线性回归与Logistic回归(代码实现)
线性回归
一维线性回归
最小二乘法，偏导数为0
import torch
from torch.autograd import Variable
import matplotlib.pyplot as plt
import numpy as np
import torch.nn as nn
import torch.optim as optim
x_train = np.array([[3.3], [4.4], [5.5], [6.71], [6.93], [4.168], [9.779], [6.182], [7.59], [2.167], [7.042],
[10.791], [5.313], [7.997], [3.1]], dtype=np.float32)
y_train = np.array([[1.7], [2.76], [2.09], [3.19], [1.694], [1.573], [3.366], [2.596], [2.53], [1.221],
[2.827], [3.465], [1.65], [2.904], [1.3]],dtype=np.float32)
x_train = torch.from_numpy(x_train)
y_train = torch.from_numpy(y_train)
class LinearRegression(nn.Module):
def __init__(self):
super(LinearRegression, self).__init__()
self.linear = nn.Linear(1, 1)
def forward(self, x):
assert isinstance(x, object)
out = self.linear(x)
return out
if torch.cuda.is_available():
model = LinearRegression().cuda()
else:
model = LinearRegression()
# 定义损失函数和优化函数，使用均方误差作为优化函数，使用梯度下降进行优化
criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.01)
# 开始训练模型
num_epochs = 1000
for epoch in range(num_epochs):
inputs = Variable(x_train)
target = Variable(y_train)
# forward
out = model(inputs)
loss = criterion(out, target)
# backward
optimizer.zero_grad() # 归零梯度
loss.backward()
optimizer.step()
if (epoch+1) % 20 == 0:
print('Epoch[{}/{}],loss:{:.6f}'.format(epoch+1, num_epochs, loss.item()))
if __name__ == '__main__':
model.eval()
predict = model(Variable(x_train))
predict = predict.data.numpy()
plt.plot(x_train.numpy(), y_train.numpy(), 'ro', label='Original data')
plt.plot(x_train.numpy(), predict, label='Fitting Line')
plt.show()
多维线性回归
import torch
import numpy as np
import matplotlib.pyplot as plt
from torch import nn
# -------------------------------------数据准备--------------------------------------
# 目标权重和偏置
w = torch.FloatTensor([2.0, 3.0, 4.0]).unsqueeze(1)
b = torch.FloatTensor([0.5])
# 一次生成32个数据
def create_data(batch_size=32):
random = torch.randn(batch_size)
random = random.unsqueeze(1) # 添加一个维度
# 纵向连接tensor
x = torch.cat([random ** i for i in range(1, 4)], 1) # b/x/^2/x^3
# 矩阵乘法
y = x.mm(w) + b[0] # mm表示矩阵相乘，mul为对应元素相乘
if torch.cuda.is_available():
return x.cuda(), y.cuda()
return x, y
# -------------------------------------自定义模型--------------------------------------
class PloyRegression(nn.Module):
def __init__(self):
super(PloyRegression, self).__init__()
self.ploy = nn.Linear(3, 1) # 输入3维(分别表示x/x^2/x^3)，输出1维
def forward(self, x):
out = self.ploy(x)
return out
model = PloyRegression()
if torch.cuda.is_available():
model = model.cuda()
# ------------------------损失函数、优化器的选择----------------------------
criterion = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=1e-3)
# ------------------------开始训练----------------------------
# 使用均方误差，随机梯度下降
epoch = 0
while True:
# 创建数据
batch_x, batch_y = create_data() # 一次生成32个数据
# 前向传播
output = model(batch_x)
# 损失计算
loss = criterion(output, batch_y)
# 获取损失值
loss_value = loss.data.cpu().numpy()
# 梯度置零
optimizer.zero_grad()
# 反向传播
loss.backward()
# 更新参数
optimizer.step()
epoch += 1
# 损失函数小于一定的值才会退出来
if loss_value < 1e-3:
break
# 每100步打印一次损失
if (epoch + 1) % 100 == 0:
print("Epoch{}, loss:{:.6f}".format(epoch + 1, loss_value))
# -------------------------------------测试--------------------------------------
model.eval() # 开启验证模式
# 构造数据
x_train = np.array([[i] for i in range(20)], dtype=np.float32)
x_train = torch.from_numpy(x_train)
x = torch.cat([x_train ** i for i in range(1, 4)], 1)
y = x.mm(w) + b
# 绘制数据点
plt.plot(x_train.numpy(), y.numpy(), 'ro')
# 提取拟合参数
w_get = model.ploy.weight.data.T
b_get = model.ploy.bias.data
print('w:{},b:{}'.format(w_get.cpu().numpy(), b_get.cpu().numpy()))
# 计算预测值
Y_get = x.mm(w_get.cpu()) + b_get.cpu()
plt.plot(x_train.numpy(), Y_get.numpy(), '-')
plt.show()
分类问题
二分类算法———Logistic
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
# 设置随机种子
seed_value = 2024
np.random.seed(seed_value)
# Sigmoid激活函数
def sigmoid(z):
return 1 / (1 + np.exp(-z))
# 定义逻辑回归算法
class LogisticRegression:
def __init__(self, learning_rate=0.003, iterations=100):
self.learning_rate = learning_rate # 学习率
self.iterations = iterations # 迭代次数
def fit(self, X, y):
# 初始化参数
self.weights = np.random.randn(X.shape[1])
self.bias = 0
# 梯度下降
for i in range(self.iterations):
# 计算sigmoid函数的预测值, y_hat = w * x + b
y_hat = sigmoid(np.dot(X, self.weights) + self.bias)
# 计算损失函数
loss = (-1 / len(X)) * np.sum(y * np.log(y_hat) + (1 - y) * np.log(1 - y_hat))
# 计算梯度
dw = (1 / len(X)) * np.dot(X.T, (y_hat - y))
db = (1 / len(X)) * np.sum(y_hat - y)
# 更新参数
self.weights -= self.learning_rate * dw
self.bias -= self.learning_rate * db
# 打印损失函数值
if i % 10 == 0:
print(f"Loss after iteration {i}: {loss}")
# 预测
def predict(self, X):
y_hat = sigmoid(np.dot(X, self.weights) + self.bias)
y_hat[y_hat >= 0.5] = 1
y_hat[y_hat < 0.5] = 0
return y_hat
# 精度
def score(self, y_pred, y):
accuracy = (y_pred == y).sum() / len(y)
return accuracy
# 导入数据
iris = load_iris()
X = iris.data[:, :2]
y = (iris.target != 0) * 1
# 划分训练集、测试集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=seed_value)
# 训练模型
model = LogisticRegression(learning_rate=0.03, iterations=1000)
model.fit(X_train, y_train)
# 结果
y_train_pred = model.predict(X_train)
y_test_pred = model.predict(X_test)
score_train = model.score(y_train_pred, y_train)
score_test = model.score(y_test_pred, y_test)
print('训练集Accuracy: ', score_train)
print('测试集Accuracy: ', score_test)
# 可视化决策边界
x1_min, x1_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
x2_min, x2_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max, 100), np.linspace(x2_min, x2_max, 100))
Z = model.predict(np.c_[xx1.ravel(), xx2.ravel()])
Z = Z.reshape(xx1.shape)
plt.contourf(xx1, xx2, Z, cmap=plt.cm.Spectral)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)
plt.xlabel("Sepal length")
plt.ylabel("Sepal width")
plt.show()
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