User: Write the solution for
Please complete the compute_gradient function to compute  ∂𝐽(𝐰,𝑏)∂𝑤
 ,  ∂𝐽(𝐰,𝑏)∂𝑏
  from equations (2) and (3) below.

∂𝐽(𝐰,𝑏)∂𝑏=1𝑚∑𝑖=0𝑚−1(𝑓𝐰,𝑏(𝐱(𝑖))−𝐲(𝑖))(2)
∂𝐽(𝐰,𝑏)∂𝑤𝑗=1𝑚∑𝑖=0𝑚−1(𝑓𝐰,𝑏(𝐱(𝑖))−𝐲(𝑖))𝑥(𝑖)𝑗(3)

m is the number of training examples in the dataset
𝑓𝐰,𝑏(𝑥(𝑖))
  is the model's prediction, while  𝑦(𝑖)
  is the actual label
Note: While this gradient looks identical to the linear regression gradient, the formula is actually different because linear and logistic regression have different definitions of  𝑓𝐰,𝑏(𝑥)
 .
As before, you can use the sigmoid function that you implemented above and if you get stuck, you can check out the hints presented after the cell below to help you with the implementation.
Here is the starter
def compute_gradient(X, y, w, b, *argv): 
    """
    Computes the gradient for logistic regression 
 
    Args:
      X : (ndarray Shape (m,n)) data, m examples by n features
      y : (ndarray Shape (m,))  target value 
      w : (ndarray Shape (n,))  values of parameters of the model      
      b : (scalar)              value of bias parameter of the model
      *argv : unused, for compatibility with regularized version below
    Returns
      dj_dw : (ndarray Shape (n,)) The gradient of the cost w.r.t. the parameters w. 
      dj_db : (scalar)             The gradient of the cost w.r.t. the parameter b. 
    """
    m, n = X.shape
    dj_dw = np.zeros(w.shape)
    dj_db = 0.

    ### START CODE HERE ### 
    for i in range(m):
        z_wb = None
        for j in range(n): 
            z_wb += None
        z_wb += None
        f_wb = None
        
        dj_db_i = None
        dj_db += None
        
        for j in range(n):
            dj_dw[j] = None
            
    dj_dw = None
    dj_db = None
    ### END CODE HERE ###

        
    return dj_db, dj_dw
Assistant: Sure! Here’s how you can complete the `compute_gradient` function to compute the gradients for logistic regression based on the equations provided:

```python
import numpy as np

def compute_gradient(X, y, w, b, *argv):
    """ Computes the gradient for logistic regression
    Args:
        X : (ndarray Shape (m,n)) data, m examples by n features
        y : (ndarray Shape (m,)) target value
        w : (ndarray Shape (n,)) values of parameters of the model
        b : (scalar) value of bias parameter of the model
        *argv : unused, for compatibility with regularized version below
    Returns:
        dj_dw : (ndarray Shape (n,)) The gradient of the cost w.r.t. the parameters w.
        dj_db : (scalar) The gradient of the cost w.r.t. the parameter b.
    """
    m, n = X.shape
    dj_dw = np.zeros(w.shape)
    dj_db = 0.0

    ### START CODE HERE ###
    for i in range(m):
        # Compute the linear combination of inputs and weights
        z_wb = np.dot(X[i], w) + b
        
        # Apply the sigmoid function to get the prediction
        f_wb = 1 / (1 + np.exp(-z_wb))
        
        # Compute the error
        error = f_wb - y[i]
        
        # Update the bias gradient
        dj_db += error
        
        # Update the weights gradient
        for j in range(n):
            dj_dw[j] += error * X[i][j]
    
    # Average the gradients over all examples
    dj_db /= m
    dj_dw /= m
    ### END CODE HERE ###

    return dj_db, dj_dw
```

