手动实现softmax回归
import torch
import torchvision
import numpy as np
import xiaobei_pytorch as xb
3.6.1 获取数据
batch_size = 256
train_iter,test_iter = xb.load_data_fashion_mnist(batch_size=batch_size)
3.6.2 初始化参数模型
输入的fashion_mnist数据是28$\times$28 = 784 个像素的图像，输出10个类别，单层神经网络输出层的个数为10，softmax的权重和偏差数量为 784$\times$10和1$\times$10的矩阵
# 输入与输出
num_inputs = 784
num_outputs = 10
# 权重和偏差
W = torch.tensor(np.random.normal(0,0.01,(num_inputs,num_outputs)),dtype=torch.float)
b = torch.zeros(num_outputs,dtype = torch.float)
开启梯度跟随
W.requires_grad_(requires_grad = True)
b.requires_grad_(requires_grad = True)
tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], requires_grad=True)
3.6.3 tensor 按维度操作
我们想对矩阵的列或者行元素进行求和 dim=0或者dim=1
X = torch.tensor([[1,2,3],[4,5,6]])
print(X.sum(dim = 0, keepdim = True))
print(X.sum(dim = 1, keepdim = True))
tensor([[5, 7, 9]])
tensor([[ 6],
[15]])
def softmax(X):
X_exp = X.exp()
partition = X_exp.sum(dim = 1, keepdim=True)
return X_exp / partition
X = torch.rand((2,5))
# y = torch.rand(2,2)
print(X)
X_prob = softmax(X)
print(X_prob,X_prob.sum(dim = 1))
tensor([[0.7006, 0.1504, 0.8269, 0.8514, 0.3227],
[0.4950, 0.9123, 0.5274, 0.6243, 0.6404]])
tensor([[0.2193, 0.1265, 0.2489, 0.2550, 0.1503],
[0.1711, 0.2597, 0.1767, 0.1947, 0.1979]]) tensor([1.0000, 1.0000])
3.6.4 定义模型
把图像展开成一维向量 乘以权重W 加上偏差b
def net(X):
# torch.mm 矩阵相乘 view（）改变矩阵维度为1行 num_input列
f_x = torch.mm(X.view((-1,num_inputs)),W) + b
return softmax(f_x)
3.6.5 定义损失函数
y_hat = torch.tensor([[0.1,0.3,0.6],[0.3,0.2,0.5]])
y = torch.LongTensor([0,2])
y_hat.gather(1,y.view(-1,1))
tensor([[0.1000],
[0.5000]])
def cross_entropy(y_hat, y):
return -torch.log(y_hat.gather(1, y.view(-1,1)))
3.6.6 计算分类准确性
a = torch.randn(3,5)
print(a)
print(a.argmax(dim=1))
def accuracy(y_hat, y):
# y_hat 是预测概率分布 y 是真实值
# argmax(dim = 1) 矩阵中每行最大值的索引
return ((y_hat.argmax(dim=1)==y).float().mean().item())
tensor([[-1.7017, -0.2468, 0.5864, -0.7538, -1.5446],
[-0.1572, -0.1219, 0.0282, -0.7416, -0.5916],
[ 0.2229, 1.2182, -2.1934, -0.3435, 1.4544]])
tensor([2, 2, 4])
print(accuracy(y_hat,y))
0.5
def evaluate_accuracy(data_iter,net):
acc_sum,n = 0.0,0
for X,y in data_iter:
# print(len(X)) 小批量数据集 每个X中有 256个图像
# print((net(X).argmax(dim=1)==y).float().sum().item())
acc_sum += (net(X).argmax(dim=1)==y).float().sum().item()
n+=y.shape[0]
# print(n)
return acc_sum/n
#用随机初始的网络模型net 对数据集进行分类 准确率应该是10分类的倒数0.1左右
print(evaluate_accuracy(test_iter,net))
0.077
3.6.7 训练模型
- 目前搭建随机网络模型net
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):
#模型训练次数 5次
train_l_num, train_acc_num,n = 0.0,0.0,0
for X,y in train_iter:
#X 为小批量256个图像 28*28 y为标签
# 计算X softmax下的值 与损失函数值
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:
xb.sgd(params,lr,batch_size)
else:
optimizer.step()
train_l_num += l.item()
train_acc_num += (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_num/n, train_acc_num/n, test_acc))
num_epochs ,lr = 5,0.1
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs,batch_size, [W, b], lr)
epoch 1, loss 0.4351,train_acc 0.852,test_acc 0.836
epoch 2, loss 0.4333,train_acc 0.852,test_acc 0.824
epoch 3, loss 0.4303,train_acc 0.853,test_acc 0.838
epoch 4, loss 0.4275,train_acc 0.855,test_acc 0.839
epoch 5, loss 0.4257,train_acc 0.855,test_acc 0.839
3.6.8 预测
X,y = iter(test_iter).next()
true_labels = xb.get_fashion_mnist_labels(y.numpy())
pred_labels = xb.get_fashion_mnist_labels(net(X).argmax(dim = 1).numpy())
titles = [true +'\n' + pred for true,pred in zip(true_labels,pred_labels)]
xb.show_fashion_mnist(X[10:19],titles[10:19])
