吴恩达机器学习ex5代码

import numpy as np
import pandas as pd
from scipy.io import loadmat
import matplotlib.pyplot as plt
import scipy.optimize as opt

'''===================================函数部分=================================='''
'''数据可视化'''
def plot(X,y):
    fig,ax = plt.subplots(figsize=(10,8))
    ax.scatter(X, y, c='r', marker='x')
    ax.set_xlabel('Change in water level(x)')
    ax.set_ylabel('Water flowing out of the dam(y)')
    plt.show()



'''代价函数，正则'''
def costReg(theta,X,y,lbd):
    X = np.matrix(X)
    y = np.matrix(y)
    theta = np.matrix(theta)

    cost = 1/(2*len(X)) * np.sum(np.power(([email protected]), 2))
    reg = lbd/(2*len(X)) * np.sum(np.power(theta[:,1:], 2))
    return cost + reg



'''梯度下降，正则'''
def gradientReg(theta,X,y,learning_rate):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)

    j = theta.shape[1]   #2
    sum_grad = np.zeros((1,j))
    for i in range(j):
        sum_grad[:,0] = (1 / len(X)) * np.sum((X @ theta.T - y).T * X[:,0])
        reg = (learning_rate * theta[:, i]) / len(X)
        sum_grad[:,i] = (1 / len(X)) * np.sum((X @ theta.T - y).T * X[:,i]) + reg
    return sum_grad



'''计算预测值'''
def predict(Theta,X):
    Theta = np.matrix(Theta)
    y_predict = X * Theta.T
    return y_predict



'''学习曲线函数training subset'''
def learning_curve(theta,Xv,yv,Xt,yt,n,lbd):   # 2 <= n <= 11
    error_train = np.zeros((n, 1)) #11
    error_val = np.zeros((n, 1))  #11
    for i in range(1,n+1): #1~11
        Xtt = Xt[0:i, :]  #2,3,4,5,6,7,8,9,10,11,12   注意，这里不要写Xt = Xt[0:i, :], python不知道把输入的Xt给谁
        ytt = yt[0:i, :]  #2,3,4,5,6,7,8,9,10,11,12
        min = opt.minimize(fun=costReg, x0=theta, args=(Xtt,ytt,lbd), method='TNC', jac=gradientReg)
        theta = min.x
        # print('ddd',theta)
        error_train[i-1,0] = costReg(theta,Xtt,ytt,0)
        error_val[i-1,0] = costReg(theta,Xv,yv,0)
    return error_train, error_val



'''特征变量扩展函数'''
def feature(X,p):
    X_feature = np.zeros((X.shape[0],p))
    for i in range(1,p+1):
        X_feature[::,i-1] = np.power(X,i).flatten()   #[::,i-1]指替换第i-1列，注意，替换的对象必须是（12，）格式，所以要拍平一下
    return X_feature



'''标准化'''
def norm(X):
    sigma = np.std(X, axis=0, ddof=1)   #axis=0计算每一列的标准差，ddof=1表示自由度为1
    mean = np.mean(X, axis=0)
    norm = (X-mean)/sigma
    return norm, mean, sigma



'''绘制lambda与error之间的关系'''
def lmd_error(lmd_lst,Xv,yv,Xt,yt):
    error_t = np.zeros((len(lmd_lst),1))
    error_v = np.zeros((len(lmd_lst),1))
    for i in range(len(lmd_lst)):
        min = opt.minimize(fun=costReg, x0=np.ones(p+1), args=(Xt,yt,lmd_lst[i]), method='TNC', jac=gradientReg)
        theta2 = min.x
        print(theta2)
        error_t[i,0] = costReg(theta2,Xt,yt,0)
        error_v[i,0] = costReg(theta2,Xv,yv,0)
    return error_t,error_v

'''===================================计算部分=================================='''
'''导入数据'''
data = loadmat('D:\新大陆\吴恩达机器学习\ex5\ex5data1.mat')
X_raw = data['X']
y_raw = data['y']
print('X_raw:',X_raw.shape)   #12,1
print('y_raw:',y_raw.shape)   #12,1
# print(data)



'''数据可视化'''
# plot(X_raw,y_raw)



'''X_raw处理，加X0'''
X = np.insert(X_raw,0,np.ones(1),axis=1)   #axis=1，插入一列，axis=0，插入一行
print('X:',X.shape)



'''创建初始theta'''
theta = np.ones(X.shape[1])   #特别注意



'''计算原始代价'''
print('original cost:',costReg(theta,X,y_raw,lbd=1))



'''计算原始梯度'''
print(gradientReg(theta,X,y_raw,learning_rate=1))



'''计算梯度下降有最小值时的theta'''
min = opt.minimize(fun=costReg, x0=theta, args=(X,y_raw,0), method='TNC', jac=gradientReg)   #相比特征变量扩展以后的情况，这里的假设函数阶数太低了，用正则没什么效果。
Theta = min.x   #array(2,)



