ML03.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "984352e7-cf0d-4b2d-9e0a-2ca9a4fee758",
   "metadata": {},
   "source": [
    "> 本节课学习激活函数，链式求导（反向传播的理论基础之一），并补充拟合、优化器等概念\n",
    "\n",
    "上一节课我们实现了利用均方误差梯度下降的方式的机器学习，也解释了相关概念，但如何在线性模型的基础上进一步解决分类问题？这就需要用到激活函数。\n",
    "\n",
    "## 数学基础\n",
    "\n",
    "本节课需要用到的数学基础是sigmoid函数，并把前一节课中的求导法则中的链式法则重点实战进一步了解反向传播和梯度下降。\n",
    "\n",
    "### Sigmoid函数\n",
    "\n",
    "sigmoid函数是一种常用的数学函数，其公式为：\n",
    "\n",
    "$$\\sigma(x) = \\frac{1}{1+e^{-x}}$$\n",
    "\n",
    "其中，x为自变量，$\\sigma(x)$为因变量，e为自然常数。\n",
    "\n",
    "sigmoid函数的图像为一条S形曲线，其取值范围为(0,1)。在机器学习和神经网络中，sigmoid函数常用来作为激活函数，用于将输入信号映射到0到1之间的概率值，以进行分类或回归等任务。\n",
    "\n",
    "sigmoid函数具有以下性质：\n",
    "\n",
    "1. 在x=0处，sigmoid函数的取值为0.5。\n",
    "\n",
    "2. 随着x的增大，sigmoid函数的取值趋近于1。\n",
    "\n",
    "3. 随着x的减小，sigmoid函数的取值趋近于0。\n",
    "\n",
    "4. sigmoid函数在x=正无穷和x=负无穷处的取值分别为1和0。\n",
    "\n",
    "5. sigmoid函数在x=0处的导数最大，且导数值为0.25，这使得它在反向传播算法中常用于计算误差梯度。导数：$$f'(x) = \\frac{e^{-x}}{(1 + e^{-x})^2}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "656d255f-d6f7-4fb6-b088-92fdcafd68de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义Sigmoid函数\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# 生成横坐标数据\n",
    "x = np.linspace(-15, 15, 100)\n",
    "\n",
    "# 计算纵坐标数据\n",
    "y = sigmoid(x)\n",
    "\n",
    "# 绘制函数图像\n",
    "plt.plot(x, y)\n",
    "plt.title('Sigmoid Function')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b9a7ca-6e0b-4ee0-8638-e5ccb9ef04a9",
   "metadata": {},
   "source": [
    "### 链式法则\n",
    "\n",
    "求导的链式法则是导数运算中的一种规则，适用于复合函数求导。\n",
    "\n",
    "复合函数 $y = f(g(x))$ 对 $x$ 的导数为：\n",
    "\n",
    "$$ (f(g(x)))'=f'(g(x))\\cdot g'(x) $$\n",
    "\n",
    "设有函数 $y = f(u)$ 和 $u = g(x)$，则根据链式法则：\n",
    "\n",
    "$$\\frac{dy}{dx} = \\frac{dy}{du} \\cdot \\frac{du}{dx}$$\n",
    "\n",
    "其中，$\\frac{dy}{du}$ 表示外层函数 $f(u)$ 对内层变量 $u$ 的导数，$\\frac{du}{dx}$ 表示内层函数 $g(x)$ 对自变量 $x$ 的导数。\n",
    "\n",
    "换句话说，求导的链式法则指导我们先求每个变量的导数，然后按照一定的规则结合起来求解复合函数的导数。\n",
    "\n",
    "例如，若 $y = (3x^2 + 2x + 1)^3$，则可以看成是两个函数的复合，一个内层函数 $u = 3x^2 + 2x + 1$，一个外层函数 $y = u^3$。应用链式法则，我们可以得到 $\\frac{dy}{dx} = \\frac{dy}{du} \\cdot \\frac{du}{dx} = 3u^2 * (6x+2)$，代入原式中即可求得 y 对 x 的导数。\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$$z = wx + b$$\n",
    "\n",
    "$$y = \\frac{1}{1+e^{-z}} = sigmoid(z)$$\n",
    "\n",
    "其中，$x$是输入特征，$w$是权重，$b$是偏置。我们的目标是学习最佳的权重和偏置，使得模型的预测结果尽可能接近真实标签。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50c87c21-119d-4431-bf79-7a30698ef327",
   "metadata": {},
   "source": [
    "## 机器学习\n",
    "\n",
    "有了新的数学基础知识，在机器学习之前继续补充新的基础概念，本节课新的概念是激活函数。\n",
    "\n",
    "### 激活函数\n",
    "\n",
    "在神经网络中，激活函数（activation function）是对神经元的输出进行非线性变换的函数，它将输入信号经过处理后输出一个非线性的结果，通常在前向传播的过程中先执行激活函数，将数据在神经网络中传递。激活函数的引入可以增强神经网络的表达能力，使得神经网络能够学习非线性的关系，从而提高网络的性能。\n",
    "\n",
    "常见的激活函数包括：\n",
    "\n",
    "1. Sigmoid函数：Sigmoid函数将输入值映射到(0,1)之间，具有平滑的S形曲线。Sigmoid函数在早期的神经网络中被广泛使用，但由于存在梯度消失问题，在深度网络中逐渐被其他激活函数所取代。\n",
    "\n",
    "2. ReLU函数：ReLU函数是一个简单而有效的非线性激活函数，它将输入值映射到`[0,∞)`之间，具有斜率为1的线性增长区域和清晰的零区域，可以有效地缓解梯度消失问题。\n",
    "\n",
    "3. Leaky ReLU函数：Leaky ReLU函数是对ReLU函数的改进，它在零区域的负半轴上引入了一个小斜率，以解决ReLU函数在负半轴上可能存在的“死亡神经元”问题。\n",
    "\n",
    "4. Tanh函数：Tanh函数将输入值映射到(-1,1)之间，与Sigmoid函数类似，但具有更强的非线性特性。\n",
    "\n",
    "5. Softmax函数：Softmax函数常用于多分类问题，它将多个神经元的输出归一化到(0,1)之间，并且归一化后的输出值和为1，可以看作是对概率分布的建模。\n",
    "\n",
    "在选择激活函数时，需要根据具体的问题和网络结构来进行选择，以获得最好的性能。\n",
    "\n",
    "本在节课中我们重点使用sigmoid函数来演示机器学习二分类问题。至少上面提到的其它概念，我们先暂时无视好了。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af032e9d-cdb4-4559-9537-0500d895c089",
   "metadata": {},
   "source": [
    "### 学习\n",
    "\n",
    "在前两节课中我们在使用机器学习之前都用了直接计算的方式求结果做对比，本节课开始，只有学习，没有计算。\n",
    "\n",
    "为了学习分类这种非线性问题，我们先看准备一些示例数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bf969be3-3f15-4fa7-b30e-657e796898cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [0.00469548 0.0187898  0.02010755 0.0202184  0.03918779 0.06022547\n",
