预备知识

数据预处理

1. 读取数据集

import os

os.makedirs(os.path.join('..', 'data'), exist_ok=True)
data_file = os.path.join('..', 'data', 'house_tiny.csv')
with open(data_file, 'w') as f:
    f.write('NumRooms,Alley,Price\n')  # 列名
    f.write('NA,Pave,127500\n')  # 每行表示一个数据样本
    f.write('2,NA,106000\n')
    f.write('4,NA,178100\n')
    f.write('NA,NA,140000\n')

# 如果没有安装pandas，只需取消对以下行的注释来安装pandas
# !pip install pandas
import pandas as pd

data = pd.read_csv(data_file)
print(data)

2. 处理缺失值

inputs, outputs = data.iloc[:, 0:2], data.iloc[:, 2]
inputs = inputs.fillna(inputs.mean())
print(inputs)

inputs = pd.get_dummies(inputs, dummy_na=True)
print(inputs)

3. 转换为张量格式

import tensorflow as tf

X, y = tf.constant(inputs.values), tf.constant(outputs.values)
X, y

线性神经网络

线性回归

线性回归的从零开始实现

数据流水线、模型、损失函数和小批量随机梯度下降优化器

%matplotlib inline
import random
import tensorflow as tf
from d2l import tensorflow as d2l

1. 生成数据集

def synthetic_data(w, b, num_examples):  #@save
    """生成y=Xw+b+噪声"""
    X = tf.zeros((num_examples, w.shape[0]))
    X += tf.random.normal(shape=X.shape)
    y = tf.matmul(X, tf.reshape(w, (-1, 1))) + b
    y += tf.random.normal(shape=y.shape, stddev=0.01)
    y = tf.reshape(y, (-1, 1))
    return X, y

true_w = tf.constant([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)

print('features:', features[0],'\nlabel:', labels[0])

d2l.set_figsize()
d2l.plt.scatter(features[:, (1)].numpy(), labels.numpy(), 1);

2. 读取数据集
   data_iter函数：接收批量大小、特征矩阵和标签向量作为输入，生成大小为batch_size的小批量。 每个小批量包含一组特征和标签。

def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    # 这些样本是随机读取的，没有特定的顺序
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        j = tf.constant(indices[i: min(i + batch_size, num_examples)])
        yield tf.gather(features, j), tf.gather(labels, j)

batch_size = 10

for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break

3. 初始化模型参数

w = tf.Variable(tf.random.normal(shape=(2, 1), mean=0, stddev=0.01),
                trainable=True)
b = tf.Variable(tf.zeros(1), trainable=True)

4. 定义模型

def linreg(X, w, b):  #@save
    """线性回归模型"""
    return tf.matmul(X, w) + b

5. 定义损失函数

def squared_loss(y_hat, y):  #@save
    """均方损失"""
    return (y_hat - tf.reshape(y, y_hat.shape)) ** 2 / 2

6. 定义优化算法
   sgd 函数：实现小批量随机梯度下降更新。 该函数接受模型参数集合、学习速率和批量大小作为输入。每 一步更新的大小由学习速率lr决定。

def sgd(params, grads, lr, batch_size):  #@save
    """小批量随机梯度下降"""
    for param, grad in zip(params, grads):
        param.assign_sub(lr*grad/batch_size)

7. 训练

lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        with tf.GradientTape() as g:
            l = loss(net(X, w, b), y)  # X和y的小批量损失
        # 计算l关于[w,b]的梯度
        dw, db = g.gradient(l, [w, b])
        # 使用参数的梯度更新参数
        sgd([w, b], [dw, db], lr, batch_size)
    train_l = loss(net(features, w, b), labels)
    print(f'epoch {epoch + 1}, loss {float(tf.reduce_mean(train_l)):f}')

print(f'w的估计误差: {true_w - tf.reshape(w, true_w.shape)}')
print(f'b的估计误差: {true_b - b}')

线性回归的简洁实现

1. 生成数据集

import numpy as np
import tensorflow as tf
from d2l import tensorflow as d2l

true_w = tf.constant([2, -3.4])
true_b = 4.2
features, labels = d2l.synthetic_data(true_w, true_b, 1000)

2. 读取数据集
   is_train：表示是否希望数据迭代器对象在每个迭代周期内打乱数据

def load_array(data_arrays, batch_size, is_train=True):  #@save
    """构造一个TensorFlow数据迭代器"""
    dataset = tf.data.Dataset.from_tensor_slices(data_arrays)
    if is_train:
        dataset = dataset.shuffle(buffer_size=1000)
    dataset = dataset.batch(batch_size)
    return dataset

batch_size = 10
data_iter = load_array((features, labels), batch_size)

next(iter(data_iter))

3. 定义模型
   我们首先定义一个模型变量net，它是一个Sequential类的实例。 Sequential类将多个层串联在一起。 当给定输入数据时，Sequential实例将数据传入到第一层， 然后将第一层的输出作为第二层的输入，以此类推。
   在Keras中，全连接层在Dense类中定义。 由于我们只想得到一个标量输出，所以我们将该数字设置为1。

# keras是TensorFlow的高级API
net = tf.keras.Sequential()
net.add(tf.keras.layers.Dense(1))

4. 初始化模型参数
   TensorFlow中的initializers模块提供了多种模型参数初始化方法。 在Keras中最简单的指定初始化方法是在创建层时指定kernel_initializer。 在这里，我们重新创建了net。

initializer = tf.initializers.RandomNormal(stddev=0.01)
net = tf.keras.Sequential()
net.add(tf.keras.layers.Dense(1, kernel_initializer=initializer))

5. 定义损失函数
   计算均方误差使用的是MeanSquaredError类，也称为平方范数。 默认情况下，它返回所有样本损失的平均值。

loss = tf.keras.losses.MeanSquaredError()

6. 定义优化算法
   小批量随机梯度下降算法是一种优化神经网络的标准工具， Keras在optimizers模块中实现了该算法的许多变种。 小批量随机梯度下降只需要设置learning_rate值，这里设置为0.03。

trainer = tf.keras.optimizers.SGD(learning_rate=0.03)

7. 训练

num_epochs = 3
for epoch in range(num_epochs):
    for X, y in data_iter:
        with tf.GradientTape() as tape:
            l = loss(net(X, training=True), y)
        grads = tape.gradient(l, net.trainable_variables)
        trainer.apply_gradients(zip(grads, net.trainable_variables))
    l = loss(net(features), labels)
    print(f'epoch {epoch + 1}, loss {l:f}')

w = net.get_weights()[0]
print('w的估计误差：', true_w - tf.reshape(w, true_w.shape))
b = net.get_weights()[1]
print('b的估计误差：', true_b - b)

Softmax回归（分类问题）

图像分类数据集

%matplotlib inline
import tensorflow as tf
from d2l import tensorflow as d2l

d2l.use_svg_display()

1. 读取数据集

mnist_train, mnist_test = tf.keras.datasets.fashion_mnist.load_data()

len(mnist_train[0]), len(mnist_test[0])
mnist_train[0][0].shape

def get_fashion_mnist_labels(labels):  #@save
    """返回Fashion-MNIST数据集的文本标签"""
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]

def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  #@save
    """绘制图像列表"""
    figsize = (num_cols * scale, num_rows * scale)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        ax.imshow(img.numpy())
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])
    return axes

X = tf.constant(mnist_train[0][:18])
y = tf.constant(mnist_train[1][:18])
show_images(X, 2, 9, titles=get_fashion_mnist_labels(y));

1. 读取小批量

batch_size = 256
train_iter = tf.data.Dataset.from_tensor_slices(
    mnist_train).batch(batch_size).shuffle(len(mnist_train[0]))

timer = d2l.Timer()
for X, y in train_iter:
    continue
f'{timer.stop():.2f} sec'

2. 整合所有组件

def load_data_fashion_mnist(batch_size, resize=None):   #@save
    """下载Fashion-MNIST数据集，然后将其加载到内存中"""
    mnist_train, mnist_test = tf.keras.datasets.fashion_mnist.load_data()
    # 将所有数字除以255，使所有像素值介于0和1之间，在最后添加一个批处理维度，
    # 并将标签转换为int32。
    process = lambda X, y: (tf.expand_dims(X, axis=3) / 255,
                            tf.cast(y, dtype='int32'))
    resize_fn = lambda X, y: (
        tf.image.resize_with_pad(X, resize, resize) if resize else X, y)
    return (
        tf.data.Dataset.from_tensor_slices(process(*mnist_train)).batch(
            batch_size).shuffle(len(mnist_train[0])).map(resize_fn),
        tf.data.Dataset.from_tensor_slices(process(*mnist_test)).batch(
            batch_size).map(resize_fn))

train_iter, test_iter = load_data_fashion_mnist(32, resize=64)
for X, y in train_iter:
    print(X.shape, X.dtype, y.shape, y.dtype)
    break

