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

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   "source": [
    "# Linear Regression Implementation from Scratch"
   ]
  },
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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",
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    "Construct labels through:\n",
    "$$\\mathbf{y}= \\mathbf{X} \\mathbf{w} + b + \\mathbf\\epsilon$$\n",
    "with $\\mathbf{w} = [2, -3.4]^\\top$ and $b = 4.2$."
   ]
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    "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": [
    "Check the generated data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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     "end_time": "2019-07-03T21:57:33.993865Z",
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     "name": "stdout",
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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>"
      ]
     },
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     },
     "output_type": "display_data"
    }
   ],
   "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": [
    "Reading a mini-batch data, namely `batch_size` randomly sampled examples, each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:57:34.003662Z",
     "start_time": "2019-07-03T21:57:33.996680Z"
    },
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     "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": [
    "Check what a mini-batch looks like."
   ]
  },
  {
   "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",
      "[[ 1.0380163   0.8255258 ]\n",
      " [-0.23647429 -0.2963644 ]\n",
      " [-0.24017854 -0.34283012]\n",
      " [-0.48774993 -0.02261727]\n",
      " [ 0.09210896 -0.1585041 ]\n",
      " [-0.4844843   2.3336477 ]\n",
      " [-0.10980018 -0.43571743]\n",
      " [-0.26519665  1.5181851 ]\n",
      " [-1.0743258  -1.0601982 ]\n",
      " [ 0.8806273   1.9885163 ]]\n",
      "y =\n",
      "[ 3.4770956   4.7410684   4.876036    3.310762    4.9234405  -4.7084603\n",
      "  5.450973   -1.4937832   5.6719446  -0.79267937]\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": [
    "Randomly initialize model parameters and attach gradients"
   ]
  },
  {
   "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": [
    "Define the model and loss function"
   ]
  },
  {
   "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": [
    "Optimization algorithm"
   ]
  },
  {
   "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": [
    "Training"
   ]
  },
  {
   "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 0.040481\n",
      "epoch 2, loss 0.000160\n",
      "epoch 3, loss 0.000050\n",
      "Error in estimating w [4.0352345e-04 3.6478043e-05]\n",
      "Error in estimating b [0.00053549]\n"
     ]
    }
   ],
   "source": [
    "lr, num_epochs = 0.03, 3  # Learning rate and number of data epochs\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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