      " 0.0641475  0.07103606 0.0871293  0.09394051 0.09609841 0.09710128\n",
      " 0.10204481 0.11037514 0.11827443 0.11872772 0.12019656 0.1289263\n",
      " 0.13179786 0.13818295 0.14335329 0.15896958 0.16130952 0.18319136\n",
      " 0.19658236 0.20887676 0.21038256 0.24442559 0.2532916  0.26455561\n",
      " 0.26538949 0.28280696 0.28940609 0.2961402  0.31542835 0.31798318\n",
      " 0.31856895 0.3595079  0.36371077 0.36872517 0.38344152 0.41426299\n",
      " 0.41466194 0.4236548  0.43703195 0.43758721 0.43860151 0.45615033\n",
      " 0.46147936 0.46631077 0.4686512  0.52184832 0.52324805 0.52889492\n",
      " 0.54488318 0.5488135  0.56660145 0.56804456 0.56843395 0.57019677\n",
      " 0.5759465  0.58651293 0.60276338 0.60484552 0.61209572 0.616934\n",
      " 0.6176355  0.63992102 0.64589411 0.65310833 0.65632959 0.66676672\n",
      " 0.66741038 0.67063787 0.6818203  0.69247212 0.6976312  0.71518937\n",
      " 0.7163272  0.73926358 0.77423369 0.77815675 0.78052918 0.79172504\n",
      " 0.79915856 0.82099323 0.82894003 0.83261985 0.83794491 0.87001215\n",
      " 0.891773   0.92559664 0.9292962  0.94374808 0.94466892 0.96366276\n",
      " 0.97645947 0.97676109 0.97861834 0.98837384]\n",
      "Y: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的x值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化y值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 遍历x值数组，生成对应的y值\n",
    "    for i, x in enumerate(xs):\n",
    "        # 生成正态分布的扰动\n",
    "        noise = np.random.normal(scale=0.01)\n",
    "        # 计算y值\n",
    "        yi = x + noise\n",
    "        # 将y值转换为0或1\n",
    "        ys[i] = int(yi > 0.5)\n",
    "    return xs, ys\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 打印数据集\n",
    "print(\"X:\", X)\n",
    "print(\"Y:\", Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c2a4f80-6f4d-4f55-8d7e-9b680bb0ce37",
   "metadata": {},
   "source": [
    "上以生成数据集为了方便学习，先做了排序处理，我们看看图像：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c2e8da0b-afd3-44c4-840a-48e1045a8ef7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 绘制散点图\n",
    "plt.scatter(X, Y)\n",
    "\n",
    "# 初始化模型参数\n",
    "w = 1\n",
    "b = 0\n",
    "\n",
    "# 计算模型的预测值\n",
    "Z = w * X + b\n",
    "\n",
    "# 绘制模型的直线\n",
    "plt.plot(X, Z)\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7f9d759-2612-43ed-86c8-311b4cd78eb0",
   "metadata": {},
   "source": [
    "我们来分析一下，结合激活函数，我们可以建立如下模型：\n",
    "\n",
    "$$y=sigmoid(wx+b)$$\n",
    "\n",
    "以上模型是个复合函数，可以表示为：\n",
    "\n",
    "$$y=sigmoid(z)$$\n",
    "$$z=wx+b$$\n",
    "\n",
    "在上一节的机器学习中，使用均方误差梯度下降来学习，我们分别以w和b为变量来求导，然后用梯度下降调整参数，对预测值$\\hat{y}$：\n",
    "\n",
    "$$e=(y-\\hat{y})^2$$\n",
    "\n",
    "这里我们一样求$e$对$w$和$e$对$b$的导数，因为加上激活函数后模型成为复合函数，为了方便求导，用$a$来表示$\\hat{y}$，\n",
    "\n",
    "$$e=(y-a)^2$$\n",
    "\n",
    "下面求$e$对$w$的导数和$e$对$b$的导数，使用链式法则来处理：\n",
    "\n",
    "$$\\frac{de}{dw}=\\frac{de}{da}\\cdot\\frac{da}{dz}\\cdot\\frac{dz}{dw}$$\n",
    "\n",
    "$$\\frac{de}{db}=\\frac{de}{da}\\cdot\\frac{da}{dz}\\cdot\\frac{dz}{db}$$\n",
    "\n",
    "分别求每个函数的导数：\n",
    "\n",
    "$$\\frac{de}{da}=2(y-a)(-1)=-2(y-a)$$\n",
    "\n",
    "$$\\frac{da}{dz}=a(1-a)$$\n",
    "\n",
    "$$\\frac{dz}{dw}=x$$\n",
    "\n",
    "$$\\frac{dz}{db}=1$$\n",
    "\n",
    "最终求导结果：\n",
    "\n",
    "$$\\frac{de}{dw}=\\frac{de}{da}\\cdot\\frac{da}{dz}\\cdot\\frac{dz}{dw}=-2(y-a)a(1-a)x$$\n",
    "\n",
    "$$\\frac{de}{db}=\\frac{de}{da}\\cdot\\frac{da}{dz}\\cdot\\frac{dz}{db}=-2(y-a)a(1-a)$$\n",
    "\n",
    "梯度下降：\n",
    "\n",
    "$$w=w-\\alpha\\cdot\\frac{de}{dw}$$\n",
    "\n",
    "$$b=b-\\alpha\\cdot\\frac{de}{db}$$\n",
    "\n",
    "\n",
    "\n",
    "以上对函数求导中，有很多人搞不懂$$\\frac{da}{dz}=a(1-a)$$下面我们来推导一下，先把复合函数每部分都找出来：\n",
    "\n",
    "$$a=\\frac{1}{1+e^{-z}}=\\frac{1}b$$\n",
    "$$b=1+e^{-z}=1+c$$\n",
    "$$c=e^{-z}=e^d$$\n",
    "$$d=-z$$\n",
    "\n",
    "用链式法则可以表示为\n",
    "\n",
    "$$\\frac{da}{dz}=\\frac{da}{db}\\cdot\\frac{db}{dc}\\cdot\\frac{dc}{dd}\\cdot\\frac{dd}{dz}$$\n",
