code/09-Softmax回归/09-从零实现softmax回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# softmax回归的从零开始实现\n",
    "\n",
    "就像我们从零开始实现线性回归一样，\n",
    "你应该知道实现softmax回归的细节"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "origin_pos": 4,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from IPython import display\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size = 256\n",
    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将展平每个图像，把它们看作长度为784的向量。\n",
    "因为我们的数据集有10个类别，所以网络输出维度为10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "\n",
    "W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)\n",
    "#均值为0，方差为0.01初始化W权重\n",
    "b = torch.zeros(num_outputs, requires_grad=True)\n",
    "#全0初始化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "给定一个矩阵`X`，我们可以对所有元素求和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "origin_pos": 10,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[5., 7., 9.]]),\n",
       " tensor([[ 6.],\n",
       "         [15.]]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X.sum(0, keepdim=True), X.sum(1, keepdim=True)\n",
    "#keepdim=True避免sum损失维度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现softmax\n",
    "\n",
    "$$\n",
    "\\mathrm{softmax}(\\mathbf{X})_{ij} = \\frac{\\exp(\\mathbf{X}_{ij})}{\\sum_k \\exp(\\mathbf{X}_{ik})}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "origin_pos": 14,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    X_exp = torch.exp(X)\n",
    "    partition = X_exp.sum(1, keepdim=True)\n",
    "    #按行求和并保持维度不变\n",
    "    return X_exp / partition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "我们将每个元素变成一个非负数。\n",
    "此外，依据概率原理，每行总和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.3675, 0.0448, 0.0666, 0.0761, 0.4450],\n",
       "         [0.2670, 0.3483, 0.0597, 0.2074, 0.1175]]),\n",
       " tensor([1.0000, 1.0000]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.normal(0, 1, (2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob, X_prob.sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现softmax回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "origin_pos": 19,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)\n",
    "#对X reshape使其能够与W做内积"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "创建一个数据样本`y_hat`，其中包含2个样本在3个类别的预测概率，\n",
    "以及它们对应的标签`y`。\n",
    "使用`y`作为`y_hat`中概率的索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "origin_pos": 21,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.5000])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.tensor([0, 2])\n",
    "y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y_hat[[0, 1], y]\n",
    "#取出预测值对应的数值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现交叉熵损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "origin_pos": 24,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.3026, 0.6931])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    return - torch.log(y_hat[range(len(y_hat)), y])\n",
    "\n",
    "cross_entropy(y_hat, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将预测类别与真实`y`元素进行比较"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "origin_pos": 29,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def accuracy(y_hat, y):  \n",
    "    \"\"\"计算预测正确的数量\"\"\"\n",
    "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:\n",
    "        y_hat = y_hat.argmax(axis=1)\n",
    "        #argmax返回每行最大值的索引\n",
    "    cmp = y_hat.type(y.dtype) == y\n",
    "    #cmp为01向量，表示y_hat和y相同索引的个数\n",
    "    return float(cmp.type(y.dtype).sum())\n",
    "    #返回cmp中所有相同索引的和\n",
    "accuracy(y_hat, y) / len(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "我们可以评估在任意模型`net`的精度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "origin_pos": 32,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def evaluate_accuracy(net, data_iter):  \n",
    "    \"\"\"计算在指定数据集上模型的精度\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.eval()\n",
    "        #eval()停用dropout和batchnorm\n",
    "    metric = Accumulator(2)\n",
    "    #创建两个元素的列表\n",
    "    with torch.no_grad():\n",
    "        for X, y in data_iter:\n",
    "            metric.add(accuracy(net(X), y), y.numel())\n",
    "            #累加获得预测正确的个数和总个数\n",
    "    return metric[0] / metric[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "`Accumulator`实例中创建了2个变量，\n",
    "分别用于存储正确预测的数量和预测的总数量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "origin_pos": 36,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0949"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Accumulator:  \n",
    "    \"\"\"在n个变量上累加\"\"\"\n",
    "    def __init__(self, n):\n",
    "        self.data = [0.0] * n\n",
    "\n",
    "    def add(self, *args):\n",
    "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
    "        #对数据累加\n",
    "\n",
    "    def reset(self):\n",
    "        self.data = [0.0] * len(self.data)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]\n",
    "\n",
