Locally weighted linear regression (LWLR) 的原理及其 normal equation 的证明

原理讲解

caimouse 在他的关于 Locally weighted linear regression 的文章中指出了一些基本原理的 python 代码实现。

引用他的代码是这样的

#python 3.5.3  蔡军生    
#http://edu.youkuaiyun.com/course/detail/2592    
#  计算加权回归
 
import numpy as np
import random
import matplotlib.pyplot as plt
 
 
def gaussian_kernel(x, x0, c, a=1.0):
    """
    Gaussian kernel.
    :Parameters:
      - `x`: nearby datapoint we are looking at.
      - `x0`: data point we are trying to estimate.
      - `c`, `a`: kernel parameters.
    """
    # Euclidian distance
    diff = x - x0
    dot_product = diff * diff.T
    return a * np.exp(dot_product / (-2.0 * c**2))
 
 
def get_weights(training_inputs, datapoint, c=1.0):
    """
    Function that calculates weight matrix for a given data point and training
    data.
    :Parameters:
      -