Softmax回归

Softmax回归是个分类问题，他将预测值映射在[0，1]之间，从而可以预测概率。相较于线性回归，它只是增加了一个激活函数以及输出层的个数。并且关于Weight参数的个数可以看出来增加了三倍。

简单实现步骤

构建Fashion-MNIST数据集
Fashion-MNIST数据集是图像数据，是一个Class=10的分类任务
构建模型并初始化参数
这里由于数据的是图像数据，我们需要读取图片数据(RGB)转为一维的tensor数据(不使用卷积操作)，所以相比于线性回归，Softmax回归只不过是最后用了Softmax函数映射成了概率。
定义损失函数
由于这里是分类问题，常用交叉熵损失
定义优化器
这里使用SGD，一般Adam在图像分类问题收敛不好。
Train

输入数据

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

搭建网络

# 初始化参数
def init_weights(m):if type(m) == nn.Linear:nn.init.normal_(m.weight, std=0.01)net = nn.Sequential(nn.Fltten(), nn.Linear(28*28, 10))
net.apply(init_weights)

继承nn.Modult类版本：

class Net(nn.Module):def __init__(self, input_dim, output_dim):super(Net, self).__init__()self.flat = nn.Flatten()self.linear = nn.Linear(input_dim, output_dim)def forward(self, x):return self.linear(self.flat(x))

损失函数

# 损失函数
loss = nn.CrossEntropyLoss()

优化器

# 优化器
trainer = torch.optim.SGD(net.parameters(), lr=0.1)

train

这里直接导入d2l库的训练模块train_ch3

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

可能有bug->RuntimeError: DataLoader worker (pid(s) 9528, 8320) exited unexpectedly
是因为电脑进程数不够导致的。
修改源码:

d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer,  num_workers=0)

解决BUG!
完整代码：

import torch
from torch import nn
from d2l import torch as d2l
import matplotlib.pyplot as plt# 初始化参数
def init_weights(m):if type(m) == nn.Linear:nn.init.normal_(m.weight, std=0.01)batch_size = 32
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, num_workers=0)
# net = nn.Sequential(nn.Flatten(), nn.Linear(28*28, 10))class Net(nn.Module):def __init__(self, input_dim, output_dim):super(Net, self).__init__()self.flat = nn.Flatten()self.linear = nn.Linear(input_dim, output_dim)def forward(self, x):return self.linear(self.flat(x))net = Net(28*28, 10)net.apply(init_weights)
# 损失函数
loss = nn.CrossEntropyLoss()
# 优化器
trainer = torch.optim.SGD(net.parameters(), lr=0.1)
num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)
plt.show()

epoch大约6、7模型训练就比较好了。epoch大于10可能会过拟合。

附：train_ch3具体文档实现:

def evaluate_accuracy(net, data_iter):  #@save"""计算在指定数据集上模型的精度。"""if isinstance(net, torch.nn.Module):net.eval()  # 将模型设置为评估模式metric = Accumulator(2)  # 正确预测数、预测总数for X, y in data_iter:metric.add(accuracy(net(X), y), y.numel())return metric[0] / metric[1]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 = y_hat.argmax(axis=1)cmp = y_hat.type(y.dtype) == yreturn float(cmp.type(y.dtype).sum())class Accumulator:  #@save"""在`n`个变量上累加。"""def __init__(self, n):self.data = [0.0] * ndef 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]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, fmtsdef 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] * nif 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_epoch_ch3(net, train_iter, loss, updater):  #@save"""训练模型一个迭代周期（定义见第3章）。"""# 将模型设置为训练模式if isinstance(net, torch.nn.Module):net.train()# 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y_hat = net(X)l = loss(y_hat, y)if isinstance(updater, torch.optim.Optimizer):# 使用PyTorch内置的优化器和损失函数updater.zero_grad()l.backward()updater.step()metric.add(float(l) * len(y), accuracy(y_hat, y),y.size().numel())else:# 使用定制的优化器和损失函数l.sum().backward()updater(X.shape[0])metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())# 返回训练损失和训练准确率return metric[0] / metric[2], metric[1] / metric[2]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_metricsassert train_loss < 0.5, train_lossassert train_acc <= 1 and train_acc > 0.7, train_accassert test_acc <= 1 and test_acc > 0.7, test_acc

d2lSoftmaxpytorch

文章目录

Softmax回归

输入数据

搭建网络

损失函数

优化器

train

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