    "分别求出对应的导数：\n",
    "$$\\frac{da}{db}=-b^{-2}$$\n",
    "$$\\frac{db}{dc}=1$$\n",
    "$$\\frac{dc}{dd}=e^d$$\n",
    "$$\\frac{dd}{dz}=-1$$\n",
    "\n",
    "根据链式求导法则可以求得导数为$$\\frac{da}{dz}=-(1+e^{-z})^{-2} \\cdot 1 \\cdot e^{-z} \\cdot -1=\\frac{e^{-z}}{(1+e^{-z})^2}=\\frac{1}{1+e^{-z}}\\cdot\\frac{e^{-z}}{1+e^{-z}}=\\frac{1}{1+e^{-z}}\\cdot\\frac{1+e^{-z}-1}{1+e^{-z}}=\\frac{1}{1+e^{-z}}\\cdot(\\frac{1+e^{-z}}{1+e^{-z}}-\\frac{1}{1+e^{-z}})=a(1-a)$$\n",
    "\n",
    "下面开始实现学习:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b4280590-4a2f-4c08-8e63-b7c7598e4577",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1000000 次学习结果 w = 71.44724913562072, b = -35.365001139658816\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 激活函数\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# 设置超参数学习率\n",
    "alpha = 0.5\n",
    "# 初始化参数权重w和截距b\n",
    "w = 0\n",
    "b = 0\n",
    "# 设置超参数迭代次数\n",
    "epochs = 10000\n",
    "\n",
    "for m in range(epochs):\n",
    "    for i in range(n):\n",
    "        x = X[i]\n",
    "        y = Y[i]\n",
    "        y_pre = w * x + b\n",
    "        a = sigmoid(y_pre)\n",
    "        dw = -2 * (y - a) * a * (1 - a) * x\n",
    "        db = -2 * (y - a) * a * (1 - a)\n",
    "        w -= alpha * dw\n",
    "        b -= alpha * db\n",
    "\n",
    "print(\"第 {} 次学习结果 w = {}, b = {}\".format(n * (m + 1), w, b))\n",
    "\n",
    "y_pre = w * X + b\n",
    "plt.scatter(X, Y)\n",
    "# plt.plot(X, y_pre)\n",
    "plt.plot(X, sigmoid(y_pre))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da223fe1-6d0c-49ba-b190-af30729c40a7",
   "metadata": {},
   "source": [
    "以上代码实现了简单的逻辑回归模型做二分类问题预测，但这并不是我们要的最终模型，我们最终要求的其实是分类的决策边界，决策边界是模型输出等于0.5时的点。对于逻辑回归模型，使用sigmoid函数，我们知道$\\sigma(x)$在$x=0$时值为0.5，所以$ w \\cdot x + b = 0 $，因此$ x = -\\frac{b}{w} $\n",
    "\n",
    "为方便小伙伴们测试，整理完整代码如下：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "41cb3c10-1de3-479c-ad2d-95b1cdfa6054",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1000000 次学习结果 w = 71.44724913562072, b = -35.365001139658816\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成数据集的函数\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子，保证每次生成的数据集相同\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的 x 值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化 y 值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 遍历 x 值数组，生成对应的 y 值\n",
    "    for i, x in enumerate(xs):\n",
    "        # 生成正态分布的扰动，模拟真实数据中的噪声\n",
    "        noise = np.random.normal(scale=0.01)\n",
    "        # 计算 y 值，加入噪声\n",
    "        yi = x + noise\n",
    "        # 将 y 值转换为 0 或 1，用于二分类问题\n",
    "        ys[i] = int(yi > 0.5)\n",
    "    return xs, ys\n",
    "\n",
    "# sigmoid 激活函数\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 设置超参数：学习率\n",
    "alpha = 0.5\n",
    "# 初始化参数：权重 w 和截距 b\n",
    "w = 0\n",
    "b = 0\n",
    "# 设置超参数：迭代次数\n",
    "epochs = 10000\n",
    "\n",
    "# 迭代训练模型\n",
    "for m in range(epochs):\n",
    "    # 遍历数据集中的每个样本\n",
    "    for i in range(n):\n",
    "        x = X[i]\n",
    "        y = Y[i]\n",
    "        # 计算模型的输出值 y_pre 和激活值 a\n",
    "        y_pre = w * x + b\n",
    "        a = sigmoid(y_pre)\n",
    "        # 计算参数的梯度 dw 和 db\n",
    "        dw = -2 * (y - a) * a * (1 - a) * x\n",
    "        db = -2 * (y - a) * a * (1 - a)\n",
    "        # 更新参数 w 和 b\n",
    "        w -= alpha * dw\n",
    "        b -= alpha * db\n",
    "\n",
    "# 输出最终训练结果\n",
    "print(\"第 {} 次学习结果 w = {}, b = {}\".format(n * (m + 1), w, b))\n",
    "\n",
    "# 计算模型的预测结果并可视化\n",
    "y_pre = w * X + b\n",
    "plt.scatter(X, Y)\n",
    "# plt.plot(X, y_pre)\n",
    "plt.plot(X, sigmoid(y_pre), label='Model Prediction')\n",
    "\n",
    "# 计算决策边界\n",
    "decision_boundary = -b / w\n",
    "plt.axvline(x=decision_boundary, color='r', linestyle='--', label='Decision Boundary')\n",
