为一个(450,13)维的输入样本写一个kernel regression

以下是一个可能的kernel regression实现：

import numpy as np

def kernel_regression(X, y, x_new, kernel_func, bandwidth):
    """
    Kernel regression function
    
    Parameters:
    X (ndarray): input data, shape (n_samples, n_features)
    y (ndarray): output data, shape (n_samples,)
    x_new (ndarray): new input sample, shape (n_features,)
    kernel_func (function): kernel function, takes two inputs and returns a scalar
    bandwidth (float): kernel bandwidth
    
    Returns:
    float: predicted output for the new input sample
    """
    n_samples = X.shape[0]
    k_values = np.zeros(n_samples)
    for i in range(n_samples):
        k_values[i] = kernel_func(X[i], x_new, bandwidth)
    weights = k_values / np.sum(k_values)
    return np.dot(weights, y)

def gaussian_kernel(x1, x2, bandwidth):
    """
    Gaussian kernel function
    
    Parameters:
    x1 (ndarray): input sample, shape (n_features,)
    x2 (ndarray): input sample, shape (n_features,)
    bandwidth (float): kernel bandwidth
    
    Returns:
    float: kernel value
    """
    diff = x1 - x2
    return np.exp(-0.5 * np.dot(diff, diff) / (bandwidth ** 2))

# Example usage
X = np.random.rand(100, 450)
y = np.random.rand(100)
x_new = np.random.rand(450)
predicted_y = kernel_regression(X, y, x_new, gaussian_kernel, 0.1)
print(predicted_y)

此实现使用高斯核函数，但可以很容易地更改为其他核函数。`bandwidth`参数控制核函数的宽度，影响预测的平滑度。较大的带宽会产生更平滑的预测，但可能会导致过度拟合。