{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3e211967",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# 线性回归的简洁实现\n",
    ":label:`sec_linear_concise`\n",
    "\n",
    "在过去的几年里，出于对深度学习强烈的兴趣，\n",
    "许多公司、学者和业余爱好者开发了各种成熟的开源框架。\n",
    "这些框架可以自动化基于梯度的学习算法中重复性的工作。\n",
    "在 :numref:`sec_linear_scratch`中，我们只运用了：\n",
    "（1）通过张量来进行数据存储和线性代数；\n",
    "（2）通过自动微分来计算梯度。\n",
    "实际上，由于数据迭代器、损失函数、优化器和神经网络层很常用，\n",
    "现代深度学习库也为我们实现了这些组件。\n",
    "\n",
    "本节将介绍如何(**通过使用深度学习框架来简洁地实现**)\n",
    " :numref:`sec_linear_scratch`中的(**线性回归模型**)。\n",
    "\n",
    "## 生成数据集\n",
    "\n",
    "与 :numref:`sec_linear_scratch`中类似，我们首先[**生成数据集**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c88734d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:52.522009Z",
     "iopub.status.busy": "2023-08-18T07:01:52.521295Z",
     "iopub.status.idle": "2023-08-18T07:01:54.610713Z",
     "shell.execute_reply": "2023-08-18T07:01:54.609677Z"
    },
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "from torch.utils import data\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c26b741f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.616404Z",
     "iopub.status.busy": "2023-08-18T07:01:54.615685Z",
     "iopub.status.idle": "2023-08-18T07:01:54.643472Z",
     "shell.execute_reply": "2023-08-18T07:01:54.642512Z"
    },
    "origin_pos": 5,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = d2l.synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6fd8db7",
   "metadata": {
    "origin_pos": 6
   },
   "source": [
    "## 读取数据集\n",
    "\n",
    "我们可以[**调用框架中现有的API来读取数据**]。\n",
    "我们将`features`和`labels`作为API的参数传递，并通过数据迭代器指定`batch_size`。\n",
    "此外，布尔值`is_train`表示是否希望数据迭代器对象在每个迭代周期内打乱数据。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "955f5cc0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.648232Z",
     "iopub.status.busy": "2023-08-18T07:01:54.647744Z",
     "iopub.status.idle": "2023-08-18T07:01:54.653335Z",
     "shell.execute_reply": "2023-08-18T07:01:54.652317Z"
    },
    "origin_pos": 8,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def load_array(data_arrays, batch_size, is_train=True):  #@save\n",
    "    \"\"\"构造一个PyTorch数据迭代器\"\"\"\n",
    "    dataset = data.TensorDataset(*data_arrays)\n",
    "    return data.DataLoader(dataset, batch_size, shuffle=is_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c041eafa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.657592Z",
     "iopub.status.busy": "2023-08-18T07:01:54.656999Z",
     "iopub.status.idle": "2023-08-18T07:01:54.661787Z",
     "shell.execute_reply": "2023-08-18T07:01:54.660785Z"
    },
    "origin_pos": 11,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "batch_size = 10\n",
    "data_iter = load_array((features, labels), batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "503e6815",
   "metadata": {
    "origin_pos": 12
   },
   "source": [
    "使用`data_iter`的方式与我们在 :numref:`sec_linear_scratch`中使用`data_iter`函数的方式相同。为了验证是否正常工作，让我们读取并打印第一个小批量样本。\n",
    "与 :numref:`sec_linear_scratch`不同，这里我们使用`iter`构造Python迭代器，并使用`next`从迭代器中获取第一项。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7c6919b8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.665574Z",
     "iopub.status.busy": "2023-08-18T07:01:54.664999Z",
     "iopub.status.idle": "2023-08-18T07:01:54.673523Z",
     "shell.execute_reply": "2023-08-18T07:01:54.672688Z"
    },
    "origin_pos": 13,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([[-1.3116, -0.3062],\n",
       "         [-1.5653,  0.4830],\n",
       "         [-0.8893, -0.9466],\n",
       "         [-1.2417,  1.6891],\n",
       "         [-0.7148,  0.1376],\n",
       "         [-0.2162, -0.6122],\n",
       "         [ 2.4048, -0.3211],\n",
       "         [-0.1516,  0.4997],\n",
       "         [ 1.5298, -0.2291],\n",
       "         [ 1.3895,  1.2602]]),\n",
       " tensor([[ 2.6073],\n",
       "         [-0.5787],\n",
       "         [ 5.6339],\n",
       "         [-4.0211],\n",
       "         [ 2.3117],\n",
