为什么使用内核技巧的 LMS 中的参数测试版会爆炸？

如何解决为什么使用内核技巧的 LMS 中的参数测试版会爆炸？

我正在尝试使用内核技巧解决 LMS 问题。参考资料取自 this 注释。

我的问题是 beta 的值会暴涨。它在大约 5 或 6 次迭代中达到 10e17 的数量级。我注意到的一件事是，beta 中的符号条目会随着循环中 beta 的连续更新而波动（从正到负，反之亦然）。

此外，降低 alpha（学习率）的值也无济于事。我尝试了 alpha = 0.01 但测试版的价值仍然爆炸。 这是代码

import numpy as np
import pandas as pd

file = pd.read_csv("weatherHistory.csv")

#selecting only the required columns
useful_index = [3,4,5,6,7,8,10]
file = file.iloc[:,useful_index]

# getting training set and test set
file_randomized = file.sample(frac=1,random_state=1)

# useable data size
usable_dataset_size = 1200

# training set size
training_set_index = int(0.75 * usable_dataset_size)

# get rid of unnecessary data
file = file_randomized[:usable_dataset_size]

# make training and test set
training_set = file[:training_set_index]
test_set = file[training_set_index:]

# Select the columns
input_index = [0,2,3,6]
X = training_set.iloc[:,input_index]
output_index = [1]
Y = training_set.iloc[:,output_index]

# Convert to numpy into suitable format
X = X.to_numpy()
n = X.shape[0]
d = X.shape[1]
Y = Y.to_numpy()

# This function calculates K(phi(x),phi(y))

def kernel_matrix(K,degree=1):
    """K is the matrix of dot product. This applies kernel function to the matrix"""
    result = np.zeros(K.shape)
    for i in range(0,degree+1):
        result += np.power(K,i)
    return result

# Main training function
def lms_with_kt(X,Y,alpha,degree = 1,num_iters = 1000):
    """X: nxd vector,Y: nx1 vector,beta: nx1 zero vector,alpha: number,degree: number"""
    # normalize x
    x_min = X.min(axis = 0,keepdims=True)
    x_max = X.max(axis = 0,keepdims=True)
    X = (X - x_min) / (x_max - x_min)
    n = X.shape[0]
    
    # add the column of 1 in the front
    X = np.hstack((np.ones((n,1)),X))
    
    # make K_matrix (kernel matrix)
    K = np.matmul(X,X.T)
    K = kernel_matrix(K,degree)
    # initialize beta
    beta = np.zeros((n,1))

    # update beta
    for i in range(num_iters):
        beta += alpha * (Y - np.matmul(K,beta))
    print(beta)
        
    def predict(x):
        """x: 1xd matrix"""
        x_norm = (x - x_min) / (x_max - x_min)
        n_predict = x_norm.shape[0]
        x_norm = np.hstack((np.ones((n_predict,x_norm))
        K_for_prediction = np.matmul(X,x_norm.T)
        K_for_prediction = kernel_matrix(K_for_prediction,degree)
        return np.dot(beta.T,K_for_prediction)

    return predict

predictor = lms_with_kt(X,0.1,1000)

数据集的链接是 here。