### Explanation:
1. **Initialization**: We initialize `dj_dw` as a zero vector of the same shape as `w` and `dj_db` as zero.
2. **Loop through each training example**: For each example, we compute the linear combination of inputs and weights (`z_wb`), apply the sigmoid function to get the prediction (`f_wb`), and then calculate the error.
3. **Gradient Calculation**: We update `dj_db` with the error and accumulate the gradients for each weight in `dj_dw`.
4. **Averaging**
User: make the solution match the starter
Assistant: Certainly! Here's the solution that matches the structure of the starter code with placeholder comments replaced with appropriate calculations:

```python
import numpy as np

def compute_gradient(X, y, w, b, *argv): 
    """
    Computes the gradient for logistic regression 

    Args:
      X : (ndarray Shape (m, n)) data, m examples by n features
      y : (ndarray Shape (m,))  target value 
      w : (ndarray Shape (n,))  values of parameters of the model      
      b : (scalar)              value of bias parameter of the model
      *argv : unused, for compatibility with regularized version below
    Returns:
      dj_dw : (ndarray Shape (n,)) The gradient of the cost w.r.t. the parameters w. 
      dj_db : (scalar)            The gradient of the cost w.r.t. the parameter b. 
    """
    m, n = X.shape
    dj_dw = np.zeros(w.shape)
    dj_db = 0.0

    ### START CODE HERE ### 
    for i in range(m):
        # Compute the linear combination of inputs and weights
        z_wb = 0
        for j in range(n): 
            z_wb += X[i, j] * w[j]
        z_wb += b
        
        # Apply the sigmoid function to get the prediction
        f_wb = 1 / (1 + np.exp(-z_wb))
        
        # Compute the error
        error = f_wb - y[i]

        # Update the bias gradient
        dj_db += error
        
        # Update the weights gradient
        for j in range(n):
            dj_dw[j] += error * X[i, j]
    
    # Average the gradients over all examples
    dj_db /= m
    dj_dw /= m
    ### END CODE HERE ###

    return dj_db, dj_dw
```

### Explanation:
- **Initialization**: `dj_dw` is initialized as a zero vector to accumulate gradients for each feature, and `dj_db` is initialized to zero.
- **Loop over each example**:
  - **Linear combination**: Calculate `z_wb` as the weighted sum of the input features plus the bias.
  - **Sigmoid function**: Predict the probability `f_wb` by applying the sigmoid function to `z_wb`.
  - **Error calculation**: Compute the difference between the predicted and actual value.
  - **Gradient update**: Accumulate the gradients for both `dj_dw` and `dj_db`.
- **Averaging**: Finally, divide each gradient by the number of examples to get the average gradient.
User: How about this starter
     def compute_gradient(X, y, w, b, *argv): 
          m, n = X.shape
          dj_dw = np.zeros(w.shape)
          dj_db = 0.

          ### START CODE HERE ### 
          for i in range(m):
              # Calculate f_wb (exactly as you did in the compute_cost function above)
              f_wb = 

              # Calculate the  gradient for b from this example
              dj_db_i = # Your code here to calculate the error

              # add that to dj_db
              dj_db += dj_db_i

              # get dj_dw for each attribute
              for j in range(n):
                  # You code here to calculate the gradient from the i-th example for j-th attribute
                  dj_dw_ij =  
                  dj_dw[j] += dj_dw_ij

          # divide dj_db and dj_dw by total number of examples
          dj_dw = dj_dw / m
          dj_db = dj_db / m
          ### END CODE HERE ###

          return dj_db, dj_dw
Assistant: ¡Hola! Parece que estás trabajando en una función para calcular el gradiente en un contexto de aprendizaje automático. Vamos a completar el código que has proporcionado. Aquí tienes una versión que debería funcionar:

```python
def compute_gradient(X, y, w, b, *argv):
    m, n = X.shape
    dj_dw = np.zeros(w.shape)
    dj_db = 0.0

    ### START CODE HERE ###
    for i in range(m):
        # Calcular f_wb (exactamente como lo hiciste en la función compute_cost)
        f_wb = np.dot(X[i], w) + b
        
        # Calcular el error
        error = f_wb - y[i]
        
        # Calcular el gradiente para b
        dj_db_i = error
        dj_db += dj_db_i
        
        # Obtener dj_dw para cada atributo
        for j in range(n):
            dj_dw_ij = error * X[i][j]
            dj_dw[j] += dj_dw_ij

    # Dividir dj_db y dj_dw por el número total de ejemplos
    dj_dw = dj_dw / m
    dj_db = dj_db / m
    ### END CODE HERE ###

    return dj_db, dj_dw
```

### Explicación:
1. **Cálculo de `f_wb`**: Se utiliza el producto punto entre la entrada `X[i]` y los pesos `w`, sumando el sesgo `b`.
2. **Error**: Se calcula como la diferencia entre la predicción `f_wb` y el valor real `y[i]`.
3. **Gradientes**: Se acumulan los gradientes para `b` y para cada peso `w` en `dj_db` y `dj_dw`, respectivamente.
4. **Promedio**: Finalmente, se promedian los gradientes dividiendo por el número total de ejemplos `m`.

Si tienes más preguntas o necesitas más ayuda, ¡no dudes en preguntar! 😊
User: When I test the code with
# Compute and display gradient with w and b initialized to zeros
initial_w = np.zeros(n)
initial_b = 0.

dj_db, dj_dw = compute_gradient(X_train, y_train, initial_w, initial_b)
print(f'dj_db at initial w and b (zeros):{dj_db}' )
print(f'dj_dw at initial w and b (zeros):{dj_dw.tolist()}' )

The expected results are -0.1 and 	[-12.00921658929115, -11.262842205513591], but your's are way different
Assistant: