mxnet/linear_regression_gluon.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": 3,
   "metadata": {},
   "outputs": [],
   "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": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(\n",
       " [1.1630785 0.4838046]\n",
       " <NDArray 2 @cpu(0)>, \n",
       " [4.879625]\n",
       " <NDArray 1 @cpu(0)>)"
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     "execution_count": 5,
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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": 6,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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",
    "Gluon提供了data包来读取数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet.gluon import data as gdata\n",
    "\n",
    "batch_size = 10\n",
    "# 将训练数据的特征和标签组合\n",
    "dataset = gdata.ArrayDataset(features, labels)\n",
    "# 随机读取小批量\n",
    "data_iter = gdata.DataLoader(dataset, batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[[-1.9584894   0.3811466 ]\n",
      " [-0.55021375 -1.5918757 ]\n",
      " [-0.9457527  -1.8475903 ]\n",
      " [ 1.6698817   0.5393773 ]\n",
      " [ 1.1348199  -0.4925288 ]\n",
      " [-0.3367721  -1.253791  ]\n",
      " [ 0.95956105  0.14733684]\n",
      " [-0.7230168   0.88875777]\n",
      " [ 0.06527644 -0.9506362 ]\n",
      " [ 0.50472885 -0.48745614]]\n",
      "<NDArray 10x2 @cpu(0)> \n",
      "[-1.0243565  8.525719   8.591789   5.711088   8.140179   7.782056\n",
      "  5.623976  -0.2697006  7.5680094  6.874393 ]\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:\n",
    "    print(X, y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. 定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet.gluon import nn\n",
    "\n",
    "net = nn.Sequential()\n",
    "net.add(nn.Dense(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. 初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet import init\n",
    "\n",
    "net.initialize(init.Normal(sigma=0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. 定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet.gluon import loss as gloss\n",
    "\n",
    "loss = gloss.L2Loss()  # 平方损失又称L2范数损失"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. 定义优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet import gluon\n",
    "\n",
    "trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.03})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. 训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.034991\n",
      "epoch 2, loss: 0.000126\n",
      "epoch 3, loss: 0.000049\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 3\n",
    "for epoch in range(1, num_epochs + 1):\n",
    "    for X, y in data_iter:\n",
    "        with autograd.record():\n",
    "            l = loss(net(X), y)\n",
    "        l.backward()\n",
    "        trainer.step(batch_size)\n",
    "    l = loss(net(features), labels)\n",
    "    print('epoch %d, loss: %f' % (epoch, l.mean().asnumpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8. 访问模型训练出来的真实值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([2, -3.4], \n",
       " [[ 1.999432 -3.399479]]\n",
       " <NDArray 1x2 @cpu(0)>)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dense = net[0]\n",
    "true_w, dense.weight.data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.2, \n",
       " [4.200508]\n",
       " <NDArray 1 @cpu(0)>)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "true_b, dense.bias.data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9. 思考"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1） 如果将l = loss(net(X), y)替换成l = loss(net(X), y).mean()，我们需要将trainer.step(batch_size)相应地改成trainer.step(1)。这是为什么呢？\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2） 查阅MXNet文档，看看gluon.loss和init模块里提供了哪些损失函数和初始化方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['CTCLoss',\n",
       " 'HingeLoss',\n",
       " 'HuberLoss',\n",
       " 'HybridBlock',\n",
       " 'KLDivLoss',\n",
       " 'L1Loss',\n",
       " 'L2Loss',\n",
       " 'LogisticLoss',\n",
       " 'Loss',\n",
       " 'SigmoidBCELoss',\n",
       " 'SigmoidBinaryCrossEntropyLoss',\n",
       " 'SoftmaxCELoss',\n",
       " 'SoftmaxCrossEntropyLoss',\n",
       " 'SquaredHingeLoss',\n",
       " 'TripletLoss',\n",
       " '__all__',\n",
       " '__builtins__',\n",
       " '__cached__',\n",
       " '__doc__',\n",
       " '__file__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " '_apply_weighting',\n",
       " '_reshape_like',\n",
       " 'absolute_import',\n",
       " 'ndarray',\n",
       " 'numeric_types']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mxnet.gluon import loss as gloss\n",
    "\n",
    "dir(gloss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）如何访问dense.weight的梯度？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method Parameter.grad of Parameter dense0_weight (shape=(1, 2), dtype=float32)>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dense.weight.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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