       "         [ 5.8492],\n",
       "         [10.0926],\n",
       "         [ 2.1932],\n",
       "         [ 8.0441],\n",
       "         [ 2.6943]])]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(iter(data_iter))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f57af75",
   "metadata": {
    "origin_pos": 14
   },
   "source": [
    "## 定义模型\n",
    "\n",
    "当我们在 :numref:`sec_linear_scratch`中实现线性回归时，\n",
    "我们明确定义了模型参数变量，并编写了计算的代码，这样通过基本的线性代数运算得到输出。\n",
    "但是，如果模型变得更加复杂，且当我们几乎每天都需要实现模型时，自然会想简化这个过程。\n",
    "这种情况类似于为自己的博客从零开始编写网页。\n",
    "做一两次是有益的，但如果每个新博客就需要工程师花一个月的时间重新开始编写网页，那并不高效。\n",
    "\n",
    "对于标准深度学习模型，我们可以[**使用框架的预定义好的层**]。这使我们只需关注使用哪些层来构造模型，而不必关注层的实现细节。\n",
    "我们首先定义一个模型变量`net`，它是一个`Sequential`类的实例。\n",
    "`Sequential`类将多个层串联在一起。\n",
    "当给定输入数据时，`Sequential`实例将数据传入到第一层，\n",
    "然后将第一层的输出作为第二层的输入，以此类推。\n",
    "在下面的例子中，我们的模型只包含一个层，因此实际上不需要`Sequential`。\n",
    "但是由于以后几乎所有的模型都是多层的，在这里使用`Sequential`会让你熟悉“标准的流水线”。\n",
    "\n",
    "回顾 :numref:`fig_single_neuron`中的单层网络架构，\n",
    "这一单层被称为*全连接层*（fully-connected layer），\n",
    "因为它的每一个输入都通过矩阵-向量乘法得到它的每个输出。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b7cb683",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "在PyTorch中，全连接层在`Linear`类中定义。\n",
    "值得注意的是，我们将两个参数传递到`nn.Linear`中。\n",
    "第一个指定输入特征形状，即2，第二个指定输出特征形状，输出特征形状为单个标量，因此为1。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "85c54a1a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.677177Z",
     "iopub.status.busy": "2023-08-18T07:01:54.676580Z",
     "iopub.status.idle": "2023-08-18T07:01:54.680914Z",
     "shell.execute_reply": "2023-08-18T07:01:54.680130Z"
    },
    "origin_pos": 20,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "# nn是神经网络的缩写\n",
    "from torch import nn\n",
    "\n",
    "net = nn.Sequential(nn.Linear(2, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc18b2c1",
   "metadata": {
    "origin_pos": 23
   },
   "source": [
    "## (**初始化模型参数**)\n",
    "\n",
    "在使用`net`之前，我们需要初始化模型参数。\n",
    "如在线性回归模型中的权重和偏置。\n",
    "深度学习框架通常有预定义的方法来初始化参数。\n",
    "在这里，我们指定每个权重参数应该从均值为0、标准差为0.01的正态分布中随机采样，\n",
    "偏置参数将初始化为零。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7452e3b",
   "metadata": {
    "origin_pos": 25,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "正如我们在构造`nn.Linear`时指定输入和输出尺寸一样，\n",
    "现在我们能直接访问参数以设定它们的初始值。\n",
    "我们通过`net[0]`选择网络中的第一个图层，\n",
    "然后使用`weight.data`和`bias.data`方法访问参数。\n",
    "我们还可以使用替换方法`normal_`和`fill_`来重写参数值。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "31716c55",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.684561Z",
     "iopub.status.busy": "2023-08-18T07:01:54.684036Z",
     "iopub.status.idle": "2023-08-18T07:01:54.690673Z",
     "shell.execute_reply": "2023-08-18T07:01:54.689754Z"
    },
    "origin_pos": 29,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net[0].weight.data.normal_(0, 0.01)\n",
    "net[0].bias.data.fill_(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94568f78",
   "metadata": {
    "origin_pos": 33,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9592f9a",
   "metadata": {
    "origin_pos": 35
   },
   "source": [
    "## 定义损失函数\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a431ee3",
   "metadata": {
    "origin_pos": 37,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "[**计算均方误差使用的是`MSELoss`类，也称为平方$L_2$范数**]。\n",
    "默认情况下，它返回所有样本损失的平均值。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "19a417ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.695575Z",
     "iopub.status.busy": "2023-08-18T07:01:54.694922Z",
     "iopub.status.idle": "2023-08-18T07:01:54.699373Z",
     "shell.execute_reply": "2023-08-18T07:01:54.698348Z"
    },
    "origin_pos": 41,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "loss = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30dbe343",
   "metadata": {
    "origin_pos": 44
   },
   "source": [
    "## 定义优化算法\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2663da90",
   "metadata": {