Softmax回归的从零开始实现

import tensorflow as tf
from IPython import display
from d2l import tensorflow as d2l

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

1. 初始化模型参数

num_inputs = 784
num_outputs = 10

W = tf.Variable(tf.random.normal(shape=(num_inputs, num_outputs),
                                 mean=0, stddev=0.01))
b = tf.Variable(tf.zeros(num_outputs))

2. 定义softmax操作

X = tf.constant([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
tf.reduce_sum(X, 0, keepdims=True), tf.reduce_sum(X, 1, keepdims=True)

def softmax(X):
    X_exp = tf.exp(X)
    partition = tf.reduce_sum(X_exp, 1, keepdims=True)
    return X_exp / partition  # 这里应用了广播机制

X = tf.random.normal((2, 5), 0, 1)
X_prob = softmax(X)
X_prob, tf.reduce_sum(X_prob, 1)

3. 定义模型

def net(X):
    return softmax(tf.matmul(tf.reshape(X, (-1, W.shape[0])), W) + b)

4. 定义损失函数

y_hat = tf.constant([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
y = tf.constant([0, 2])
tf.boolean_mask(y_hat, tf.one_hot(y, depth=y_hat.shape[-1]))

def cross_entropy(y_hat, y):
    return -tf.math.log(tf.boolean_mask(
        y_hat, tf.one_hot(y, depth=y_hat.shape[-1])))

cross_entropy(y_hat, y)

5. 分类精度

def accuracy(y_hat, y):  #@save
    """计算预测正确的数量"""
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
        y_hat = tf.argmax(y_hat, axis=1)
    cmp = tf.cast(y_hat, y.dtype) == y
    return float(tf.reduce_sum(tf.cast(cmp, y.dtype)))

accuracy(y_hat, y) / len(y)

def evaluate_accuracy(net, data_iter):  #@save
    """计算在指定数据集上模型的精度"""
    metric = Accumulator(2)  # 正确预测数、预测总数
    for X, y in data_iter:
        metric.add(accuracy(net(X), y), d2l.size(y))
    return metric[0] / metric[1]

class Accumulator:  #@save
    """在n个变量上累加"""
    def __init__(self, n):
        self.data = [0.0] * n

    def add(self, *args):
        self.data = [a + float(b) for a, b in zip(self.data, args)]

    def reset(self):
        self.data = [0.0] * len(self.data)

    def __getitem__(self, idx):
        return self.data[idx]

evaluate_accuracy(net, test_iter)

6. 训练

def train_epoch_ch3(net, train_iter, loss, updater):  #@save
    """训练模型一个迭代周期（定义见第3章）"""
    # 训练损失总和、训练准确度总和、样本数
    metric = Accumulator(3)
    for X, y in train_iter:
        # 计算梯度并更新参数
        with tf.GradientTape() as tape:
            y_hat = net(X)
            # Keras内置的损失接受的是（标签，预测），这不同于用户在本书中的实现。
            # 本书的实现接受（预测，标签），例如我们上面实现的“交叉熵”
            if isinstance(loss, tf.keras.losses.Loss):
                l = loss(y, y_hat)
            else:
                l = loss(y_hat, y)
        if isinstance(updater, tf.keras.optimizers.Optimizer):
            params = net.trainable_variables
            grads = tape.gradient(l, params)
            updater.apply_gradients(zip(grads, params))
        else:
            updater(X.shape[0], tape.gradient(l, updater.params))
        # Keras的loss默认返回一个批量的平均损失
        l_sum = l * float(tf.size(y)) if isinstance(
            loss, tf.keras.losses.Loss) else tf.reduce_sum(l)
        metric.add(l_sum, accuracy(y_hat, y), tf.size(y))
    # 返回训练损失和训练精度
    return metric[0] / metric[2], metric[1] / metric[2]

class Animator:  #@save
    """在动画中绘制数据"""
    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,
                 ylim=None, xscale='linear', yscale='linear',
                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,
                 figsize=(3.5, 2.5)):
        # 增量地绘制多条线
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes, ]
        # 使用lambda函数捕获参数
        self.config_axes = lambda: d2l.set_axes(
            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # 向图表中添加多个数据点
        if not hasattr(y, "__len__"):
            y = [y]
        n = len(y)
        if not hasattr(x, "__len__"):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] for _ in range(n)]
        for i, (a, b) in enumerate(zip(x, y)):
            if a is not None and b is not None:
                self.X[i].append(a)
                self.Y[i].append(b)
        self.axes[0].cla()
        for x, y, fmt in zip(self.X, self.Y, self.fmts):
            self.axes[0].plot(x, y, fmt)
        self.config_axes()
        display.display(self.fig)
        display.clear_output(wait=True)

