{
"cells": [
{
"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"
},
"attributes": {
"classes": [],
"id": "",
"n": "1"
}
},
"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"
}
},
"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"
},
"attributes": {
"classes": [],
"id": "",
"n": "6"
}
},
"outputs": [
{
"data": {
"text/plain": [
"((2, 5), array([1.0000001, 1. ]))"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"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"
}
},
"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"
},
"attributes": {
"classes": [],
"id": "",
"n": "11"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.0925"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"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"
},
"attributes": {
"classes": [],
"id": "",
"n": "15"
}
},
"outputs": [],
"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"
},
"attributes": {
"classes": [],
"id": "",
"n": "17"
}
},
"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",
"start_time": "2019-07-03T22:03:02.940645Z"
},
"attributes": {
"classes": [],
"id": "",
"n": "18"
},
"scrolled": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
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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)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"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": {
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"n": "19"
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"scrolled": true
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"outputs": [
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"\n",
"\n",
"\n",
"\n"
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"text/plain": [
""
]
},
"metadata": {
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"output_type": "display_data"
}
],
"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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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
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"toc": {
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"title_cell": "Table of Contents",
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