This implement a linear weighted linear regression method to overcome underfetting in linear regression

lwlr.py

def lwlr(testPoint, xArr, yArr, k=0.1):
    """
    Generate an estimate for any point in the x space

    Parameters
    ----------
    testPoint: float
       point in the x space
    xArr : List
       Our data      
    yArr: List
        our predicted value
    k: float
        user-defined constant that determine how much to weight the point

    Returns
    -------
    ws : float
       regression weight
    """    
    xMat = mat(xArr); yMat = mat(yArr).T
    # Create diagonal matrix
    m = shape(xMat)[0]
    weights = mat(eye((m)))
    # Populate weights with exponentially decaying values
    for j in range(m):
        diffMat = testPoint - xMat[j,:]
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
        
    # find extimate for testpoint
    xTwx = xMat.T * (weights * xMat)
    if linalg.det(xTwx) == 0.0:
        print("This matrix is singular, cannot do inverse")
        return
    
    ws = xTwx.I * (xMat.T * (weights*yMat))
    return testPoint*ws

def lwlrTest(testArr, xArr, yArr, k=1.0):
    """
    Generate an estimate for any point in the x space

    Parameters
    ----------
    testPoint: float
       point in the x space
    xArr : List
       Our data      
    yArr: List
        our predicted value
    k: float
        user-defined constant that determine how much to weight the point

    Returns
    -------
    ws : float
       regression weight
    """ 
    # Get arbituary yHat to be of same length as test data
    m = shape(testArr)[0]
    yHat = zeros(m)
    # Replace each entry by its weight
    for i in range(m):
        yHat[i] = lwlr(testArr[i], xArr, yArr, k)
    return yHat