    "\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$y$\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2635ea17-9c03-491d-807a-994753b3de79",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "在项目目录中有一个文件<code>ML03.py</code>是以上代码增加了动态绘制的动画，你可以用python运行看看效果，这样能更直观的感受训练的过程。\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8bc446c-3f1d-48d5-a0b7-3d80b568fff1",
   "metadata": {},
   "source": [
    "\n",
    "本节课的代码是最简单的逻辑回归模型的实现，这里大家一样可以修改超参数看看训练效果。\n",
    "\n",
    "在后续的课程中我们会对上以代码做优化，如：\n",
    "\n",
    "1. 使用矩阵运算代替循环：在代码中，每次迭代都需要遍历整个数据集，对每个样本进行计算和更新。这种方式效率比较低下，可以使用矩阵运算来代替循环，从而提高计算效率。\n",
    "2. 使用随机梯度下降算法：在代码中，每次迭代都需要遍历整个数据集，这种方式计算量比较大，可以使用随机梯度下降算法，每次只随机选取一个样本进行计算和更新，从而减少计算量。\n",
    "3. 添加正则化项：在代码中，没有添加正则化项，可能会导致模型过拟合。可以添加正则化项，限制模型的复杂度，从而提高泛化能力。\n",
    "4. 使用更好的初始化方式：在代码中，参数权重 w 和截距 b 都是初始化为 0，这种方式可能会导致模型收敛速度比较慢。可以使用更好的初始化方式，比如 Xavier 初始化或 He 初始化，从而加速模型的收敛。\n",
    "5. 使用其他优化算法：在代码中，使用的是简单的梯度下降算法，可以使用其他优化算法，比如 Adam 算法、RMSProp 算法等，从而加速模型的收敛。\n",
    "\n",
    "在学习优化之前，我们先基于目前掌握的知识，看看如下面的数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9bc675ce-5929-4eba-9b6d-c697d67e52fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 生成数据集的函数\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子，保证每次生成的数据集相同\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的 x 值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化 y 值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 遍历 x 值数组，生成对应的 y 值\n",
    "    for i, x in enumerate(xs):\n",
    "        # 生成正态分布的扰动，模拟真实数据中的噪声\n",
    "        noise = np.random.normal(scale=0.01)\n",
    "        # 计算 y 值，加入噪声\n",
    "        yi = x + noise\n",
    "        # 将 y 值转换为 0 或 1，用于二分类问题\n",
    "        ys[i] = int(yi < 0.5)\n",
    "    return xs, ys\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 打印数据集\n",
    "# print(\"X:\", X)\n",
    "# print(\"Y:\", Y)\n",
    "\n",
    "# 绘制散点图\n",
    "plt.scatter(X, Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "420d88d9-6fc7-473d-b0df-e39e759b3f4a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1000000 次学习结果 w = -71.44724913562065, b = 35.36500113965878\n"
     ]
    },
    {
     "data": {
      "image/png": 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vvnBKAxBH8rMyVO9qYxIrgJBE/W6arVu36sEHH9RTTz2lHTt26JVXXtHmzZv1wAMPBD1m1apVamxs9P8cOnQo2mUCiCBWYQUQjrB6RvLy8mSz2VRfX99je319vQoKCgIes3r1ai1atEg33XSTJOnCCy9Uc3Ozbr75Zt11112yWvvmIYfDIYfDEU5pAOJI11ojDNMAGFhYPSN2u10zZsxQdXW1f5vX61V1dbVKS0sDHtPS0tIncNhsNkmSYRjh1gsgAYzxrTVCzwiAEITVMyJJ5eXlWrJkiWbOnKlZs2Zp7dq1am5u1tKlSyVJixcv1rhx41RZWSlJmj9/vh5//HFdfPHFKikp0aeffqrVq1dr/vz5/lACILn4h2mYMwIgBGGHkQULFujYsWO65557VFdXp+nTp6uqqso/qfXgwYM9ekLuvvtuWSwW3X333fryyy81ZswYzZ8/Xz//+c8jdxUA4oovjBxjmAZACCxGAoyVuFwu5eTkqLGxUdnZ2WaXA2AAtYdO6vp176kwJ0M1q/6b2eUAMEmo3988mwZAxDmzfT0jbfJ64/7/dwCYjDACIOLyRjhksUgdXkPHW1iFFUD/CCMAIi7dZtWozDOrsDKJFcAACCMAoqLr6b1MYgXQP8IIgKjIz2atEQChIYwAiIqu23sJIwD6RxgBEBVdC58xTAOgf4QRAFHBw/IAhIowAiAqfHNG6ukZATAAwgiAqHBm0zMCIDSEEQBRkd/tyb0J8NQJACYijACICt86I+4Or1ytHSZXAyCeEUYAREVGuk3ZGZ0PBmfhMwD9IYwAiBoWPgMQCsIIgKjJZ0l4ACEgjACImq6Fz+gZARAcYQRA1DBMAyAUhBEAUePrGWHhMwD9IYwAiBp6RgCEgjACIGp4ci+AUBBGAEQNT+4FEArCCICo8Q3TNLs9am5jFVYAgRFGAETNCEeaMu02ScwbARAcYQRAVDFUA2AghBEAUdX96b0AEAhhBEBUjcn2LQlPGAEQGGEEQFQ5fT0jDNMACIIwAiCq8ukZATAAwgiAqOLJvQAGQhgBEFX+Caw8uRdAEIQRAFHFMA2AgRBGAESVb5imsbVdp9s9JlcDIB4RRgBEVc6wdNnTOn/V8MA8AIEQRgBElcVi0ZgRDNUACI4wAiDqfPNGjnFHDYAACCMAos638Fk9d9QACIAwAiDquu6ooWcEQF+EEQBR1/XkXnpGAPRFGAEQdTy5F0B/CCMAoo4n9wLoD2EEQNT5hmm4mwZAIIQRAFHnG6b5qtmtDo/X5GoAxBvCCICoGz3cLpvVIsOQGk65zS4HQJwhjACIOqvVorwRdklSvYuhGgA9EUYAxIQzmztqAARGGAEQE/61RpjECqAXwgiAmBjjW2uEhc8A9EIYARATXT0jhBEAPRFGAMQET+4FEAxhBEBMsCQ8gGAIIwBigoflAQiGMAIgJvzDNKfa5PUaJlcDIJ4QRgDERN4IhywWyeM19FUzq7AC6EIYARAT6TarRg/vXIWVtUYAdEcYARAzY5jECiAAwgiAmPFNYj3GJFYA3QwqjKxbt07FxcXKyMhQSUmJtm3b1u/+J0+e1PLly1VYWCiHw6Fzzz1XW7ZsGVTBABIXS8IDCCQt3AM2bdqk8vJyrV+/XiUlJVq7dq3mzp2rvXv3Kj8/v8/+brdb11xzjfLz8/Xyyy9r3Lhx+vzzz5WbmxuJ+gEkEN8dNQzTAOgu7DDy+OOPa9myZVq6dKkkaf369dq8ebOee+45rVy5ss/+zz33nI4fP673339f6enpkqTi4uKhVQ0gIeXzfBoAAYQ1TON2u7V9+3aVlZV1vYDVqrKyMtXU1AQ85vXXX1dpaamWL18up9OpqVOn6sEHH5TH4wl6nra2Nrlcrh4/ABIfwzQAAgkrjDQ0NMjj8cjpdPbY7nQ6VVdXF/CYffv26eWXX5bH49GWLVu0evVqPfbYY/rZz34W9DyVlZXKycnx/xQVFYVTJoA4xTANgECifjeN1+tVfn6+nnnmGc2YMUMLFizQXXfdpfXr1wc9ZtWqVWpsbPT/HDp0KNplAoiB7sM0hsEqrAA6hTVnJC8vTzabTfX19T2219fXq6CgIOAxhYWFSk9Pl81m8287//zzVVdXJ7fbLbvd3ucYh8Mhh8MRTmkAEsCYM8M0bo9Xja3tys3s++8fQOoJq2fEbrdrxowZqq6u9m/zer2qrq5WaWlpwGNmz56tTz/9VF6v17/tk08+UWFhYcAgAiB5ZaTblDOscyI7QzUAfMIepikvL9eGDRv0wgsvaPfu3brtttvU3Nzsv7tm8eLFWrVqlX//2267TcePH9cdd9yhTz75RJs3b9aDDz6o5cuXR+4qACQMnt4LoLewb+1dsGCBjh07pnvuuUd1dXWaPn26qqqq/JNaDx48KKu1K+MUFRXpjTfe0IoVK3TRRRdp3LhxuuOOO3TnnXdG7ioAJIz8bIf+dvQUd9QA8LMYCTCLzOVyKScnR42NjcrOzja7HABDsGJTrV7d+aVW/v1k3XrlJLPLARBFoX5/82waADHFMA2A3ggjAGJqDAufAeiFMAIgpvKzz6w1wt00AM4gjACIKad/mIaeEQCdCCMAYoqeEQC9EUYAxJRvAmuL26NTbR0mVwMgHhBGAMTUcEeahts7Hw/BUA0AiTACwAQM1QDojjACIOa6bu8ljAAgjAAwQT531ADohjACIObyszqHaY7RMwJAhBEAJsjP7uwZqadnBIAIIwBM4MxmzgiALoQRADHnG6YhjACQCCMATMAEVgDdEUYAxJyvZ8R1ukOn2z0mVwPAbIQRADGXPSxN9rTOXz/cUQOAMAIg5iwWS9dQTRNDNUCqI4wAMEXXvBF6RoBURxgBYAruqAHgQxgBYAoWPgPgQxgBYAonT+4FcAZhBIApeHIvAB/CCABTsPAZAB/CCABT8OReAD6EEQCm8E1g/arZrXaP1+RqAJiJMALAFKMy7UqzWiRJDafoHQFSGWEEgCmsVovyRrDwGQDCCAAT+YZquKMGSG2EEQCm8U1iZeEzILURRgCYhp4RABJhBICJfGuNHOPJvUBKI4wAMI3/YXlMYAVSGmEEgGnyWRIegAgjAEzUNWeEYRoglRFGAJjGN0zTcMotj9cwuRoAZiGMADBN3gi7LBbJ4zV0vNltdjkATEIYAWCaNJtVo4fbJTFUA6QywggAU3FHDQDCCABTMYkVAGEEgKn8t/fSMwKkLMIIAFP5h2lYawRIWYQRAKZimAYAYQSAqViFFQBhBICpxnA3DZDyCCMATNX15N42GQarsAKpiDACwFRjzoQRt8erxtZ2k6sBYAbCCABTZaTblJuZLkmqZ6gGSEmEEQCm65rEyh01QCoijAAwHUvCA6mNMALAdNzeC6Q2wggA041h4TMgpRFGAJiOJeGB1EYYAWA6/1ojzBkBUhJhBIDpuJsGSG2EEQCmy8/uHKapd7EKK5CKBhVG1q1bp+LiYmVkZKikpETbtm0L6biNGzfKYrHo+uuvH8xpASQpX89Ia7tHp9o6TK4GQKyFHUY2bdqk8vJyVVRUaMeOHZo2bZrmzp2ro0eP9nvcgQMH9C//8i+aM2fOoIsFkJyGO9I0wpEmiUmsQCoKO4w8/vjjWrZsmZYuXaopU6Zo/fr1yszM1HPPPRf0GI/Ho+9973u67777dPbZZw+pYADJyT9vhEmsQMoJK4y43W5t375dZWVlXS9gtaqsrEw1NTVBj7v//vuVn5+v73//+yGdp62tTS6Xq8cPgOQ2hkmsQMoKK4w0NDTI4/HI6XT22O50OlVXVxfwmHfffVfPPvusNmzYEPJ5KisrlZOT4/8pKioKp0wACcg3ifUYwzRAyonq3TRNTU1atGiRNmzYoLy8vJCPW7VqlRobG/0/hw4dimKVAOIBS8IDqSstnJ3z8vJks9lUX1/fY3t9fb0KCgr67P/ZZ5/pwIEDmj9/vn+b1+vtPHFamvbu3atJkyb1Oc7hcMjhcIRTGoAE1zVnhGEaINWE1TNit9s1Y8YMVVdX+7d5vV5VV1ertLS0z/6TJ0/Whx9+qNraWv/Pddddp6uuukq1tbUMvwDwy8+mZwRIVWH1jEhSeXm5lixZopkzZ2rWrFlau3atmpubtXTpUknS4sWLNW7cOFVWViojI0NTp07tcXxubq4k9dkOILU5s3wLn9EzAqSasMPIggULdOzYMd1zzz2qq6vT9OnTVVVV5Z/UevDgQVmtLOwKIDz0jACpy2IkwNrLLpdLOTk5amxsVHZ2ttnlAIiCxtZ2Tbvvj5KkPQ9cq4x0m8kVARiqUL+/6cIAEBeyM9LkSOv8lcTCZ0BqIYwAiAsWi6XbUA3zRoBUQhgBEDfyz0xiZd4IkFoIIwDiBmuNAKmJMAIgbrAKK5CaCCMA4obv+TSEESC1EEYAxA1fzwgLnwGphTACIG7w5F4gNRFGAMQN5owAqYkwAiBu+MLI8Wa33B1ek6sBECuEEQBxY2SmXWlWiySp4RS9I0CqIIwAiBtWq0VjGKoBUg5hBEBcYeEzIPUQRgDElTEsCQ+kHMIIgLjS9bA8wgiQKggjAOKK09czwjANkDIIIwDiCj0jQOohjACIK10Ln9EzAqQKwgiAuJLvH6ahZwRIFYQRAHHFN0zTcKpNHq9hcjUAYoEwAiCujB5ul8UieQ3pq2Z6R4BUQBgBEFfSbFaNHu5b+IwwAqQCwgiAuOObxHqMO2qAlEAYARB3fPNG6llrBEgJhBEAccfJkvBASiGMAIg7XQuf0TMCpALCCIC40/XkXnpGgFRAGAEQd3hyL5BaCCMA4o5vmIa7aYDUQBgBEHe639prGKzCCiQ7wgiAuDPmTBhxe7w62dJucjUAoo0wAiDuONJsys1Ml8S8ESAVEEYAxCXfUA0LnwHJjzACIC45s7mjBkgVhBEAcck3b4SFz4DkRxgBEJfyfWuNsPAZkPQIIwDiEk/uBVIHYQRAXOL5NEDqIIwAiEv5LAkPpAzCCIC41P1heazCCiQ3wgiAuOQbpmlt9+hUW4fJ1QCIJsIIgLiUaU9TliNNklTPHTVAUiOMAIhbY5jECqQEwgiAuMXtvUBqIIwAiFssfAakBsIIgLiVz5LwQEogjACIW10Ln9EzAiQzwgiAuMUwDZAaCCMA4hbDNEBqIIwAiFsM0wCpgTACIG7lZ3cO0zSd7lCr22NyNQCihTACIG5lOdKUkd75a4qhGiB5EUYAxC2LxcLTe4EUQBgBENe6P70XQHIijACIa/k8nwZIeoQRAHGNYRog+Q0qjKxbt07FxcXKyMhQSUmJtm3bFnTfDRs2aM6cORo5cqRGjhypsrKyfvcHgO7GMEwDJL2ww8imTZtUXl6uiooK7dixQ9OmTdPcuXN19OjRgPtv3bpV3/3ud/X222+rpqZGRUVF+sY3vqEvv/xyyMUDSH4sfAYkP4thGEY4B5SUlOjSSy/Vk08+KUnyer0qKirSD3/4Q61cuXLA4z0ej0aOHKknn3xSixcvDumcLpdLOTk5amxsVHZ2djjlAkhw//7JMS15bpvOc2bpjRVXmF0OgDCE+v0dVs+I2+3W9u3bVVZW1vUCVqvKyspUU1MT0mu0tLSovb1do0aNCrpPW1ubXC5Xjx8AqcnJBFYg6YUVRhoaGuTxeOR0OntsdzqdqqurC+k17rzzTo0dO7ZHoOmtsrJSOTk5/p+ioqJwygSQRHwTWE+0tMvd4TW5GgDRENO7adasWaONGzfq1VdfVUZGRtD9Vq1apcbGRv/PoUOHYlglgHgyMjNd6TaLJOnYKSaxAskoLZyd8/LyZLPZVF9f32N7fX29CgoK+j320Ucf1Zo1a/TWW2/poosu6ndfh8Mhh8MRTmkAkpTFYtGYEQ4dbjyto67TGpc7zOySAERYWD0jdrtdM2bMUHV1tX+b1+tVdXW1SktLgx738MMP64EHHlBVVZVmzpw5+GoBpKQx2aw1AiSzsHpGJKm8vFxLlizRzJkzNWvWLK1du1bNzc1aunSpJGnx4sUaN26cKisrJUkPPfSQ7rnnHr344osqLi72zy0ZMWKERowYEcFLAZCsum7vJYwAySjsMLJgwQIdO3ZM99xzj+rq6jR9+nRVVVX5J7UePHhQVmtXh8vTTz8tt9utf/qnf+rxOhUVFbr33nuHVj2AlOALI8dc3FEDJKOww4gk3X777br99tsD/t3WrVt7/PnAgQODOQUA+LEkPJDceDYNgLjne1hePT0jQFIijACIe10Ln9EzAiQjwgiAuMcwDZDcCCMA4p5vAutXp9rk8Yb1OC0ACYAwAiDujR7hkNUieY3OQAIguRBGAMQ9m9Wi0SOYNwIkK8IIgITQtfAZd9QAyYYwAiAh+MOIi54RINkQRgAkBO6oAZIXYQRAQnCy8BmQtAgjABICT+4FkhdhBEBC4Mm9QPIijABICDy5F0hehBEACSH/zDDNsVNtMgxWYQWSCWEEQEIYc2bRs3aPoRMt7SZXAyCSCCMAEoI9zaqRmemSWPgMSDaEEQAJw7/WCAufAUmFMAIgYThzOsPI4ZOtJlcCIJIIIwASxjljRkiS9tY3mVwJgEgijABIGJMLsyRJe+sII0AyIYwASBiTCzrDyJ66Jm7vBZIIYQRAwjjXmSWb1aLjzW4daeSOGiBZEEYAJIyMdJvOPzNUs/PgSXOLARAxhBEACWV6Ua4kqfbQCXMLARAxhBEACWV60UhJUu2hk+YWAiBiCCMAEoqvZ+TDLxvV7vGaWwyAiCCMAEgoZ+cNV3ZGmk63e7nFF0gShBEACcVqtWjamd6RnQzVAEmBMAIg4Vzsm8TKHTVAUiCMAEg408/KlcQdNUCyIIwASDjTxudKkj471qzG1nZziwEwZIQRAAln9AiHJozOlCT9lXkjQMIjjABISL5bfFmJFUh8hBEACalk4mhJ0u//6zAPzQMSHGEEQEL61rRCDUu36W9HT+k/DzCRFUhkhBEACSk7I13/MH2sJOnFP39ucjUAhoIwAiBhLSw5S5K05cM6HW92m1wNgMEijABIWBeNz9WF43Lk9nj18vZDZpcDYJAIIwASmq935LfbDsnrZSIrkIgIIwAS2nXTxmqEI037G5pVs+8rs8sBMAiEEQAJbbgjTddf7JvIetDkagAMBmEEQMJbOGuCJOmNj+t0tOm0ydUACBdhBEDCmzI2WxeflasOr6GX/vKF2eUACBNhBEBS+F5JZ+/Ib7cdlIeJrEBCIYwASArfuqhQ2Rlp+uJEq9752zGzywEQBsIIgKSQkW7Tf58xXhITWYFEQxgBkDS+d2bNkerd9TrS2GpyNQBCRRgBkDTOyc/SrImj5DWkTf/JiqxAoiCMAEgqvt6RjdsOqcPjNbkaAKEgjABIKtdOLdCo4XbVuU7rT3uOml0OgBAQRgAkFUeaTf/jzETW/1PzuQyD23yBeEcYAZB0FpacJZvVonc/bdCz7+43uxwAAyCMAEg6E0YP193fPF+S9OCW3ar66IjJFQHoD2EEQFK68bJi/Y8Z4+U1pFt/vUO3v7hD9S6eWwPEI8IIgKRksVj0s3+cqv85e6KsFun3/3VEZY/9u154/wDLxQNxxmIkwOwul8ulnJwcNTY2Kjs72+xyAJjA4zX0wWdfqWZfgySLSiaOktVqUcOpNuVnZWjWxFGyWS3+fbftP666xlYdb3arpd2j13Z+qc+ONUuSLhyXo5//41RdMDZH7+49pmfe3SfX6XZdOC5Hcy8o0MnWdv9rStK2/cd1tOl0wPN0r6l00mhdWjxK2z8/ocMnWlT7xUlJFhWPztSi0mLZ0/r+/5+v1qNNp5U33CFZpIZTbf7/Puo6rePNbo0a4VBBduf5PV5Dv6o5oP1fNcsi6eKikSrMHRa0Xt82X3t0fy3ftUiSu8OrX9Uc0OfHWzRhVPCae9fdu11CfT99NTWcatPJ1nZZzrTh188e3eM6urdLf+fqXdOMCSO1/fMT/uvOzbTrZEvw6w+l3oGudyjt0vtzG6jOUN6jYDW4O7x64f39+s8DJzTcbtO3LxmvkrNHa/vnJwb9Pg4k1O/vQYWRdevW6ZFHHlFdXZ2mTZumJ554QrNmzQq6/0svvaTVq1frwIED+trXvqaHHnpI8+bNC/l8hBEgtVV9dEQrX/lQJ1vag+5TmJOhivlTJEn3/dsuHWnsOySTnZGmdo+h1naPLJIsFqm/TpLczHRJ6nHe7ucJVJPFIgX6rWq1SMvmTNSqeVN6XFewWoPJtNvU2u4JeI5A9Qba1vtarp1aqMotu7ThP/b3aI9ANQeru/trDWSg686022RPswZ9vwOdK9BrWgd4f0OtOdTrHUq79NcmvtfYefDEgO9RsBqmjsvWW7uOqndzWKQe28J5H0MRtTCyadMmLV68WOvXr1dJSYnWrl2rl156SXv37lV+fn6f/d9//31dccUVqqys1Le+9S29+OKLeuihh7Rjxw5NnTo1ohcDIPlUfXREt/56x4D79f6l2p9z8ofr06PNg6onnPMEcssVnV8cVR8d0W2/3jGk14oEi6SyKfl6c1fwNVl8NUsKWrfv/6WfvuGSfr/IInHdvc81lNe0qP+aQ73eobRLJNrklism6uKzRka8bYcqamGkpKREl156qZ588klJktfrVVFRkX74wx9q5cqVffZfsGCBmpub9fvf/96/7etf/7qmT5+u9evXR/RiACQXj9fQ7DXVqnO1mV1KxFgt0sf3XaurH9saVo+ImawWac8Dfy+b1aLLH/pT0LotkgpyMvTunVcHHcLo7/hw+M717z++Slc+8vagX7O/mgeqN9QahnKOcK7DmZ2hughM0h7ofQxHqN/faeG8qNvt1vbt27Vq1Sr/NqvVqrKyMtXU1AQ8pqamRuXl5T22zZ07V6+99lrQ87S1tamtreuXj8vlCqdMAEli2/7jSRVEpM5hg+uefDdhgojUWfMNv/hAo0Y4+q3bkHSk8bSWv7hDhTkZff7+SOPpiF2371w3/OKDIb1mfzUPVG+oNQzlHKEypIgEEd9rHWk8rW37j6t00uiIvOZAwgojDQ0N8ng8cjqdPbY7nU7t2bMn4DF1dXUB96+rqwt6nsrKSt13333hlAYgCR1tSpwv7HD87egps0sI27YDJ0Let+qj4L/fIy2cuvozlJpDrSGW7RIJsfz3F1YYiZVVq1b16E1xuVwqKioysSIAZsjP6vt/18lg2vgc/fWLRrPLCMvsSaM1Jsuh12oPD7jv9dPHatzIYX22f3miNaTjw63rvc++GvLrBKo51HpDrWEo5zBDLP/9hRVG8vLyZLPZVF9f32N7fX29CgoKAh5TUFAQ1v6S5HA45HA4wikNQBKaNXGUCrIdSTVUY7VIG28u1dWPbVVd42nTJ7CGwmqRfrl0lmxWi/68/3jQun1zDR77zvSgc0b+vP94ROeM/HLpLF35yNuDbsv+avbVO9D1DlRDKOeI1JyRetfQP1O+en23hcdCWIue2e12zZgxQ9XV1f5tXq9X1dXVKi0tDXhMaWlpj/0l6c033wy6PwD42KwW3XvdBSHtG+o0O4s67zwYrKGuwLBszkQNs9v8twdHbkWHwbFIumZK3zshu1s2Z6LsaVbZrJagdfv+XDF/StBJj77jh3rN3c9lT7MOuS2D1Rzq9fZXw0DtEqk2ufmKibr3uqF/pkJ5H6Mh7BVYy8vLtWHDBr3wwgvavXu3brvtNjU3N2vp0qWSpMWLF/eY4HrHHXeoqqpKjz32mPbs2aN7771Xf/nLX3T77bdH7ioAJK1rpxZq/Q2X+NfLCKYgJ0Prb7hE62+4JODkSalzDYWnb7hEq+ZN0fobLgm6oJdPbmZ6n/N2P0+gmixBfn9bLT1vkb12aqGevuESFQSpNZhMuy3oOQLVG2ibj689Niy+VLdc0blSbX8191d3wZnXGuh2UN/xwd4jSRput/X7fvc+V7CaBvouLQyh5lCvdyjtMlCbFJ75zA30HgWroTAnQ9dMyQ8YUnpvC/V9jLRBLXr25JNP+hc9mz59uv71X/9VJSUlkqS/+7u/U3FxsZ5//nn//i+99JLuvvtu/6JnDz/8MIueAQjLUFZgDbbipsdrsAIrK7CGVS8rsIYnqiuwxhphBACAxBPq9zcPygMAAKYijAAAAFMRRgAAgKkIIwAAwFSEEQAAYCrCCAAAMBVhBAAAmIowAgAATEUYAQAApgrrqb1m8S0S63K5TK4EAACEyve9PdBi7wkRRpqamiRJRUVFJlcCAADC1dTUpJycnKB/nxDPpvF6vTp8+LCysrJkCfa4yjC4XC4VFRXp0KFDPOsmBmjv2KGtY4v2ji3aO7Yi0d6GYaipqUljx46V1Rp8ZkhC9IxYrVaNHz8+4q+bnZ3NBzqGaO/Yoa1ji/aOLdo7toba3v31iPgwgRUAAJiKMAIAAEyVkmHE4XCooqJCDofD7FJSAu0dO7R1bNHesUV7x1Ys2zshJrACAIDklZI9IwAAIH4QRgAAgKkIIwAAwFSEEQAAYKqkDSPr1q1TcXGxMjIyVFJSom3btvW7/0svvaTJkycrIyNDF154obZs2RKjSpNDOO29YcMGzZkzRyNHjtTIkSNVVlY24PuDLuF+tn02btwoi8Wi66+/ProFJplw2/vkyZNavny5CgsL5XA4dO655/L7JAzhtvfatWt13nnnadiwYSoqKtKKFSt0+vTpGFWbuN555x3Nnz9fY8eOlcVi0WuvvTbgMVu3btUll1wih8Ohc845R88//3zkCjKS0MaNGw273W4899xzxscff2wsW7bMyM3NNerr6wPu/9577xk2m814+OGHjV27dhl33323kZ6ebnz44YcxrjwxhdveCxcuNNatW2fs3LnT2L17t3HjjTcaOTk5xhdffBHjyhNPuG3ts3//fmPcuHHGnDlzjH/4h3+ITbFJINz2bmtrM2bOnGnMmzfPePfdd439+/cbW7duNWpra2NceWIKt71/85vfGA6Hw/jNb35j7N+/33jjjTeMwsJCY8WKFTGuPPFs2bLFuOuuu4xXXnnFkGS8+uqr/e6/b98+IzMz0ygvLzd27dplPPHEE4bNZjOqqqoiUk9ShpFZs2YZy5cv9//Z4/EYY8eONSorKwPu/53vfMf45je/2WNbSUmJccstt0S1zmQRbnv31tHRYWRlZRkvvPBCtEpMGoNp646ODuOyyy4zfvGLXxhLliwhjIQh3PZ++umnjbPPPttwu92xKjGphNvey5cvN66++uoe28rLy43Zs2dHtc5kE0oY+clPfmJccMEFPbYtWLDAmDt3bkRqSLphGrfbre3bt6usrMy/zWq1qqysTDU1NQGPqamp6bG/JM2dOzfo/ugymPburaWlRe3t7Ro1alS0ykwKg23r+++/X/n5+fr+978fizKTxmDa+/XXX1dpaamWL18up9OpqVOn6sEHH5TH44lV2QlrMO192WWXafv27f6hnH379mnLli2aN29eTGpOJdH+nkyIB+WFo6GhQR6PR06ns8d2p9OpPXv2BDymrq4u4P51dXVRqzNZDKa9e7vzzjs1duzYPh909DSYtn733Xf17LPPqra2NgYVJpfBtPe+ffv0pz/9Sd/73ve0ZcsWffrpp/rBD36g9vZ2VVRUxKLshDWY9l64cKEaGhp0+eWXyzAMdXR06NZbb9VPf/rTWJScUoJ9T7pcLrW2tmrYsGFDev2k6xlBYlmzZo02btyoV199VRkZGWaXk1Sampq0aNEibdiwQXl5eWaXkxK8Xq/y8/P1zDPPaMaMGVqwYIHuuusurV+/3uzSktLWrVv14IMP6qmnntKOHTv0yiuvaPPmzXrggQfMLg1hSrqekby8PNlsNtXX1/fYXl9fr4KCgoDHFBQUhLU/ugymvX0effRRrVmzRm+99ZYuuuiiaJaZFMJt688++0wHDhzQ/Pnz/du8Xq8kKS0tTXv37tWkSZOiW3QCG8xnu7CwUOnp6bLZbP5t559/vurq6uR2u2W326NacyIbTHuvXr1aixYt0k033SRJuvDCC9Xc3Kybb75Zd911l6xW/n87UoJ9T2ZnZw+5V0RKwp4Ru92uGTNmqLq62r/N6/WqurpapaWlAY8pLS3tsb8kvfnmm0H3R5fBtLckPfzww3rggQdUVVWlmTNnxqLUhBduW0+ePFkffvihamtr/T/XXXedrrrqKtXW1qqoqCiW5SecwXy2Z8+erU8//dQf+iTpk08+UWFhIUFkAINp75aWlj6BwxcEDR67FlFR/56MyDTYOLNx40bD4XAYzz//vLFr1y7j5ptvNnJzc426ujrDMAxj0aJFxsqVK/37v/fee0ZaWprx6KOPGrt37zYqKiq4tTcM4bb3mjVrDLvdbrz88svGkSNH/D9NTU1mXULCCLete+NumvCE294HDx40srKyjNtvv93Yu3ev8fvf/97Iz883fvazn5l1CQkl3PauqKgwsrKyjN/+9rfGvn37jD/+8Y/GpEmTjO985ztmXULCaGpqMnbu3Gns3LnTkGQ8/vjjxs6dO43PP//cMAzDWLlypbFo0SL//r5be3/84x8bu3fvNtatW8etvaF44oknjLPOOsuw2+3GrFmzjA8++MD/d1deeaWxZMmSHvv/7ne/M84991zDbrcbF1xwgbF58+YYV5zYwmnvCRMmGJL6/FRUVMS+8AQU7me7O8JI+MJt7/fff98oKSkxHA6HcfbZZxs///nPjY6OjhhXnbjCae/29nbj3nvvNSZNmmRkZGQYRUVFxg9+8APjxIkTsS88wbz99tsBfw/72nfJkiXGlVde2eeY6dOnG3a73Tj77LONX/7ylxGrx2IY9GUBAADzJN2cEQAAkFgIIwAAwFSEEQAAYCrCCAAAMBVhBAAAmIowAgAATEUYAQAApiKMAAAAUxFGAACAqQgjAADAVIQRAABgKsIIAAAw1f8HToN6F34/cjQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成数据集的函数\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子，保证每次生成的数据集相同\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的 x 值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化 y 值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 遍历 x 值数组，生成对应的 y 值\n",
    "    for i, x in enumerate(xs):\n",
    "        # 生成正态分布的扰动，模拟真实数据中的噪声\n",
    "        noise = np.random.normal(scale=0.01)\n",
    "        # 计算 y 值，加入噪声\n",
    "        yi = x + noise\n",
    "        # 将 y 值转换为 0 或 1，用于二分类问题\n",
    "        ys[i] = int(yi < 0.5)\n",
    "    return xs, ys\n",
    "\n",
    "# sigmoid 激活函数\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 设置超参数：学习率\n",
    "alpha = 0.5\n",
    "# 初始化参数：权重 w 和截距 b\n",
    "w = 0\n",
    "b = 0\n",
    "# 设置超参数：迭代次数\n",
    "epochs = 10000\n",
    "\n",
    "# 迭代训练模型\n",
    "for m in range(epochs):\n",
    "    # 遍历数据集中的每个样本\n",
    "    for i in range(n):\n",
    "        x = X[i]\n",