def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  #@save
    """训练模型（定义见第3章）"""
    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],
                        legend=['train loss', 'train acc', 'test acc'])
    for epoch in range(num_epochs):
        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
        test_acc = evaluate_accuracy(net, test_iter)
        animator.add(epoch + 1, train_metrics + (test_acc,))
    train_loss, train_acc = train_metrics
    assert train_loss < 0.5, train_loss
    assert train_acc <= 1 and train_acc > 0.7, train_acc
    assert test_acc <= 1 and test_acc > 0.7, test_acc

class Updater():  #@save
    """用小批量随机梯度下降法更新参数"""
    def __init__(self, params, lr):
        self.params = params
        self.lr = lr

    def __call__(self, batch_size, grads):
        d2l.sgd(self.params, grads, self.lr, batch_size)

updater = Updater([W, b], lr=0.1)

num_epochs = 10
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)

7. 预测

def predict_ch3(net, test_iter, n=6):  #@save
    """预测标签（定义见第3章）"""
    for X, y in test_iter:
        break
    trues = d2l.get_fashion_mnist_labels(y)
    preds = d2l.get_fashion_mnist_labels(tf.argmax(net(X), axis=1))
    titles = [true +'\n' + pred for true, pred in zip(trues, preds)]
    d2l.show_images(
        tf.reshape(X[0:n], (n, 28, 28)), 1, n, titles=titles[0:n])

predict_ch3(net, test_iter)

Softmax回归的简洁实现

import tensorflow as tf
from d2l import tensorflow as d2l

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

1. 初始化模型参数

net = tf.keras.models.Sequential()
net.add(tf.keras.layers.Flatten(input_shape=(28, 28)))
weight_initializer = tf.keras.initializers.RandomNormal(mean=0.0, stddev=0.01)
net.add(tf.keras.layers.Dense(10, kernel_initializer=weight_initializer))

2. 重新审视Softmax的实现

loss = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)

3. 优化算法

trainer = tf.keras.optimizers.SGD(learning_rate=.1)

4. 训练

num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

多层感知机

激活函数（从线性到非线性）

1. ReLU函数

x = tf.Variable(tf.range(-8.0, 8.0, 0.1), dtype=tf.float32)
y = tf.nn.relu(x)
d2l.plot(x.numpy(), y.numpy(), 'x', 'relu(x)', figsize=(5, 2.5))

with tf.GradientTape() as t:
    y = tf.nn.relu(x)
d2l.plot(x.numpy(), t.gradient(y, x).numpy(), 'x', 'grad of relu',
         figsize=(5, 2.5))

2. sigmoid函数

y = tf.nn.sigmoid(x)
d2l.plot(x.numpy(), y.numpy(), 'x', 'sigmoid(x)', figsize=(5, 2.5))

with tf.GradientTape() as t:
    y = tf.nn.sigmoid(x)
d2l.plot(x.numpy(), t.gradient(y, x).numpy(), 'x', 'grad of sigmoid',
         figsize=(5, 2.5))

3. tanh函数

y = tf.nn.tanh(x)
d2l.plot(x.numpy(), y.numpy(), 'x', 'tanh(x)', figsize=(5, 2.5))

with tf.GradientTape() as t:
    y = tf.nn.tanh(x)
d2l.plot(x.numpy(), t.gradient(y, x).numpy(), 'x', 'grad of tanh',
         figsize=(5, 2.5))

多层感知机的从零开始实现

import tensorflow as tf
from d2l import tensorflow as d2l

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

1. 初始化模型参数

num_inputs, num_outputs, num_hiddens = 784, 10, 256

W1 = tf.Variable(tf.random.normal(
    shape=(num_inputs, num_hiddens), mean=0, stddev=0.01))
b1 = tf.Variable(tf.zeros(num_hiddens))
W2 = tf.Variable(tf.random.normal(
    shape=(num_hiddens, num_outputs), mean=0, stddev=0.01))
b2 = tf.Variable(tf.zeros(num_outputs))

params = [W1, b1, W2, b2]

2. 激活函数

def relu(X):
    return tf.math.maximum(X, 0)

