Pytorch手动实现softmax回归

简述

这次,将会使用到Fashion-MNIST数据集和操作

理论基础

回归

假设有输入的特征数有4个,分类的标签有3个.则回归方程为:
$o_1=x_1{w}_{11}+x_{2}w21+x_3{w}_{31}+x_4{w}_{41}+b_1$
$o_2=x_1{w}_{12}+x_{2}w22+x_3{w}_{32}+x_4{w}_{42}+b_1$
$o_3=x_1{w}_{11}+x_{2}w21+x_3{w}_{31}+x_4{w}_{43}+b_1$

softmax

这样会得$[y_1^{{}^{\prime }},y_2^{{}^{\prime }},y_3^{{}^{\prime }}]$,哪个数字更大,就取哪个.表示该样本属于这个标签.通过softmax可以得到:

损失函数

交叉熵损失函数

读取数据

使用Fashion-MNIST数据集，并设置批量大小为256

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

初始化模型参数

型的输入向量的长度是 28×28=78428×28=784：该向量的每个元素对应图像中每个像素。由于图像有10个类别，单层神经网络输出层的输出个数为10，因此softmax回归的权重和偏差参数分别为784×10和1×101×10的矩阵

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) 

实现softmax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

'''训练模型'''
num_epochs, lr = 5, 0.1
d2l.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])

整体代码

d2lzh_pytorch.py

import random
from IPython import display
import matplotlib.pyplot as plt
import torch
import torchvision
import torchvision.transforms as transforms
import matplotlib.pyplot as plt
import time
import sys


def use_svg_display():
    # 用矢量图显示
    display.set_matplotlib_formats('svg')

def set_figsize(figsize=(3.5, 2.5)):
    use_svg_display()
    # 设置图的尺寸
    plt.rcParams['figure.figsize'] = figsize

'''给定batch_size, feature, labels,做数据的打乱并生成指定大小的数据集'''
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size): #(start, staop, step)
        j = torch.LongTensor(indices[i: min(i + batch_size, num_examples)]) #最后一次可能没有一个batch
        yield features.index_select(0, j), labels.index_select(0, j)

'''定义线性回归的模型'''
def linreg(X, w, b):
    return torch.mm(X, w) + b

'''定义线性回归的损失函数'''
def squared_loss(y_hat, y):
    return (y_hat - y.view(y_hat.size())) ** 2 / 2

'''线性回归的优化算法 —— 小批量随机梯度下降法'''
def sgd(params, lr, batch_size):
    for param in params:
        param.data -= lr * param.grad / batch_size #这里使用的是param.data

'''MINIST,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]

'''定义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):
    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()

'''获取并读取Fashion-MNIST数据集;该函数将返回train_iter和test_iter两个变量'''
def load_data_fashion_mnist(batch_size):
    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())
    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
    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)

    return train_iter, test_iter

'''评估模型net在数据集data_iter的准确率'''
def evaluate_accuracy(data_iter, net):
    acc_sum, n = 0.0, 0
    for X, y in data_iter:
        acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
        n += y.shape[0]
    return acc_sum / n

'''训练模型,softmax'''
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:
                sgd(params, lr, batch_size)
            else:
                optimizer.step()

            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))

main.py

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

# 使用Fashion-MNIST数据集
'''获取和读取数据'''
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)

'''softmax运算'''
def softmax(X):
    X_exp = X.exp()
    partition = X_exp.sum(dim=1, keepdim=True)
    return X_exp/partition

'''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
d2l.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])