【动手学深度学习】---0x03：softmax回归

【动手学深度学习】—0x03：softmax回归

基础知识

• softmax回归是一个单层神经网络，输出个数等于分类问题中的类别个数。
• 交叉熵损失函数适合衡量两个概率分布的差异。

图像分类数据集

本节我们将使用torchvision包，它是服务于PyTorch深度学习框架的，主要用来构建计算机视觉模型。torchvision主要由以下几部分构成：

torchvision.datasets: 一些加载数据的函数及常用的数据集接口；
torchvision.models: 包含常用的模型结构（含预训练模型），例如AlexNet、VGG、ResNet等；
torchvision.transforms: 常用的图片变换，例如裁剪、旋转等；
torchvision.utils: 其他的一些有用的方法。

import torch
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt
import time
import sys
sys.path.append("..") # 为了导入上层目录的d2lzh_pytorch
import d2lzh_pytorch as d2l

# 所有的数据集都是torch.utils.data.Dataset的子类， 即：它们实现了__getitem__和__len__方法。因此，它们都可以传递给torch.utils.data.DataLoader，进而通过torch.multiprocessing实现批数据的并行化加载torch.utils.data.DataLoader，进而通过torch.multiprocessing实现批数据的并行化加载。
mnist_train = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='~/Datasets/FashionMNIST', train=False, download=True, transform=transforms.ToTensor())


# 本函数已保存在d2lzh包中方便以后使用，可以将数值标签转成相应的文本标签。
def get_fashion_mnist_labels(labels):
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]

# 本函数已保存在d2lzh包中方便以后使用，一个可以在一行里画出多张图像和对应标签的函数。
def show_fashion_mnist(images, labels):
    d2l.use_svg_display()
    # 这里的_表示我们忽略（不使用）的变量
    _, figs = plt.subplots(1, len(images), figsize=(12, 12))
    for f, img, lbl in zip(figs, images, labels):
        f.imshow(img.view((28, 28)).numpy())
        f.set_title(lbl)
        f.axes.get_xaxis().set_visible(False)
        f.axes.get_yaxis().set_visible(False)
    plt.show()

# 读取小批量
batch_size = 256
if sys.platform.startswith('win'):
    num_workers = 0  # 0表示不用额外的进程来加速读取数据
else:
    num_workers = 4
# torch.utils.data.DataLoader将自定义的Dataset根据batch size大小、是否shuffle等封装成一个Batch Size大小的Tensor，用于后面的训练。
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)

softmax回归从零开始实现

import torch
import torchvision
import numpy as np
import sys
sys.path.append("..") # 为了导入上层目录的d2lzh_pytorch
import d2lzh_pytorch as d2l

# 获取和读取数据集
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)


#初始化模型参数
num_inputs = 784
num_outputs = 10

W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)
b = torch.zeros(num_outputs, dtype=torch.float)

W.requires_grad_(requires_grad=True)
b.requires_grad_(requires_grad=True) 

# 对多维Tensor按维操作
# 同一列dim=0；同一行dim=1，在结果中保持维度keepdim=True
X = torch.tensor([[1, 2, 3], [4, 5, 6]])
print(X.sum(dim=0, keepdim=True))
print(X.sum(dim=1, keepdim=True))


# softamx运算
def softmax(X):
    X_exp = X.exp()
    partition = X_exp.sum(dim=1, keepdim=True)
    return X_exp / partition  # 这里应用了广播机制


# 定义模型
def net(X):
    return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)


# 定义损失函数
def cross_entropy(y_hat, y):
    return - torch.log(y_hat.gather(1, y.view(-1, 1)))


# 计算分类准确率
def accuracy(y_hat, y):
    return (y_hat.argmax(dim=1) == y).float().mean().item()

# 训练模型
num_epochs, lr = 5, 0.1

# 本函数已保存在d2lzh包中方便以后使用
def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,
              params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
        for X, y in train_iter:
            y_hat = net(X)
            l = loss(y_hat, y).sum()

            # 梯度清零
            if optimizer is not None:
                optimizer.zero_grad()
            elif params is not None and params[0].grad is not None:
                for param in params:
                    param.grad.data.zero_()

            l.backward()
            if optimizer is None:
                d2l.sgd(params, lr, batch_size)
            else:
                optimizer.step()  # “softmax回归的简洁实现”一节将用到


            train_l_sum += l.item()
            train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
            n += y.shape[0]
        test_acc = evaluate_accuracy(test_iter, net)
        print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'
              % (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))

train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)

# 预测
X, y = iter(test_iter).next()

true_labels = d2l.get_fashion_mnist_labels(y.numpy())
pred_labels = d2l.get_fashion_mnist_labels(net(X).argmax(dim=1).numpy())
titles = [true + '\n' + pred for true, pred in zip(true_labels, pred_labels)]

d2l.show_fashion_mnist(X[0:9], titles[0:9])

softmax简介实现

import torch
from torch import nn
from torch.nn import init
import numpy as np
import sys
sys.path.append("..") 
import d2lzh_pytorch as d2l

# 读取数据
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

# 定义和初始化模型
num_inputs = 784
num_outputs = 10

# 本函数已保存在d2lzh_pytorch包中方便以后使用
class FlattenLayer(nn.Module):
    def __init__(self):
        super(FlattenLayer, self).__init__()
    def forward(self, x): # x shape: (batch, *, *, ...)
        return x.view(x.shape[0], -1)
        
        
from collections import OrderedDict

net = nn.Sequential(
    FlattenLayer(),
    nn.Linear(num_inputs, num_outputs)
    OrderedDict([
        ('flatten', FlattenLayer()),
        ('linear', nn.Linear(num_inputs, num_outputs))
    ])
)


net = LinearNet(num_inputs, num_outputs)

init.normal_(net.linear.weight, mean=0, std=0.01)
init.constant_(net.linear.bias, val=0) 

# 交叉熵损失函数
loss = nn.CrossEntropyLoss()

# 定义优化函数
optimizer = torch.optim.SGD(net.parameters(), lr=0.1)

# 训练模型
num_epochs = 5
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)

函数解析

gather():dim,LongTensor;累加聚合操作

参考资料

https://tangshusen.me/Dive-into-DL-PyTorch/#/chapter03_DL-basics/3.6_softmax-regression-scratch