如何在python中实现负二项式损失函数以用于轻GBM

Question

我有一个机器学习问题，我相信负二项式损失函数会很适合，但light gbm包没有它作为标准，我正在尝试实现它，但我不知道如何获得Gradient和Hessian，有人知道我该怎么做吗？我设法达到了损失函数，但我无法达到梯度和粗麻布。

import math
def custom_asymmetric_valid(y_pred,y_true):
y_true = y_true.get_label()
p = 0.5
n = y_pred
loss = math.gamma(n) + math.gamma(y_true + 1) - math.gamma(n + y_true) - n * math.log(p) - y_true * math.log(1 - p)
return "custom_asymmetric_eval", np.mean(loss), False

现在如何获得梯度和黑森？

def custom_asymmetric_train(y_pred,y_true):
residual = (y_true.get_label() - y_pred).astype("float")
grad = ?
hess = ?
return grad, hess

有人能帮忙吗？

Answer 1

这可以通过scipy自动实现：

from scipy.misc import derivative
from scipy.special import gamma
def custom_asymmetric_train(y_pred, dtrain):
y_true = dtrain.label
p = 0.5
def loss(x,t):
loss = gamma(x) + gamma(t+1) - gamma(x+t) - x*np.log(p) - t*np.log(1-p)
return loss
partial_d = lambda x: loss(x, y_true)
grad = derivative(partial_d, y_pred, n=1, dx=1e-6)
hess = derivative(partial_d, y_pred, n=2, dx=1e-6)
return grad, hess