    "        y = Y[i]\n",
    "        # 计算模型的输出值 y_pre 和激活值 a\n",
    "        y_pre = w * x + b\n",
    "        a = sigmoid(y_pre)\n",
    "        # 计算参数的梯度 dw 和 db\n",
    "        dw = -2 * (y - a) * a * (1 - a) * x\n",
    "        db = -2 * (y - a) * a * (1 - a)\n",
    "        # 更新参数 w 和 b\n",
    "        w -= alpha * dw\n",
    "        b -= alpha * db\n",
    "\n",
    "# 输出最终训练结果\n",
    "print(\"第 {} 次学习结果 w = {}, b = {}\".format(n * (m + 1), w, b))\n",
    "\n",
    "# 计算模型的预测结果并可视化\n",
    "y_pre = w * X + b\n",
    "plt.scatter(X, Y)\n",
    "# plt.plot(X, y_pre)\n",
    "plt.plot(X, sigmoid(y_pre))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3eb566b-3b67-46e4-a828-3eddb0b6a4ac",
   "metadata": {},
   "source": [
    "以上数据集只是把数据从`>0.5`的分类为1改为`<0.5`的分类为1，对模型不需任何修改，正常分类，从训练结果可以看出模型只是参数$w$从71.45变为-71.45。\n",
    "\n",
    "再看看能不能解决更复杂的分类问题，如下数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "30ca1741-f441-47af-a067-c2b27a376731",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 生成数据集的函数\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子，保证每次生成的数据集相同\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的 x 值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化 y 值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 计算中间部分的索引范围\n",
    "    mid = int(counts * 0.4), int(counts * 0.6)\n",
    "    # 将中间部分的 y 值设为 1\n",
    "    ys[mid[0]:mid[1]] = 1\n",
    "    # 加入噪声\n",
    "    ys += np.random.normal(scale=0.01, size=counts)\n",
    "    # 将 y 值限制在 0 和 1 之间\n",
    "    ys = np.clip(ys, 0, 1)\n",
    "    return xs, ys\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 打印数据集\n",
    "# print(\"X:\", X)\n",
    "# print(\"Y:\", Y)\n",
    "\n",
    "# 绘制散点图\n",
    "plt.scatter(X, Y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ff5d05a9-8fa7-42c6-8287-c02c2202644c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第 1000000 次学习结果 w = -1.154305695213669, b = -1.1708057735335682\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成数据集的函数\n",
    "def get_data(counts, seed=0):\n",
    "    # 设置随机数种子，保证每次生成的数据集相同\n",
    "    np.random.seed(seed)\n",
    "    # 生成随机的 x 值，并进行排序\n",
    "    xs = np.sort(np.random.rand(counts))\n",
    "    # 初始化 y 值的数组\n",
    "    ys = np.zeros(counts)\n",
    "    # 计算中间部分的索引范围\n",
    "    mid = int(counts * 0.4), int(counts * 0.6)\n",
    "    # 将中间部分的 y 值设为 1\n",
    "    ys[mid[0]:mid[1]] = 1\n",
    "    # 加入噪声\n",
    "    ys += np.random.normal(scale=0.01, size=counts)\n",
    "    # 将 y 值限制在 0 和 1 之间\n",
    "    ys = np.clip(ys, 0, 1)\n",
    "    return xs, ys\n",
    "\n",
    "# sigmoid 激活函数\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "# 数据大小\n",
    "n = 100\n",
    "# 生成数据集\n",
    "X, Y = get_data(n)\n",
    "\n",
    "# 设置超参数：学习率\n",
    "alpha = 0.5\n",
    "# 初始化参数：权重 w 和截距 b\n",
    "w = 0\n",
    "b = 0\n",
    "# 设置超参数：迭代次数\n",
    "epochs = 10000\n",
    "\n",
    "# 迭代训练模型\n",
    "for m in range(epochs):\n",
    "    # 遍历数据集中的每个样本\n",
    "    for i in range(n):\n",
    "        x = X[i]\n",
    "        y = Y[i]\n",
    "        # 计算模型的输出值 y_pre 和激活值 a\n",
    "        y_pre = w * x + b\n",
    "        a = sigmoid(y_pre)\n",
    "        # 计算参数的梯度 dw 和 db\n",
    "        dw = -2 * (y - a) * a * (1 - a) * x\n",
    "        db = -2 * (y - a) * a * (1 - a)\n",
    "        # 更新参数 w 和 b\n",
    "        w -= alpha * dw\n",
    "        b -= alpha * db\n",
    "\n",
    "# 输出最终训练结果\n",
    "print(\"第 {} 次学习结果 w = {}, b = {}\".format(n * (m + 1), w, b))\n",
    "\n",
    "# 计算模型的预测结果并可视化\n",
    "y_pre = w * X + b\n",
    "plt.scatter(X, Y)\n",
    "# plt.plot(X, y_pre)\n",
    "plt.plot(X, sigmoid(y_pre))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae7e1fc4-5fa4-4bb4-a2c8-b312cb6a80f3",
   "metadata": {},
   "source": [
    "从训练结果看，很明显$y=sigmoid(wx+b)$模型已经解决不了这个问题了，不管怎么调整超参数都没用，怎么办？对比前面示例中一个权重$w$为正和一个权重$w$为负的模型，如果把这二个结合起来是不是能解决问题呢？答案是肯定的，但怎么做？请关注下节课**神经网络**。\n"
   ]
  }
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