'''画回归函数'''
A = np.linspace(start=X_raw.min(), stop=X_raw.max(), num=100)   #array(100,)
AA = np.insert(np.reshape(A,(100,1)),0,np.ones(100),axis=1)   #array(100,2)
B = predict(Theta,AA)   #(100,1)
fix,ax = plt.subplots(figsize=(12,8))
ax.scatter(X_raw,y_raw,c='r',marker='x')
ax.plot(A,B,c='b')
ax.set_xlabel('Change in water level(x)')
ax.set_ylabel('Water flowing out of the dam(y)')
ax.set_title('Linear Fit')
# plt.show()



'''计算error_train & error_val并画学习曲线'''
X_val = data['Xval']
X_val_insert = np.insert(X_val,0,np.ones(X_val.shape[0]),axis=1)   #array(21,2)
y_val = data['yval']
error_train, error_val = learning_curve(theta,X_val_insert,y_val,X,y_raw,11,0)
# print(error_train,error_val)

fix,ax = plt.subplots(figsize=(12,8))
ax.plot(np.linspace(start=2,stop=12,num=11),error_train,c='b',label='Train')
ax.plot(np.linspace(start=2,stop=12,num=11),error_val,c='g',label='Cross Validation')
ax.legend(loc=1)
ax.set_xlabel('Number of training examples')
ax.set_ylabel('Error')
ax.set_title('Learning curve for linear regression')
# plt.show()



'''将train test val 3个集子进行特征变量扩展'''
p = 6   #不知道为啥取6的时候才符合pdf上的图像，取8的时候稍微有点不一样
X_test = data['Xtest']
y_test = data['ytest']
X_train_exp = feature(X_raw,p)   #12,p
# print(X_raw)
# print(X_train_exp.shape)
X_test_exp = feature(X_test,p)   #12,p
# print(X_test_exp)
X_val_exp = feature(X_val,p)   #12,p
# print(X_val_exp)



'''将数据进行norm处理'''
X_train_norm, X_train_mean, X_train_sigma = norm(X_train_exp)   #12,p
# print(X_train_sigma.shape)
X_test_norm, aa, bb = norm(X_test_exp)   #21,p
X_val_norm, cc, dd = norm(X_val_exp)   #21,p
# print(X_val_norm.shape)



'''特征扩展后的函数图像'''
theta1 = np.zeros(p+1)
X_train_norm_insert = np.insert(X_train_norm,0,np.ones(X_train_norm.shape[0]),axis=1)
# print(X_train_norm_insert.shape)

#调整lmd为：0,0.001,0.003,0.1,0.3,1,3,10,100
lmd = 1
min = opt.minimize(fun=costReg, x0=theta1, args=(X_train_norm_insert,y_raw,lmd), method='TNC', jac=gradientReg)
#这里假设函数中theta数量就比较大了，需要有一个lbd来正则。这里写0，是因为需要看一下在不正则的情况下，过拟合是多么严重
theta1 = min.x
# print(theta1)

C = np.reshape(np.linspace(start=-80, stop=60, num=100), (100,1))
C_exp = feature(C, p)
C_norm = (C_exp - X_train_mean) / X_train_sigma   #特别注意，仔细看这里的mean和sigma用的是谁的
# print(C_norm.shape)
C_insert = np.insert(C_norm,0,np.ones(C_norm.shape[0]),axis=1)
D = predict(theta1,C_insert)
fig,ax = plt.subplots(figsize=(12,8))
ax.plot(C,D,c='b', linestyle='dashed')
ax.scatter(X_raw,y_raw,c='r',marker='x')
ax.set_xlabel('Change in water level(x)')
ax.set_ylabel('Water flowing out of the dam(y)')
ax.set_title('Polynomial Regression Fit (lambda = 0.000000)')
plt.show()



'''特征扩展后的学习曲线'''
X_val_norm_insert = np.insert(X_val_norm,0,np.ones(X_val_norm.shape[0]),axis=1)
error_train2, error_val2 = learning_curve(theta1,X_val_norm_insert,y_val,X_train_norm_insert,y_raw,11,lmd)

fix,ax = plt.subplots(figsize=(12,8))
ax.plot(np.linspace(start=2,stop=12,num=11),error_train2,c='b',label='Train')
ax.plot(np.linspace(start=2,stop=12,num=11),error_val2,c='g',label='Cross Validation')
ax.legend(loc=1)
ax.set_xlabel('Number of training examples')
ax.set_ylabel('Error')
ax.set_title('Learning curve for linear regression')
plt.show()



'''绘制lambda与error之间的关系'''
lmd_lst = [0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]   #取11个，因为error_train2 和 error_val2内部正好各自有11个数
print(len(lmd_lst))
error_t,error_v = lmd_error(lmd_lst,X_val_norm_insert,y_val,X_train_norm_insert,y_raw)
print(error_v)
fix,ax = plt.subplots(figsize=(12,8))
ax.plot(np.linspace(start=0,stop=10,num=10),error_t,c='b',label='Train')
ax.plot(np.linspace(start=0,stop=10,num=10),error_v,c='g',label='Cross Validation')
ax.legend(loc=1)
ax.set_xlabel('lambda')
ax.set_ylabel('Error')
plt.show()

第一篇完整自己写的代码，

感谢所有机器学习道路上的引路人。