notebooks-1/6-softmax-regression-scratch.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Softmax 回归的从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.348783Z",
     "start_time": "2019-07-03T22:03:00.100284Z"
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     "id": "",
     "n": "1"
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   },
   "outputs": [],
   "source": [
    "import d2l\n",
    "from mxnet import autograd, np, npx, gluon\n",
    "from IPython import display\n",
    "npx.set_np()\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": [
    "初始模型参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.358820Z",
     "start_time": "2019-07-03T22:03:02.352386Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
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   },
   "outputs": [],
   "source": [
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "\n",
    "W = np.random.normal(0, 0.01, (num_inputs, num_outputs))\n",
    "b = np.zeros(num_outputs)\n",
    "\n",
    "W.attach_grad()\n",
    "b.attach_grad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现 softmax 计算子。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.427233Z",
     "start_time": "2019-07-03T22:03:02.361623Z"
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    "attributes": {
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     "id": "",
     "n": "6"
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   },
   "outputs": [
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "def softmax(X):\n",
    "    X_exp = np.exp(X)\n",
    "    partition = X_exp.sum(axis=1, keepdims=True)\n",
    "    return X_exp / partition  # The broadcast mechanism is applied here\n",
    "\n",
    "X = np.random.normal(size=(2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob.shape, X_prob.sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.434175Z",
     "start_time": "2019-07-03T22:03:02.430034Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
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   },
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(np.dot(X.reshape((-1, num_inputs)), W) + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义损失函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.440123Z",
     "start_time": "2019-07-03T22:03:02.436124Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    }
   },
   "outputs": [],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    return - np.log(y_hat[range(len(y_hat)), y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "实现分类精度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.919658Z",
     "start_time": "2019-07-03T22:03:02.441863Z"
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    "attributes": {
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     "n": "11"
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    "slideshow": {
     "slide_type": "-"
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     "execution_count": 6,
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   "source": [
    "def accuracy(y_hat, y):\n",
    "    return float((y_hat.argmax(axis=1) == y.astype('float32')).sum())\n",
    "\n",
    "def evaluate_accuracy(net, data_iter):\n",
    "    metric = d2l.Accumulator(2) # num_corrected_examples, num_examples\n",
    "    for X, y in data_iter:\n",
    "        metric.add(accuracy(net(X), y), y.size)\n",
    "    return metric[0] / metric[1]\n",
    "\n",
    "evaluate_accuracy(net, test_iter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练一个周期。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.927193Z",
     "start_time": "2019-07-03T22:03:02.921495Z"
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   "source": [
    "def train_epoch_ch3(net, train_iter, loss, updater):\n",
    "    metric = d2l.Accumulator(3) # 训练损失和，训练精度和，样本数。\n",
    "    if isinstance(updater, gluon.Trainer):\n",
    "        updater = updater.step\n",
    "    for X, y in train_iter:\n",
    "        with autograd.record():\n",
    "            y_hat = net(X)\n",
    "            l = loss(y_hat, y)\n",
    "        l.backward()\n",
    "        updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.size)\n",
    "    # Return training loss and training accuracy\n",
    "    return metric[0]/metric[2], metric[1]/metric[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "整个训练函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:02.938271Z",
     "start_time": "2019-07-03T22:03:02.930873Z"
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   },
   "outputs": [],
   "source": [
    "def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):\n",
    "    trains, test_accs = [], []\n",
    "    animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],\n",
    "                            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,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:37.341014Z",
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    "attributes": {
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     "id": "",
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    "scrolled": true,
    "slideshow": {
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   "outputs": [
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   "source": [
    "num_epochs, lr = 10, 0.1\n",
    "updater = lambda batch_size: d2l.sgd([W, b], lr, batch_size)\n",
    "train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)"
   ]
  },
  {
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   "metadata": {
    "slideshow": {
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    }
   },
   "source": [
    "预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:03:37.687138Z",
     "start_time": "2019-07-03T22:03:37.342981Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "19"
    },
    "scrolled": true
   },
   "outputs": [
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   ],
   "source": [
    "def predict_ch3(net, test_iter, n=6):\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(X[0:n].reshape((n,28,28)), 1, n, titles=titles[0:n])\n",
    "\n",
    "predict_ch3(net, test_iter)"
   ]
  }
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