【统计学习】过拟合

import numpy as np
import scipy as sp
from scipy.optimize import leastsq
import matplotlib.pyplot as plt
%matplotlib inline

#三角函数
def real_func(x: np.array):
    return np.sin(2 * np.pi * x)

#多项式
def fit_func(p, x: np.array):
    #print("=======p======", type(p))
    #print(p)
    _func = np.poly1d(p)
    return _func(x)
#残差
def residuals_func(p, x, y):
    return fit_func(p, x) - y

def rediduals_func_regual(p, x, y):
    regularization = 0.0001
    ret = fit_func(p, x) - y
    return np.append(ret, np.sqrt(0.5 * regularization * np.square(p)))    

def fitting(M=0):
    """
    M    为 多项式的次数
    """
    # 随机初始化多项式参数
    p_init = np.random.rand(M + 1)
    print("======随机参数====", p_init)
    # 最小二乘法
    
    p_lsq = leastsq(residuals_func, p_init, args=(x, y))
    print('Fitting Parameters:', p_lsq[0])

    # 真实
    plt.plot(x_points, real_func(x_points), label='real')
    #拟合曲线
    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')
    #噪声
    plt.plot(x, y, 'bo', label='noise')
    plt.legend()
    return p_lsq

x = np.linspace(0, 1, 10)
x_points = np.linspace(0, 1, 1000)
y_ = real_func(x)
#随机产生的噪声
y = [np.random.normal(0, 0.1) + y1 for y1 in y_]

def fitting_regual(M=9):
    """
    M    为 多项式的次数
    """
    # 随机初始化多项式参数
    p_init = np.random.rand(M + 1)
    print("======随机参数====", p_init)
    # 最小二乘法        

    p_lsq_regual = leastsq(rediduals_func_regual, p_init, args=(x, y))
    print('Fitting Parameters:', p_lsq_regual[0])
    # 真实
    plt.plot(x_points, real_func(x_points), label='real')        
    #带正则项
    plt.plot(x_points, fit_func(p_lsq_regual[0], x_points), label='regularization')
    #噪声
    plt.plot(x, y, 'bo', label='noise')
    plt.legend()
    return p_lsq_regual