Reputation: 113
I have a machine learning problem that I believe the negative binomial loss function would fit well, but the light gbm package doesn't have it as a standard, I'm trying to implement it, but I'm don't know how to get Gradient and Hessian, does anyone know how I can do this? I managed to get to the loss function, but I can't get to the gradient and hessian.
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
Now how to get the Gradient and Hessian?
def custom_asymmetric_train(y_pred,y_true):
residual = (y_true.get_label() - y_pred).astype("float")
grad = ?
hess = ?
return grad, hess
Anyone could help?
Upvotes: 4
Views: 1690
Reputation: 22021
this is possible with scipy automatically:
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
Upvotes: 3