This function computes the stable version of BCE cost

compute_stable_bce_cost.py

def compute_stable_bce_cost(Y, Z):
    """
    This function computes the "Stable" Binary Cross-Entropy(stable_bce) Cost and returns the Cost and its
    derivative w.r.t Z_last(the last linear node) .
    The Stable Binary Cross-Entropy Cost is defined as:
    => (1/m) * np.sum(max(Z,0) - ZY + log(1+exp(-|Z|)))
    Args:
        Y: labels of data
        Z: Values from the last linear node

    Returns:
        cost: The "Stable" Binary Cross-Entropy Cost result
        dZ_last: gradient of Cost w.r.t Z_last
    """
    m = Y.shape[1]

    cost = (1/m) * np.sum(np.maximum(Z, 0) - Z*Y + np.log(1+ np.exp(- np.abs(Z))))
    dZ_last = (1/m) * ((1/(1+np.exp(- Z))) - Y)  # from Z computes the Sigmoid so P_hat - Y, where P_hat = sigma(Z)

    return cost, dZ_last