, X_b[rand_i], y[rand_i])\n",
    "        theta = theta - learning_rate(cur_iter) * gradient\n",
    "\n",
    "    return theta"
   ],
   "outputs": [],
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-25T22:48:19.147753Z",
     "start_time": "2024-08-25T22:48:18.443701Z"
    }
   },
   "source": [
    "%%time\n",
    "X_b = np.hstack([np.ones((len(X), 1)), X])\n",
    "initial_theta = np.zeros(X_b.shape[1])\n",
    "theta = sgd(X_b, y, initial_theta, n_iters=m)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 688 ms, sys: 4.49 ms, total: 692 ms\n",
      "Wall time: 700 ms\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-25T22:48:21.931510Z",
     "start_time": "2024-08-25T22:48:21.926039Z"
    }
   },
   "source": [
    "theta"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.00181245, 4.03910019])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 11
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": ""
  }
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