Question

对于一项作业，我必须同时实现铰链损耗及其偏导数计算功能。我得到了铰链损失函数本身，但是我很难理解如何计算其偏导数w.r.t.预测输入。我尝试了不同的方法，但是没有一个起作用。

任何帮助，提示和建议将不胜感激！

这里是铰链损失函数本身的解析表达式：

这是我的Hinge损失函数实现：

def hinge_forward(target_pred, target_true):
    """Compute the value of Hinge loss 
        for a given prediction and the ground truth
    # Arguments
        target_pred: predictions - np.array of size `(n_objects,)`
        target_true: ground truth - np.array of size `(n_objects,)`
    # Output
        the value of Hinge loss 
        for a given prediction and the ground truth
        scalar
    """
    output = np.sum((np.maximum(0, 1 - target_pred * target_true)) / target_pred.size)

    return output

现在我需要计算这个梯度：

这是我尝试进行铰链损耗梯度计算的方法：

def hinge_grad_input(target_pred, target_true):
    """Compute the partial derivative 
        of Hinge loss with respect to its input
    # Arguments
        target_pred: predictions - np.array of size `(n_objects,)`
        target_true: ground truth - np.array of size `(n_objects,)`
    # Output
        the partial derivative 
        of Hinge loss with respect to its input
        np.array of size `(n_objects,)`
    """
# ----------------
#     try 1
# ----------------
#     hinge_result = hinge_forward(target_pred, target_true)

#     if hinge_result == 0:
#         grad_input = 0
#     else:
#         hinge = np.maximum(0, 1 - target_pred * target_true)
#         grad_input = np.zeros_like(hinge)
#         grad_input[hinge > 0] = 1
#         grad_input = np.sum(np.where(hinge > 0))
# ----------------
#     try 2
# ----------------
#     hinge = np.maximum(0, 1 - target_pred * target_true)
#     grad_input = np.zeros_like(hinge)

#     grad_input[hinge > 0] = 1
# ----------------
#     try 3
# ----------------
    hinge_result = hinge_forward(target_pred, target_true)

    if hinge_result == 0:
        grad_input = 0
    else:
        loss = np.maximum(0, 1 - target_pred * target_true)
        grad_input = np.zeros_like(loss)
        grad_input[loss > 0] = 1
        grad_input = np.sum(grad_input) * target_pred

    return grad_input

Answer 1

我已经设法通过使用np.where（）函数解决了这个问题。这是代码：

def hinge_grad_input(target_pred, target_true):
    """Compute the partial derivative 
        of Hinge loss with respect to its input
    # Arguments
        target_pred: predictions - np.array of size `(n_objects,)`
        target_true: ground truth - np.array of size `(n_objects,)`
    # Output
        the partial derivative 
        of Hinge loss with respect to its input
        np.array of size `(n_objects,)`
    """
    grad_input = np.where(target_pred * target_true < 1, -target_true / target_pred.size, 0)

    return grad_input

对于y * y <1，否则为0的所有情况，梯度基本上等于-y / N。

铰链损耗函数梯度w.r.t.输入预测

1 个答案: