python中的梯度下降函數 - 損失函數或權重錯誤

Question

我正在使用梯度函數進行練習，但我仍然無法獲得預期的結果。 也就是說，我收到 2 條錯誤消息：

1. 損失函數的錯誤輸出。 檢查您如何實現矩陣乘法。

2. 權重矩陣 theta 的值錯誤。 檢查您如何更新權重矩陣。

應用該函數時（見下文），我注意到每次迭代的成本都會降低，但它仍然沒有收斂到練習中的預期結果。 我已經在公式上嘗試了幾次修改，但還沒有解決。

# gradientDescent

def gradientDescent(x, y, theta, alpha, num_iters):

Input:
    x: matrix of features which is (m,n+1)
    y: corresponding labels of the input matrix x, dimensions (m,1)
    theta: weight vector of dimension (n+1,1)
    alpha: learning rate
    num_iters: number of iterations you want to train your model for
Output:
    J: the final cost
    theta: your final weight vector
Hint: you might want to print the cost to make sure that it is going down.

### START CODE HERE ###
# get 'm', the number of rows in matrix x
m = len(x)

for i in range(0, num_iters):
    
    # get z, the dot product of x and theta
    # z = predictins
    z = np.dot(x, theta)
    h = sigmoid(z)
    loss = z - y
    
    # calculate the cost function
    J =  (-1/m) * np.sum(loss)
    print("Iteration %d | Cost: %f" % (i, J))#
            
    gradient = np.dot(x.T, loss)
    
    #update theta
    theta = theta - (1/m) * alpha * gradient
    
    
### END CODE HERE ###
J = float(J)
return J, theta

Answer 1

問題是我錯誤地應用了成本函數的公式和計算權重的公式：

𝐽=−1/𝑚×(𝐲𝑇⋅𝑙𝑜𝑔(𝐡)+(1−𝐲)𝑇⋅𝑙𝑜𝑔(1−𝐡))

𝜃=𝜃−𝛼/𝑚×(𝐱𝑇⋅(𝐡−𝐲))

解決方案是：

 J =  (-1/m) * (np.dot(y.T, np.log(h)) +  (np.dot((1-y).T, np.log(1-h)))
 theta = theta - (alpha/m) * gradient