思路
数据准备
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| xy = np.loadtxt('diabetes.csv', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1])
y_data = torch.from_numpy(xy[:, [-1]])
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x_data表示读取所有行，从第一列读到倒数第二列
y_data表示读取所有行的最后一列
模型设计
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| class Model(torch.nn.Module):
def __init__(self):
super(Model, self).__init__()
self.linear1 = torch.nn.Linear(8, 6)
self.linear2 = torch.nn.Linear(6, 4)
self.linear3 = torch.nn.Linear(4, 1)
self.sigmoid = torch.nn.Sigmoid()
def forward(self, x):
x = self.sigmoid(self.linear1(x))
x = self.sigmoid(self.linear2(x))
x = self.sigmoid(self.linear3(x))
return x
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- 三层全连接层：构建三层神经网络模型，维度变化：
8 -> 6 -> 4 -> 1，逐层降低维度 - 激活函数：每层后接Sigmoid，将输出压缩到[0, 1]范围
- 前向传播：数据依次通过各层和Sigmoid，最终输出预测值
损失函数与优化器
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| criterion = torch.nn.BCELoss(reduction='mean')
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
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$$
BCELoss(y_{pred},y_{true})=-\frac{1}{N}\sum_{i=1}^{N}[y_{true}^{(i)}\cdot log(y_{pred}^{(i)})+(1-y_{true}^{(i)})\cdot log(1-y_{pred})^{(i)}]
$$
$$
\theta_{t+1}=\theta_{t}-\eta \cdot\nabla_{\theta}\mathcal{L}(\theta_{t})
$$
训练循环
- 前向传播：输入数据得到预测值
y_pred - 计算损失：比较
y_pred与y_data - 反向传播：计算梯度
loss.backward()，清零历史梯度optimizer.zero_grad() - 参数更新：调整模型参数
optimizer.step() - 记录损失
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| for epoch in range(100):
# 前向传播
y_pred = model(x_data)
# 计算损失
loss = criterion(y_pred, y_data)
print(epoch, loss.item())
epoch_list.append(epoch)
loss_list.append(loss.item())
# 反向传播
optimizer.zero_grad()
loss.backward()
# 参数更新
optimizer.step()
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代码实现
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| import numpy as np
import torch
import matplotlib.pyplot as plt
xy = np.loadtxt('diabetes.csv', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1])
y_data = torch.from_numpy(xy[:, [-1]])
class Model(torch.nn.Module):
def __init__(self):
super(Model, self).__init__()
self.linear1 = torch.nn.Linear(8, 6)
self.linear2 = torch.nn.Linear(6, 4)
self.linear3 = torch.nn.Linear(4, 1)
self.sigmoid = torch.nn.Sigmoid()
def forward(self, x):
x = self.sigmoid(self.linear1(x))
x = self.sigmoid(self.linear2(x))
x = self.sigmoid(self.linear3(x))
return x
model = Model()
criterion = torch.nn.BCELoss(reduction='mean')
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
epoch_list = []
loss_list = []
for epoch in range(100):
# 前向传播
y_pred = model(x_data)
# 计算损失
loss = criterion(y_pred, y_data)
print(epoch, loss.item())
epoch_list.append(epoch)
loss_list.append(loss.item())
# 反向传播
optimizer.zero_grad()
loss.backward()
# 参数更新
optimizer.step()
plt.plot(epoch_list, loss_list)
plt.ylabel('loss')
plt.xlabel('epoch')
plt.show()
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