3. 模型

def net(X):
    X = tf.reshape(X, (-1, num_inputs))
    H = relu(tf.matmul(X, W1) + b1)
    return tf.matmul(H, W2) + b2

4. 损失函数

def loss(y_hat, y):
    return tf.losses.sparse_categorical_crossentropy(
        y, y_hat, from_logits=True)

5. 训练

num_epochs, lr = 10, 0.1
updater = d2l.Updater([W1, W2, b1, b2], lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)

多层感知机的简洁实现

import tensorflow as tf
from d2l import tensorflow as d2l

1. 模型

net = tf.keras.models.Sequential([
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(256, activation='relu'),
    tf.keras.layers.Dense(10)])

batch_size, lr, num_epochs = 256, 0.1, 10
loss = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
trainer = tf.keras.optimizers.SGD(learning_rate=lr)

train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

模型选择、欠拟合和过拟合

多项式回归

import math
import numpy as np
import tensorflow as tf
from d2l import tensorflow as d2l

1. 生成数据集

max_degree = 20  # 多项式的最大阶数
n_train, n_test = 100, 100  # 训练和测试数据集大小
true_w = np.zeros(max_degree)  # 分配大量的空间
true_w[0:4] = np.array([5, 1.2, -3.4, 5.6])

features = np.random.normal(size=(n_train + n_test, 1))
np.random.shuffle(features)
poly_features = np.power(features, np.arange(max_degree).reshape(1, -1))
for i in range(max_degree):
    poly_features[:, i] /= math.gamma(i + 1)  # gamma(n)=(n-1)!
# labels的维度:(n_train+n_test,)
labels = np.dot(poly_features, true_w)
labels += np.random.normal(scale=0.1, size=labels.shape)

# NumPy ndarray转换为tensor
true_w, features, poly_features, labels = [tf.constant(x, dtype=
    tf.float32) for x in [true_w, features, poly_features, labels]]

features[:2], poly_features[:2, :], labels[:2]

2. 对模型进行训练和测试

def evaluate_loss(net, data_iter, loss):  #@save
    """评估给定数据集上模型的损失"""
    metric = d2l.Accumulator(2)  # 损失的总和,样本数量
    for X, y in data_iter:
        l = loss(net(X), y)
        metric.add(tf.reduce_sum(l), d2l.size(l))
    return metric[0] / metric[1]

def train(train_features, test_features, train_labels, test_labels,
          num_epochs=400):
    loss = tf.losses.MeanSquaredError()
    input_shape = train_features.shape[-1]
    # 不设置偏置，因为我们已经在多项式中实现了它
    net = tf.keras.Sequential()
    net.add(tf.keras.layers.Dense(1, use_bias=False))
    batch_size = min(10, train_labels.shape[0])
    train_iter = d2l.load_array((train_features, train_labels), batch_size)
    test_iter = d2l.load_array((test_features, test_labels), batch_size,
                               is_train=False)
    trainer = tf.keras.optimizers.SGD(learning_rate=.01)
    animator = d2l.Animator(xlabel='epoch', ylabel='loss', yscale='log',
                            xlim=[1, num_epochs], ylim=[1e-3, 1e2],
                            legend=['train', 'test'])
    for epoch in range(num_epochs):
        d2l.train_epoch_ch3(net, train_iter, loss, trainer)
        if epoch == 0 or (epoch + 1) % 20 == 0:
            animator.add(epoch + 1, (evaluate_loss(net, train_iter, loss),
                                     evaluate_loss(net, test_iter, loss)))
    print('weight:', net.get_weights()[0].T)

3. 三阶多项式函数拟合（正常）

# 从多项式特征中选择前4个维度，即1,x,x^2/2!,x^3/3!
train(poly_features[:n_train, :4], poly_features[n_train:, :4],
      labels[:n_train], labels[n_train:])

4. 线性函数拟合（欠拟合）

# 从多项式特征中选择前2个维度，即1和x
train(poly_features[:n_train, :2], poly_features[n_train:, :2],
      labels[:n_train], labels[n_train:])

5. 高阶多项式函数拟合（过拟合）

# 从多项式特征中选取所有维度
train(poly_features[:n_train, :], poly_features[n_train:, :],
      labels[:n_train], labels[n_train:], num_epochs=1500)

