def learning_curve(X,Y,Xval,Yval,lmd): m = X.shape[0] error_train = np.zeros(m) error_val = np.zeros(m) for num in range(m): theta = train_linear_reg(X[0:num+1,:],Y[0:num+1],lmd) error_train[num],_ = linear_cost_function(X[0:num+1,:],Y[0:num+1],theta,lmd) error_val[num],_ = linear_cost_function(Xval,Yval,theta,lmd) return error_train,error_val
def validation_curve(X, Y, Xval, Yval):
lambda_vec = np.array([0., 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10])
error_train = np.zeros(lambda_vec.size)
error_val = np.zeros(lambda_vec.size)
for num in range(lambda_vec.size):
lmd = lambda_vec[num]
theta = train_linear_reg(X, Y, lmd)
error_train[num], _ = linear_cost_function(X, Y, theta, lmd)
error_val[num], _ = linear_cost_function(Xval, Yval, theta, lmd)
return lambda_vec, error_train, error_val
Yval = data['yval'].flatten()
Xtest = data['Xtest']
Ytest = data['ytest'].flatten()
plt.figure(1)
plt.scatter(X,Y,c='r',marker='x')
plt.xlabel('Change in water level (x)')
plt.ylabel('Water folowing out of the dam (y)')
# plt.show()
# ============================ 2.计算代价和梯度 ==============================
(m,n)= X.shape
theta = np.ones((n+1))
lmd=1
cost,grad = linear_cost_function(np.column_stack((np.ones(m),X)),Y,theta,lmd)
print('Cost at theta = [1 1]: {:0.6f}\n(this value should be about 303.993192)'.format(cost))
print('Gradient at theta = [1 1]: {}\n(this value should be about [-15.303016 598.250744]'.format(grad))
# =========================== 3.训练线性回归
lmd = 0
theta = train_linear_reg(np.column_stack((np.ones(m),X)),Y,lmd)
plt.plot(X,np.column_stack((np.ones(m),X)).dot(theta))
# plt.show()
# =========================== 4.线性回归的学习曲线 ==============
lmd = 0
error_train,error_val = learning_curve(np.column_stack((np.ones(m),X)),Y,
np.column_stack((np.ones(Yval.size),Xval)),Yval,lmd)
plt.figure(2)
plt.plot(range(m),error_train,range(m),error_val)
def cost_func(t):
return linear_cost_function(X, Y, t, lmd)[0]
def grad_func(t):
return linear_cost_function(X, Y, t, lmd)[1]