kernel regression python 代码

以下是一个简单的Python代码，演示如何使用核回归实现非参数回归：

import numpy as np
import matplotlib.pyplot as plt

def kernel_regression(x_train, y_train, x_test, kernel, sigma):
    n_train = len(x_train)
    n_test = len(x_test)
    y_test = np.zeros(n_test)
    for i in range(n_test):
        weights = kernel(x_train, x_test[i], sigma)
        y_test[i] = np.sum(weights * y_train) / np.sum(weights)
    return y_test

def gaussian_kernel(x, x0, sigma):
    return np.exp(-0.5 * ((x - x0) / sigma) ** 2)

# 生成一些随机数据
np.random.seed(0)
x = np.linspace(0, 10, num=100)
y = np.sin(x) + np.random.normal(scale=0.1, size=100)

# 训练集和测试集
x_train = x[::2]
y_train = y[::2]
x_test = x[1::2]

# 进行核回归
sigma = 0.5
y_test = kernel_regression(x_train, y_train, x_test, gaussian_kernel, sigma)

# 绘制结果
plt.figure(figsize=(8, 6))
plt.scatter(x_train, y_train, label='Training data')
plt.plot(x_test, y_test, label='Predictions')
plt.legend(loc='upper left')
plt.show()

在这个例子中，我们使用高斯核函数作为权重函数。您可以尝试使用其他核函数，例如线性核函数或多项式核函数，来看看它们的效果如何。