权重衰减（L2正则化）

高维线性回归

%matplotlib inline
import tensorflow as tf
from d2l import tensorflow as d2l

n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
true_w, true_b = tf.ones((num_inputs, 1)) * 0.01, 0.05
train_data = d2l.synthetic_data(true_w, true_b, n_train)
train_iter = d2l.load_array(train_data, batch_size)
test_data = d2l.synthetic_data(true_w, true_b, n_test)
test_iter = d2l.load_array(test_data, batch_size, is_train=False)

从零开始实现

1. 初始化模型参数

def init_params():
    w = tf.Variable(tf.random.normal(mean=1, shape=(num_inputs, 1)))
    b = tf.Variable(tf.zeros(shape=(1, )))
    return [w, b]

2. 定义L2范数惩罚

def l2_penalty(w):
    return tf.reduce_sum(tf.pow(w, 2)) / 2

3. 定义训练代码实现

def train(lambd):
    w, b = init_params()
    net, loss = lambda X: d2l.linreg(X, w, b), d2l.squared_loss
    num_epochs, lr = 100, 0.003
    animator = d2l.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            with tf.GradientTape() as tape:
                # 增加了L2范数惩罚项，
                # 广播机制使l2_penalty(w)成为一个长度为batch_size的向量
                l = loss(net(X), y) + lambd * l2_penalty(w)
            grads = tape.gradient(l, [w, b])
            d2l.sgd([w, b], grads, lr, batch_size)
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1, (d2l.evaluate_loss(net, train_iter, loss),
                                     d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数是：', tf.norm(w).numpy())

4. 忽略正则化直接训练

train(lambd=0)

5. 使用权重衰减

train(lambd=3)

简洁实现

def train_concise(wd):
    net = tf.keras.models.Sequential()
    net.add(tf.keras.layers.Dense(
        1, kernel_regularizer=tf.keras.regularizers.l2(wd)))
    net.build(input_shape=(1, num_inputs))
    w, b = net.trainable_variables
    loss = tf.keras.losses.MeanSquaredError()
    num_epochs, lr = 100, 0.003
    trainer = tf.keras.optimizers.SGD(learning_rate=lr)
    animator = d2l.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            with tf.GradientTape() as tape:
                # tf.keras需要为自定义训练代码手动添加损失。
                l = loss(net(X), y) + net.losses
            grads = tape.gradient(l, net.trainable_variables)
            trainer.apply_gradients(zip(grads, net.trainable_variables))
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1, (d2l.evaluate_loss(net, train_iter, loss),
                                     d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数：', tf.norm(net.get_weights()[0]).numpy())

train_concise(0)

train_concise(3)

暂退法（Dropout）

从零开始实现

import tensorflow as tf
from d2l import tensorflow as d2l


def dropout_layer(X, dropout):
    assert 0 <= dropout <= 1
    # 在本情况中，所有元素都被丢弃
    if dropout == 1:
        return tf.zeros_like(X)
    # 在本情况中，所有元素都被保留
    if dropout == 0:
        return X
    mask = tf.random.uniform(
        shape=tf.shape(X), minval=0, maxval=1) < 1 - dropout
    return tf.cast(mask, dtype=tf.float32) * X / (1.0 - dropout)

X = tf.reshape(tf.range(16, dtype=tf.float32), (2, 8))
print(X)
print(dropout_layer(X, 0.))
print(dropout_layer(X, 0.5))
print(dropout_layer(X, 1.))

1. 定义模型参数

num_outputs, num_hiddens1, num_hiddens2 = 10, 256, 256

2. 定义模型

dropout1, dropout2 = 0.2, 0.5

class Net(tf.keras.Model):
    def __init__(self, num_outputs, num_hiddens1, num_hiddens2):
        super().__init__()
        self.input_layer = tf.keras.layers.Flatten()
        self.hidden1 = tf.keras.layers.Dense(num_hiddens1, activation='relu')
        self.hidden2 = tf.keras.layers.Dense(num_hiddens2, activation='relu')
        self.output_layer = tf.keras.layers.Dense(num_outputs)

    def call(self, inputs, training=None):
        x = self.input_layer(inputs)
        x = self.hidden1(x)
        # 只有在训练模型时才使用dropout
        if training:
            # 在第一个全连接层之后添加一个dropout层
            x = dropout_layer(x, dropout1)
        x = self.hidden2(x)
        if training:
            # 在第二个全连接层之后添加一个dropout层
            x = dropout_layer(x, dropout2)
        x = self.output_layer(x)
        return x

net = Net(num_outputs, num_hiddens1, num_hiddens2)

