Home 机器学习 PyTorch

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]])

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
  • 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)
  • BCELoss（二元交叉熵损失）^1

$$
BCELoss(y_{pred},y_{true})=-\frac{1}{N}\sum_{i=1}^{N}[y_{true}^{(i)}\cdot log(y_{pred}^{(i)})+(1-y_{true}^{(i)})\cdot log(1-y_{pred})^{(i)}]
$$

  • SGD（随机梯度下降）

$$
\theta_{t+1}=\theta_{t}-\eta \cdot\nabla_{\theta}\mathcal{L}(\theta_{t})
$$

训练循环

  1. 前向传播：输入数据得到预测值y_pred
  2. 计算损失：比较y_pred与y_data
  3. 反向传播：计算梯度loss.backward()，清零历史梯度optimizer.zero_grad()
  4. 参数更新：调整模型参数optimizer.step()
  5. 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()

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()