采用梯度下降法的线性回归；成本函数值有问题

Question

我正在用梯度下降法对线性回归进行编码。通过使用for循环而不是张量

我认为我的代码在逻辑上是正确的，当我绘制图表时，θ值和线性模型看起来很好。但成本函数的价值很高。你能帮我吗

成本函数的值为1160934，这是异常的

def gradient_descent(alpha,x,y,ep=0.0001, max_repeat=10000000):
    m = x.shape[0]
    converged = False
    repeat = 0
    theta0 = 1.0
    theta3 = -1.0
#     J=sum([(theta0 +theta3*x[i]- y[i])**2 for i in range(m)]) / 2*m #######
    J=1
    
    while not converged : 
        grad0= sum([(theta0 +theta3*x[i]-y[i]) for i in range (m)]) / m
        grad1= sum([(theta0 + theta3*x[i]-y[i])*x[i] for i in range (m)])/ m
        
        temp0 = theta0 - alpha*grad0
        temp1 = theta3 - alpha*grad1
        
        theta0 = temp0
        theta3 = temp1
    
        msqe = (sum([(theta0 + theta3*x[i] - y[i]) **2 for i in range(m)]))* (1 / 2*m)
        print(theta0,theta3,msqe)
        if abs(J-msqe) <= ep:
            print ('Converged, iterations: {0}', repeat, '!!!')
            converged = True
        
        J = msqe
        repeat += 1
        
        if repeat == max_repeat:
                converged = True
                print("max 까지 갔다")
   
    return theta0, theta3, J
[theta0,theta3,J]=gradient_descent(0.001,X3,Y,ep=0.0000001,max_repeat=1000000)

print("************\n theta0 : {0}\ntheta3 : {1}\nJ : {2}\n"
          .format(theta0,theta3,J))

This is the data set

Answer 1

我认为数据集本身是相当广泛的，这就是为什么最佳拟合线显示了大量的成本函数。如果你扩展你的数据，你会看到它显著下降