3. 训练和测试

num_epochs, lr, batch_size = 10, 0.5, 256
loss = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
trainer = tf.keras.optimizers.SGD(learning_rate=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

简洁实现

net = tf.keras.models.Sequential([
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(256, activation=tf.nn.relu),
    # 在第一个全连接层之后添加一个dropout层
    tf.keras.layers.Dropout(dropout1),
    tf.keras.layers.Dense(256, activation=tf.nn.relu),
    # 在第二个全连接层之后添加一个dropout层
    tf.keras.layers.Dropout(dropout2),
    tf.keras.layers.Dense(10),
])

trainer = tf.keras.optimizers.SGD(learning_rate=lr)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

实战Kaggle比赛：预测房价

1. 下载和缓存数据集

import hashlib
import os
import tarfile
import zipfile
import requests

#@save
DATA_HUB = dict()
DATA_URL = 'http://d2l-data.s3-accelerate.amazonaws.com/'

def download(name, cache_dir=os.path.join('..', 'data')):  #@save
    """下载一个DATA_HUB中的文件，返回本地文件名"""
    assert name in DATA_HUB, f"{name} 不存在于 {DATA_HUB}"
    url, sha1_hash = DATA_HUB[name]
    os.makedirs(cache_dir, exist_ok=True)
    fname = os.path.join(cache_dir, url.split('/')[-1])
    if os.path.exists(fname):
        sha1 = hashlib.sha1()
        with open(fname, 'rb') as f:
            while True:
                data = f.read(1048576)
                if not data:
                    break
                sha1.update(data)
        if sha1.hexdigest() == sha1_hash:
            return fname  # 命中缓存
    print(f'正在从{url}下载{fname}...')
    r = requests.get(url, stream=True, verify=True)
    with open(fname, 'wb') as f:
        f.write(r.content)
    return fname

def download_extract(name, folder=None):  #@save
    """下载并解压zip/tar文件"""
    fname = download(name)
    base_dir = os.path.dirname(fname)
    data_dir, ext = os.path.splitext(fname)
    if ext == '.zip':
        fp = zipfile.ZipFile(fname, 'r')
    elif ext in ('.tar', '.gz'):
        fp = tarfile.open(fname, 'r')
    else:
        assert False, '只有zip/tar文件可以被解压缩'
    fp.extractall(base_dir)
    return os.path.join(base_dir, folder) if folder else data_dir

def download_all():  #@save
    """下载DATA_HUB中的所有文件"""
    for name in DATA_HUB:
        download(name)

2. Kaggle
3. 访问和读取数据集

# 如果你没有安装pandas，请取消下一行的注释
# !pip install pandas

%matplotlib inline
import numpy as np
import pandas as pd
import tensorflow as tf
from d2l import tensorflow as d2l

DATA_HUB['kaggle_house_train'] = (  #@save
    DATA_URL + 'kaggle_house_pred_train.csv',
    '585e9cc93e70b39160e7921475f9bcd7d31219ce')

DATA_HUB['kaggle_house_test'] = (  #@save
    DATA_URL + 'kaggle_house_pred_test.csv',
    'fa19780a7b011d9b009e8bff8e99922a8ee2eb90')

train_data = pd.read_csv(download('kaggle_house_train'))
test_data = pd.read_csv(download('kaggle_house_test'))

print(train_data.shape)
print(test_data.shape)

print(train_data.iloc[0:4, [0, 1, 2, 3, -3, -2, -1]])

all_features = pd.concat((train_data.iloc[:, 1:-1], test_data.iloc[:, 1:]))

4. 数据预处理

# 若无法获得测试数据，则可根据训练数据计算均值和标准差
numeric_features = all_features.dtypes[all_features.dtypes != 'object'].index
all_features[numeric_features] = all_features[numeric_features].apply(
    lambda x: (x - x.mean()) / (x.std()))
# 在标准化数据之后，所有均值消失，因此我们可以将缺失值设置为0
all_features[numeric_features] = all_features[numeric_features].fillna(0)

# “Dummy_na=True”将“na”（缺失值）视为有效的特征值，并为其创建指示符特征
all_features = pd.get_dummies(all_features, dummy_na=True)
all_features.shape

n_train = train_data.shape[0]
train_features = tf.constant(all_features[:n_train].values, dtype=tf.float32)
test_features = tf.constant(all_features[n_train:].values, dtype=tf.float32)
train_labels = tf.constant(
    train_data.SalePrice.values.reshape(-1, 1), dtype=tf.float32)

