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Wolves
2024-12-30 18:49:59 +08:00
parent 6361618c8e
commit 0d00e1deb4
2 changed files with 225 additions and 19 deletions
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38
lab/1_liner-regression-single.ipynb
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@@ -36,26 +36,26 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
" # 生成数据\n", "# 生成数据\n",
" def generate_data():\n", "def generate_data():\n",
" w = 1.35\n", " w = 1.35\n",
" b = 2.89\n", " b = 2.89\n",
" x_min = 0\n", " x_min = 0\n",
" x_max = 10\n", " x_max = 10\n",
" x = np.linspace(x_min, x_max, 100)\n", " x = np.linspace(x_min, x_max, 100)\n",
" y = w * x + b\n", " y = w * x + b\n",
" y += np.random.normal(scale=0.5, size=y.shape)\n", " y += np.random.normal(scale=0.5, size=y.shape)\n",
" data = np.column_stack((x, y))\n", " data = np.column_stack((x, y))\n",
" return data\n", " return data\n",
"\n", "\n",
" # 保存数据\n", "# 保存数据\n",
" def save_data(filename, data):\n", "def save_data(filename, data):\n",
" np.savetxt(filename, data, delimiter=',')\n", " np.savetxt(filename, data, delimiter=',')\n",
" print(f\"{filename} 已成功创建并写入数据。\")\n", " print(f\"{filename} 已成功创建并写入数据。\")\n",
"\n", "\n",
" # 生成并保存数据\n", "# 生成并保存数据\n",
" data = generate_data()\n", "data = generate_data()\n",
" #save_data('./1_data.txt', data)" "#save_data('./1_data.txt', data)"
] ]
}, },
{ {
@@ -100,7 +100,7 @@
"source": [ "source": [
"# 定义损失函数\n", "# 定义损失函数\n",
"def compute_loss(w,b):\n", "def compute_loss(w,b):\n",
" return np.sum((y-w*x-b)**2)/(2*len(x))\n", " return np.sum((y-w*x-b)**2)/2*len(x)\n",
"\n", "\n",
"# 等效\n", "# 等效\n",
"def compute_loss_equivalent(w,b):\n", "def compute_loss_equivalent(w,b):\n",

206
lab/2_liner-regression-multiply.ipynb Normal file
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@@ -0,0 +1,206 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# 引入库\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import os\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/Users/wolves/Downloads/project/python/pt/lab\n"
]
}
],
"source": [
"# 检查os位置\n",
"print(os.getcwd())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"生成数据方式\n",
"$$y = 1.35x + 0.75x^2 + 2.1\\sqrt{x} + 2.89$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# 生成数据\n",
"def generate_data():\n",
" w = np.array([1.35, 0.75, 2.1]) # 权重\n",
" b = 2.89 # 偏置\n",
" x_min = 1\n",
" x_max = 8\n",
" x = np.linspace(x_min, x_max, 10) # 均匀分布\n",
" X = np.array([x, x**2, np.sqrt(x)]) # 特征矩阵3x10\n",
" y = np.dot(w, X) + b # 1x10 一维向量不区分行向量和列向量\n",
" y += np.random.normal(scale=0.5, size=y.shape)\n",
" data = np.column_stack((X.T, y)) # 10x4\n",
" scaler = StandardScaler()\n",
" data = scaler.fit_transform(data)\n",
" return data\n",
"\n",
"# 保存数据\n",
"def save_data(filename, data):\n",
" np.savetxt(filename, data, delimiter=',')\n",
" print(f\"{filename} 已成功创建并写入数据。\")\n",
"\n",
"# 生成并保存数据\n",
"data = generate_data()\n",
"#save_data('./1_data.txt', data)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# 读取数据\n",
"#points = np.genfromtxt(\"./1_data.txt\", delimiter=',')\n",
"\n",
"points = data\n",
"\n",
"m = len(points[:,0])\n",
"x = points[:, :3] # 10x3\n",
"y = points[:,3] # 1x10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"原函数：\n",
"$$\n",
"\\vec{w} = {\\begin{bmatrix} w_1 & w_2 & w_3 & \\cdots & w_n \\end{bmatrix}}^T\n",
"$$\n",
"\n",
"$$\n",
"\\vec{x} = \\begin{bmatrix} x_1 & x_2 & x_3 & \\cdots & x_n \\end{bmatrix}\n",
"$$\n",
"\n",
"$$\n",
"f_{\\vec{w} \\cdot,b}(\\vec{x}) = \\vec{w} \\cdot \\vec{x} + b\n",
"$$\n",
"\n",
"损失函数: \n",
"\n",
"$$\n",
"\\text{MSE} = \\frac{1}{2m} \\sum_{i=1}^{m} \\left( y^{(i)} - \\hat{y}^{(i)} \\right)^2\n",
"$$\n",
"\n",
"梯度下降：\n",
"\n",
"分别对每个w和b求偏导数，然后更新w和b\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# 定义损失函数\n",
"def compute_loss(w, b):\n",
" return np.sum((y - (np.dot(w, x.T) + b)) ** 2) / (2 * m) # w 1x3 x.T 3x10 y 1x10 y-np.dot(w, x.T) 1x10 sum=number\n",
"\n",
"# 定义梯度下降\n",
"def gradient_descent(w, b, alpha, num_iter):\n",
" for _ in range(num_iter):\n",
" error = y - np.dot(w, x.T) - b # 1x10\n",
" # 计算梯度\n",
" dw = -np.dot(x.T , error) / m # dw 1x3 \n",
" db = -np.sum(error) / m # db 1x1\n",
" # 更新w和b\n",
" w -= alpha * dw\n",
" b -= alpha * db\n",
" return w, b"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"w: [0.30933908 0.51500581 0.17832512]\n",
"b: -3.2582270215186813e-16\n",
"loss: 0.0027531700168465624\n"
]
}
],
"source": [
"# 主函数\n",
"if __name__ == \"__main__\":\n",
" # 初始化w和b\n",
" w = np.zeros(x.shape[1])\n",
" b = 0.0\n",
" # 设置学习率\n",
" alpha = 0.01\n",
" # 设置迭代次数\n",
" num_iter = 1000\n",
" # 进行梯度下降\n",
" w,b = gradient_descent(w,b,alpha,num_iter)\n",
" print(\"w:\", w)\n",
" print(\"b:\", b)\n",
" # 计算损失\n",
" loss = compute_loss(w,b)\n",
" print(\"loss:\", loss)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 编码中遇到的错误\n",
"\n",
"梯度下降算法中，把x.T和error相乘了，正确应使用矩阵乘法。"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pt",
"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": "3.10.14"
}
},
"nbformat": 4,
"nbformat_minor": 2
}