    "origin_pos": 46,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "小批量随机梯度下降算法是一种优化神经网络的标准工具，\n",
    "PyTorch在`optim`模块中实现了该算法的许多变种。\n",
    "当我们(**实例化一个`SGD`实例**)时，我们要指定优化的参数\n",
    "（可通过`net.parameters()`从我们的模型中获得）以及优化算法所需的超参数字典。\n",
    "小批量随机梯度下降只需要设置`lr`值，这里设置为0.03。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1ae0989f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.703905Z",
     "iopub.status.busy": "2023-08-18T07:01:54.703368Z",
     "iopub.status.idle": "2023-08-18T07:01:54.708081Z",
     "shell.execute_reply": "2023-08-18T07:01:54.706987Z"
    },
    "origin_pos": 50,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "trainer = torch.optim.SGD(net.parameters(), lr=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "004056f1",
   "metadata": {
    "origin_pos": 53
   },
   "source": [
    "## 训练\n",
    "\n",
    "通过深度学习框架的高级API来实现我们的模型只需要相对较少的代码。\n",
    "我们不必单独分配参数、不必定义我们的损失函数，也不必手动实现小批量随机梯度下降。\n",
    "当我们需要更复杂的模型时，高级API的优势将大大增加。\n",
    "当我们有了所有的基本组件，[**训练过程代码与我们从零开始实现时所做的非常相似**]。\n",
    "\n",
    "回顾一下：在每个迭代周期里，我们将完整遍历一次数据集（`train_data`），\n",
    "不停地从中获取一个小批量的输入和相应的标签。\n",
    "对于每一个小批量，我们会进行以下步骤:\n",
    "\n",
    "* 通过调用`net(X)`生成预测并计算损失`l`（前向传播）。\n",
    "* 通过进行反向传播来计算梯度。\n",
    "* 通过调用优化器来更新模型参数。\n",
    "\n",
    "为了更好的衡量训练效果，我们计算每个迭代周期后的损失，并打印它来监控训练过程。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1270d706",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.712705Z",
     "iopub.status.busy": "2023-08-18T07:01:54.712113Z",
     "iopub.status.idle": "2023-08-18T07:01:54.922720Z",
     "shell.execute_reply": "2023-08-18T07:01:54.921580Z"
    },
    "origin_pos": 55,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.000248\n",
      "epoch 2, loss 0.000103\n",
      "epoch 3, loss 0.000103\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 3\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter:\n",
    "        l = loss(net(X) ,y)\n",
    "        trainer.zero_grad()\n",
    "        l.backward()\n",
    "        trainer.step()\n",
    "    l = loss(net(features), labels)\n",
    "    print(f'epoch {epoch + 1}, loss {l:f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f52dea0",
   "metadata": {
    "origin_pos": 58
   },
   "source": [
    "下面我们[**比较生成数据集的真实参数和通过有限数据训练获得的模型参数**]。\n",
    "要访问参数，我们首先从`net`访问所需的层，然后读取该层的权重和偏置。\n",
    "正如在从零开始实现中一样，我们估计得到的参数与生成数据的真实参数非常接近。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aa7cef5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T07:01:54.927464Z",
     "iopub.status.busy": "2023-08-18T07:01:54.927072Z",
     "iopub.status.idle": "2023-08-18T07:01:54.935672Z",
     "shell.execute_reply": "2023-08-18T07:01:54.934585Z"
    },
    "origin_pos": 60,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差： tensor([-0.0010, -0.0003])\n",
      "b的估计误差： tensor([-0.0003])\n"
     ]
    }
   ],
   "source": [
    "w = net[0].weight.data\n",
    "print('w的估计误差：', true_w - w.reshape(true_w.shape))\n",
    "b = net[0].bias.data\n",
    "print('b的估计误差：', true_b - b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f62d52d4",
   "metadata": {
    "origin_pos": 63
   },
   "source": [
    "## 小结\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6db4aa3",
   "metadata": {
    "origin_pos": 65,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "* 我们可以使用PyTorch的高级API更简洁地实现模型。\n",
    "* 在PyTorch中，`data`模块提供了数据处理工具，`nn`模块定义了大量的神经网络层和常见损失函数。\n",
    "* 我们可以通过`_`结尾的方法将参数替换，从而初始化参数。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb6af2c7",
   "metadata": {
    "origin_pos": 67
   },
   "source": [
    "## 练习\n",
    "\n",
    "1. 如果将小批量的总损失替换为小批量损失的平均值，需要如何更改学习率？\n",
    "1. 查看深度学习框架文档，它们提供了哪些损失函数和初始化方法？用Huber损失代替原损失，即\n",
    "    $$l(y,y') = \\begin{cases}|y-y'| -\\frac{\\sigma}{2} & \\text{ if } |y-y'| > \\sigma \\\\ \\frac{1}{2 \\sigma} (y-y')^2 & \\text{ 其它情况}\\end{cases}$$\n",
    "1. 如何访问线性回归的梯度？\n"
   ]
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   "source": [
    "[Discussions](https://discuss.d2l.ai/t/1781)\n"
   ]
  }
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