5. 训练

loss = tf.keras.losses.MeanSquaredError()

def get_net():
    net = tf.keras.models.Sequential()
    net.add(tf.keras.layers.Dense(
        1, kernel_regularizer=tf.keras.regularizers.l2(weight_decay)))
    return net

def log_rmse(y_true, y_pred):
    # 为了在取对数时进一步稳定该值，将小于1的值设置为1
    clipped_preds = tf.clip_by_value(y_pred, 1, float('inf'))
    return tf.sqrt(tf.reduce_mean(loss(
        tf.math.log(y_true), tf.math.log(clipped_preds))))

def train(net, train_features, train_labels, test_features, test_labels,
          num_epochs, learning_rate, weight_decay, batch_size):
    train_ls, test_ls = [], []
    train_iter = d2l.load_array((train_features, train_labels), batch_size)
    # 这里使用的是Adam优化算法
    optimizer = tf.keras.optimizers.Adam(learning_rate)
    net.compile(loss=loss, optimizer=optimizer)
    for epoch in range(num_epochs):
        for X, y in train_iter:
            with tf.GradientTape() as tape:
                y_hat = net(X)
                l = loss(y, y_hat)
            params = net.trainable_variables
            grads = tape.gradient(l, params)
            optimizer.apply_gradients(zip(grads, params))
        train_ls.append(log_rmse(train_labels, net(train_features)))
        if test_labels is not None:
            test_ls.append(log_rmse(test_labels, net(test_features)))
    return train_ls, test_ls

6. K折交叉验证

def get_k_fold_data(k, i, X, y):
    assert k > 1
    fold_size = X.shape[0] // k
    X_train, y_train = None, None
    for j in range(k):
        idx = slice(j * fold_size, (j + 1) * fold_size)
        X_part, y_part = X[idx, :], y[idx]
        if j == i:
            X_valid, y_valid = X_part, y_part
        elif X_train is None:
            X_train, y_train = X_part, y_part
        else:
            X_train = tf.concat([X_train, X_part], 0)
            y_train = tf.concat([y_train, y_part], 0)
    return X_train, y_train, X_valid, y_valid

def k_fold(k, X_train, y_train, num_epochs, learning_rate, weight_decay,
           batch_size):
    train_l_sum, valid_l_sum = 0, 0
    for i in range(k):
        data = get_k_fold_data(k, i, X_train, y_train)
        net = get_net()
        train_ls, valid_ls = train(net, *data, num_epochs, learning_rate,
                                   weight_decay, batch_size)
        train_l_sum += train_ls[-1]
        valid_l_sum += valid_ls[-1]
        if i == 0:
            d2l.plot(list(range(1, num_epochs + 1)), [train_ls, valid_ls],
                     xlabel='epoch', ylabel='rmse', xlim=[1, num_epochs],
                     legend=['train', 'valid'], yscale='log')
        print(f'折{i + 1}，训练log rmse{float(train_ls[-1]):f}, '
              f'验证log rmse{float(valid_ls[-1]):f}')
    return train_l_sum / k, valid_l_sum / k

7. 模型选择

k, num_epochs, lr, weight_decay, batch_size = 5, 100, 5, 0, 64
train_l, valid_l = k_fold(k, train_features, train_labels, num_epochs, lr,
                          weight_decay, batch_size)
print(f'{k}-折验证: 平均训练log rmse: {float(train_l):f}, '
      f'平均验证log rmse: {float(valid_l):f}')

8. 提交Kaggle预测

def train_and_pred(train_features, test_features, train_labels, test_data,
                   num_epochs, lr, weight_decay, batch_size):
    net = get_net()
    train_ls, _ = train(net, train_features, train_labels, None, None,
                        num_epochs, lr, weight_decay, batch_size)
    d2l.plot(np.arange(1, num_epochs + 1), [train_ls], xlabel='epoch',
             ylabel='log rmse', xlim=[1, num_epochs], yscale='log')
    print(f'训练log rmse：{float(train_ls[-1]):f}')
    # 将网络应用于测试集。
    preds = net(test_features).numpy()
    # 将其重新格式化以导出到Kaggle
    test_data['SalePrice'] = pd.Series(preds.reshape(1, -1)[0])
    submission = pd.concat([test_data['Id'], test_data['SalePrice']], axis=1)
    submission.to_csv('submission.csv', index=False)

train_and_pred(train_features, test_features, train_labels, test_data,
               num_epochs, lr, weight_decay, batch_size)