mxnet/linear_regression_raw.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# mxnet linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. 随机生成数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
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     "text": [
      "/root/anaconda3/envs/envtf/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n",
      "/root/anaconda3/envs/envtf/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n",
      "/root/anaconda3/envs/envtf/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "from mxnet import autograd, nd\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate random x1,x2 as features\n",
    "num_inputs = 2 # 2 input: x1, x2\n",
    "num_examples = 1000 # 1000 points\n",
    "true_w = [2, -3.4] # 2 weight\n",
    "true_b = 4.2 # bais\n",
    "features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))#标准差为1的正态分布\n",
    "labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b\n",
    "labels += nd.random.normal(scale=0.01, shape=labels.shape)#标准差为0.01的正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "(\n",
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     "execution_count": 3,
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   "source": [
    "features[0], labels[0]\n",
    "# features[0] is [x1,x2], label is y = x1*w1+x2*w2+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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     "metadata": {},
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    }
   ],
   "source": [
    "# display data\n",
    "# x: x1, y:y\n",
    "def use_svg_display():\n",
    "    # 用矢量图显示\n",
    "    display.set_matplotlib_formats('svg')\n",
    "\n",
    "def set_figsize(figsize=(3.5, 2.5)):\n",
    "    use_svg_display()\n",
    "    # 设置图的尺寸\n",
    "    plt.rcParams['figure.figsize'] = figsize\n",
    "\n",
    "set_figsize()\n",
    "plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. 读取数据\n",
    "\n",
    "在训练模型的时候，我们需要遍历数据集并不断读取小批量数据样本。这里我们定义一个函数：它每次返回batch_size（批量大小）个随机样本的特征和标签。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices)  # 样本的读取顺序是随机的\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = nd.array(indices[i: min(i + batch_size, num_examples)])\n",
    "        yield features.take(j), labels.take(j)  # take函数根据索引返回对应元素"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[[ 0.4231157   0.64803934]\n",
      " [-0.7887759   0.64921004]\n",
      " [ 1.2054669  -0.99645287]\n",
      " [-0.94586486  0.5678514 ]\n",
      " [-1.8886926   0.7965518 ]\n",
      " [-1.6575857   1.4283854 ]\n",
      " [-1.1784962   0.774073  ]\n",
      " [ 0.04370913  0.1237288 ]\n",
      " [-1.2387311   1.6483529 ]\n",
      " [-1.8871194   0.832024  ]]\n",
      "<NDArray 10x2 @cpu(0)> \n",
      "[ 2.8509607   0.41422766  9.992634    0.39167407 -2.284341   -3.9651418\n",
      " -0.78432673  3.8636084  -3.8805866  -2.4121945 ]\n",
      "<NDArray 10 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "# 测试这个函数\n",
    "batch_size = 10\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. 初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = nd.random.normal(scale=0.01, shape=(num_inputs, 1))\n",
    "b = nd.zeros(shape=(1,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "w.attach_grad()\n",
    "b.attach_grad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. 定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b):  # 本函数已保存在d2lzh包中方便以后使用\n",
    "    return nd.dot(X, w) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. 定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):  # y_hat is y_pred\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. 定义优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):  \n",
    "    for param in params:\n",
    "        param[:] = param - lr * param.grad / batch_size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. 训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.000050\n",
      "epoch 2, loss 0.000050\n",
      "epoch 3, loss 0.000050\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):  # 训练模型一共需要num_epochs个迭代周期\n",
    "    # 在每一个迭代周期中，会使用训练数据集中所有样本一次（假设样本数能够被批量大小整除）。X\n",
    "    # 和y分别是小批量样本的特征和标签\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        with autograd.record():\n",
    "            l = loss(net(X, w, b), y)  # l是有关小批量X和y的损失\n",
    "        l.backward()  # 小批量的损失对模型参数求梯度\n",
    "        sgd([w, b], lr, batch_size)  # 使用小批量随机梯度下降迭代模型参数\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().asnumpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, -3.4] \n",
      "[[ 1.18964  ]\n",
      " [-2.0660515]]\n",
      "<NDArray 2x1 @cpu(0)>\n",
      "4.2 \n",
      "[2.4103951]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "print(true_w, w)\n",
    "print(true_b,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8. 思考"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 为什么squared_loss函数中需要使用reshape函数？\n",
    "\n",
    "   * 首先， y.shape = (10,), y_hat.shape = (10, 1)\n",
    "   * 如果不做reshape，没法进行数学计算\n",
    "\n",
    "2. 尝试使用不同的学习率，观察损失函数值的下降快慢。\n",
    "\n",
    "lr适中\n",
    "```\n",
    "lr = 0.03\n",
    "epoch 1, loss 0.040544\n",
    "epoch 2, loss 0.000150\n",
    "epoch 3, loss 0.000050\n",
    "```\n",
    "lr较大\n",
    "```\n",
    "lr = 0.3\n",
    "epoch 1, loss 0.000052\n",
    "epoch 2, loss 0.000052\n",
    "epoch 3, loss 0.000054\n",
    "```\n",
    "lr较小\n",
    "```\n",
    "lr = 0.003\n",
    "epoch 1, loss 8.997435\n",
    "epoch 2, loss 4.984050\n",
    "epoch 3, loss 2.762571\n",
    "```\n",
    "\n",
    "\n",
    "3. 如果样本个数不能被批量大小整除，data_iter函数的行为会有什么变化？\n",
    "   * 见下面测试\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2) (150,)\n",
      "(150, 2) (150,)\n",
      "(150, 2) (150,)\n",
      "(150, 2) (150,)\n",
      "(150, 2) (150,)\n",
      "(150, 2) (150,)\n",
      "(100, 2) (100,)\n"
     ]
    }
   ],
   "source": [
    "# 测试这个函数\n",
    "batch_size = 150\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X.shape, y.shape)"
   ]
  }
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