【机器学习】深度探索：从基础概念到深度学习关键技术的全面解析——梯度下降、激活函数、正则化与批量归一化

from sklearn.linear_model import LinearRegression
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split

# 生成模拟数据
X, y = make_regression(n_samples=100, n_features=1, noise=0.1)

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# 创建并训练模型
model = LinearRegression()
model.fit(X_train, y_train)

# 预测
predictions = model.predict(X_test)

# 打印预测结果
print(predictions[:5])

import torch
import torch.nn as nn
import torch.optim as optim
from torch.utils.data import DataLoader, TensorDataset

# 转换数据为PyTorch的Tensor
X_tensor = torch.tensor(X, dtype=torch.float32)
y_tensor = torch.tensor(y, dtype=torch.float32)

# 划分数据集
train_data = TensorDataset(X_tensor[:-20], y_tensor[:-20])
test_data = TensorDataset(X_tensor[-20:], y_tensor[-20:])

# 定义数据加载器
train_loader = DataLoader(train_data, batch_size=10)
test_loader = DataLoader(test_data, batch_size=10)

# 定义神经网络模型
class SimpleNN(nn.Module):
    def __init__(self):
        super().__init__()
        self.layer1 = nn.Linear(1, 10)  # 输入层到隐藏层
        self.layer2 = nn.Linear(10, 1)   # 隐藏层到输出层

    def forward(self, x):
        x = torch.relu(self.layer1(x))  # 使用ReLU激活函数
        return self.layer2(x)

model = SimpleNN()

# 定义损失函数和优化器
criterion = nn.MSELoss()  # 均方误差损失，适用于回归问题
optimizer = optim.SGD(model.parameters(), lr=0.01)  # 随机梯度下降优化器

# 训练模型
epochs = 100
for epoch in range(epochs):
    for inputs, targets in train_loader:
        # 前向传播
        outputs = model(inputs)
        loss = criterion(outputs, targets)

        # 反向传播和优化
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

# 测试模型
model.eval()
with torch.no_grad():
    predictions = model(X_tensor[-20:])
    print(predictions.numpy())

import torch
import torch.nn as nn
import torch.optim as optim

# 假设一个简单的线性回归模型
class LinearRegressionModel(nn.Module):
    def __init__(self, input_dim, output_dim):
        super(LinearRegressionModel, self).__init__()
        self.linear = nn.Linear(input_dim, output_dim)

    def forward(self, x):
        return self.linear(x)

input_dim = 10
output_dim = 1
model = LinearRegressionModel(input_dim, output_dim)

# 定义损失函数和优化器
criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)  # 添加动量以加速收敛

# 生成模拟数据
X = torch.randn(64, input_dim)  # 小批量数据，64为批量大小
y = torch.randn(64, output_dim)

# 训练循环
num_epochs = 100
for epoch in range(num_epochs):
    # 前向传播
    outputs = model(X)
    loss = criterion(outputs, y)
    
    # 梯度清零
    optimizer.zero_grad()
    
    # 反向传播
    loss.backward()
    
    # 参数更新
    optimizer.step()
    
    # 每10个epoch打印一次损失值
    if (epoch + 1) % 10 == 0:
        print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {loss.item()}')

# 定义一个包含ReLU激活函数的全连接层
fc_layer = nn.Sequential(
    nn.Linear(10, 5),
    nn.ReLU(inplace=True)  # inplace=True表示在原地修改数据，节省内存
)

# 输入数据
X = torch.randn(1, 10)

# 前向传播
output = fc_layer(X)
print(output)

# 定义模型、损失函数和优化器（包含L2正则化）
model = LinearRegressionModel(input_dim, output_dim)
criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, weight_decay=0.001)  # weight_decay即为L2正则化系数

# 定义包含批量归一化的模型
class NormalizedModel(nn.Module):
    def __init__(self, input_dim, hidden_dim, output_dim):
        super(NormalizedModel, self).__init__()
        self.fc1 = nn.Linear(input_dim, hidden_dim)
        self.bn1 = nn.BatchNorm1d(hidden_dim)  # 批量归一化层
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(hidden_dim, output_dim)

    def forward(self, x):
        x = self.fc1(x)
        x = self.bn1(x)  # 应用批量归一化
        x = self.relu(x)
        x = self.fc2(x)
        return x

# 实例化模型并打印输出
input_dim = 10
hidden_dim = 20
output_dim = 1
model = NormalizedModel(input_dim, hidden_dim, output_dim)
X = torch.randn(64, input_dim)  # 模拟输入数据
output = model(X)
print(output)