notebooks-1/3-linear-regression-scratch.ipynb

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   "source": [
    "# 从 0 开始的线性回归"
   ]
  },
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   "source": [
    "%matplotlib inline\n",
    "import d2l\n",
    "from mxnet import autograd, np, npx\n",
    "import random\n",
    "npx.set_np()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "使用如下创建标号\n",
    "$$\\mathbf{y}= \\mathbf{X} \\mathbf{w} + b + \\mathbf\\epsilon$$\n",
    "这里 $\\mathbf{w} = [2, -3.4]^\\top$ 和 $b = 4.2$。"
   ]
  },
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   "source": [
    "def synthetic_data(w, b, num_examples):\n",
    "    X = np.random.normal(0, 1, (num_examples, len(w)))\n",
    "    y = np.dot(X, w) + b\n",
    "    y += np.random.normal(0, 0.01, y.shape)\n",
    "    return X, y\n",
    "\n",
    "true_w = np.array([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "查看创建的数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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     "end_time": "2019-07-03T21:57:33.993865Z",
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     "text": [
      "features: [2.2122064 0.7740038] \n",
      "label: 6.000587\n"
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "print('features:', features[0],'\\nlabel:', labels[0])\n",
    "d2l.set_figsize((3.5, 2.5))\n",
    "d2l.plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "读取一个小批量，也就是 `batch_size` 个随机采样到的样本。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.003662Z",
     "start_time": "2019-07-03T21:57:33.996680Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices)  # read at random\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = min(i + batch_size, num_examples)\n",
    "        batch_indices = np.array(indices[i:j])\n",
    "        yield features[batch_indices], labels[batch_indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "查看一个小批量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.075882Z",
     "start_time": "2019-07-03T21:57:34.005992Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X =\n",
      "[[-1.2064103  -0.5134857 ]\n",
      " [-0.10867531 -1.1554946 ]\n",
      " [-0.8474277   0.91881126]\n",
      " [ 0.8370042  -1.1026353 ]\n",
      " [ 1.5543168  -1.0218834 ]\n",
      " [ 0.343837    0.02602482]\n",
      " [-1.2712238  -1.9902322 ]\n",
      " [ 0.3717077   0.9300072 ]\n",
      " [-0.6205473   0.7588377 ]\n",
      " [-0.8431705  -0.42457297]]\n",
      "y =\n",
      "[ 3.5305307   7.916799   -0.62370265  9.621203   10.769879    4.792636\n",
      "  8.41412     1.7626055   0.3863677   3.9524884 ]\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print('X =\\n%s\\ny =\\n%s' % (X, y))\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "随机初始化模型权重并附上梯度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.082441Z",
     "start_time": "2019-07-03T21:57:34.077502Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [],
   "source": [
    "w = np.random.normal(0, 0.01, (2, 1))\n",
    "b = np.zeros(1)\n",
    "\n",
    "w.attach_grad()\n",
    "b.attach_grad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义模型和损失函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.090815Z",
     "start_time": "2019-07-03T21:57:34.086013Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "9"
    }
   },
   "outputs": [],
   "source": [
    "def linreg(X, w, b):\n",
    "    return np.dot(X, w) + b\n",
    "\n",
    "def squared_loss(y_hat, y):\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义优化算法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.097896Z",
     "start_time": "2019-07-03T21:57:34.093948Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "11"
    }
   },
   "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": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:42.097735Z",
     "start_time": "2019-07-03T21:57:34.100263Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "12"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.040532\n",
      "epoch 2, loss 0.000148\n",
      "epoch 3, loss 0.000050\n",
      "Error in estimating w [ 0.00038743 -0.0003047 ]\n",
      "Error in estimating b [0.00041628]\n"
     ]
    }
   ],
   "source": [
    "lr, num_epochs = 0.03, 3  # 学习率和数据迭代周期。\n",
    "net, loss = linreg, squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        with autograd.record():\n",
    "            l = loss(net(X, w, b), y)\n",
    "        l.backward()\n",
    "        sgd([w, b], lr, batch_size)\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss %f' % (epoch + 1, train_l.mean()))\n",
    "    \n",
    "print('Error in estimating w', true_w - w.reshape(true_w.shape))\n",
    "print('Error in estimating b', true_b - b)    "
   ]
  }
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