    "evaluate_accuracy(net, test_iter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Softmax回归的训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "origin_pos": 39,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_epoch_ch3(net, train_iter, loss, updater):  \n",
    "    \"\"\"训练模型一个迭代周期（定义见第3章）\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):#判断是否自己实现函数\n",
    "        net.train()\n",
    "    metric = Accumulator(3)\n",
    "    for X, y in train_iter:\n",
    "        y_hat = net(X)\n",
    "        l = loss(y_hat, y)\n",
    "        if isinstance(updater, torch.optim.Optimizer):\n",
    "            updater.zero_grad()\n",
    "            l.sum().backward()\n",
    "            updater.step()\n",
    "        else:\n",
    "            l.sum().backward()\n",
    "            updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())\n",
    "    return metric[0] / metric[2], metric[1] / metric[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义一个在动画中绘制数据的实用程序类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "origin_pos": 42,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class Animator:  \n",
    "    \"\"\"在动画中绘制数据\"\"\"\n",
    "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
    "                 ylim=None, xscale='linear', yscale='linear',\n",
    "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
    "                 figsize=(3.5, 2.5)):\n",
    "        if legend is None:\n",
    "            legend = []\n",
    "        d2l.use_svg_display()\n",
    "        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)\n",
    "        if nrows * ncols == 1:\n",
    "            self.axes = [self.axes, ]\n",
    "        self.config_axes = lambda: d2l.set_axes(\n",
    "            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
    "        self.X, self.Y, self.fmts = None, None, fmts\n",
    "\n",
    "    def add(self, x, y):\n",
    "        if not hasattr(y, \"__len__\"):\n",
    "            y = [y]\n",
    "        n = len(y)\n",
    "        if not hasattr(x, \"__len__\"):\n",
    "            x = [x] * n\n",
    "        if not self.X:\n",
    "            self.X = [[] for _ in range(n)]\n",
    "        if not self.Y:\n",
    "            self.Y = [[] for _ in range(n)]\n",
    "        for i, (a, b) in enumerate(zip(x, y)):\n",
    "            if a is not None and b is not None:\n",
    "                self.X[i].append(a)\n",
    "                self.Y[i].append(b)\n",
    "        self.axes[0].cla()\n",
    "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
    "            self.axes[0].plot(x, y, fmt)\n",
    "        self.config_axes()\n",
    "        display.display(self.fig)\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "origin_pos": 44,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  \n",
    "    \"\"\"训练模型（定义见第3章）\"\"\"\n",
    "    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],\n",
    "                        legend=['train loss', 'train acc', 'test acc'])\n",
    "    for epoch in range(num_epochs):\n",
    "        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)\n",
    "        test_acc = evaluate_accuracy(net, test_iter)\n",
    "        animator.add(epoch + 1, train_metrics + (test_acc,))\n",
    "    train_loss, train_acc = train_metrics\n",
    "    assert train_loss < 0.5, train_loss\n",
    "    assert train_acc <= 1 and train_acc > 0.7, train_acc\n",
    "    assert test_acc <= 1 and test_acc > 0.7, test_acc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "小批量随机梯度下降来优化模型的损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "origin_pos": 46,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "lr = 0.1\n",
    "\n",
    "def updater(batch_size):\n",
    "    return d2l.sgd([W, b], lr, batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练模型10个迭代周期"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "origin_pos": 49,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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    "num_epochs = 10\n",
    "train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)#调用前面的函数"
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   "source": [
    "对图像进行分类预测"
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   "execution_count": 20,
   "metadata": {
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    "tab": [
     "pytorch"
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      ],
      "text/plain": [
       "<Figure size 648x108 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def predict_ch3(net, test_iter, n=6):  \n",
    "    \"\"\"预测标签（定义见第3章）\"\"\"\n",
    "    for X, y in test_iter:\n",
    "        break\n",
    "    trues = d2l.get_fashion_mnist_labels(y)\n",
    "    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))\n",
    "    titles = [true +'\\n' + pred for true, pred in zip(trues, preds)]\n",
    "    d2l.show_images(\n",
    "        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])\n",
    "\n",
    "predict_ch3(net, test_iter)"
   ]
  }
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