我正在研究LightGBM中的自定义目标函数，发现复制内置函数是一个好的起点。LightGBM用于计算Tweedie度量的方程式（https://github.com/microsoft/LightGBM/blob/1c27a15e42f0076492fcc966b9dbcf9da6042823/src/metric/regression_metric.hpp#L300-L318）似乎与我在网上找到的Tweedie损失定义（https://towardsdatascience.com/tweedie-loss-function-for-right-skewed-data-2c5ca470678f）相匹配，但它们进行了奇怪的exp(ln(score))处理，我猜测这是为了数值稳定性。然而，他们对斜率和黑塞的方程式似乎直接在得分的对数上完成（https://github.com/microsoft/LightGBM/blob/1c27a15e42f0076492fcc966b9dbcf9da6042823/src/objective/regression_objective.hpp#L702-L732）。
我得到了结果（期望预测2或预测3与预测结果非常相似）：
gradients[i] = -label_[i] * e^((1 - rho_) * score[i]) + e^((2 - rho_) * score[i]);
我期望梯度会出现在哪里：
gradients[i] = -label_[i] * score[i]^(- rho_) + score[i]^(1 - rho_);
我的猜测是LightGBM在处理分数时将其视为ln（score），例如使用参数reg_sqrt，但我找不到文档中描述这一点的地方。
无论如何，我已尝试重新创建它们的公式和自己的计算作为自定义目标函数，但两者都似乎不起作用：
library(lightgbm)
library(data.table)
# Tweedie gradient with variance = 1.5, according to my own math
CustomObj_t1 <- function(preds, dtrain) {
labels <- dtrain$getinfo('label')
grad <- -labels * preds^(-3/2) + preds^(-1/2)
hess <- 1/2 * (3*labels*preds^(-5/2) - preds^(-3/2))
return(list(grad = grad, hess = hess))
}
# Tweedie gradient with variance = 1.5, recreating code from LightGBM github
CustomObj_t2 <- function(preds, dtrain) {
labels <- dtrain$getinfo('label')
grad <- -labels*exp(-1/2*preds) + exp(1/2*preds)
hess <- -labels*(-1/2)*exp(-1/2*preds) + 1/2*exp(1/2*preds)
return(list(grad = grad, hess = hess))
}
params = list(objective = "tweedie",
seed = 1,
metric = "rmse")
params2 = list(objective = CustomObj_t1,
seed= 1,
metric = "rmse")
params3 = list(objective = CustomObj_t2,
seed= 1,
metric = "rmse")
# Create data
set.seed(321)
db_Custom = data.table(a=runif(2000), b=runif(2000))
db_Custom[,X := (a*4+exp(b))]
# break into test and training sets
db_Test = db_Custom[1:10]
db_Custom=db_Custom[11:nrow(db_Custom),]
FeatureCols = c("a","b")
# Create dataset
ds_Custom <- lgb.Dataset(data.matrix(db_Custom[, FeatureCols, with = FALSE]), label = db_Custom[["X"]])
# Train
fit = lgb.train(params, ds_Custom, verb=-1)
#print(" ")
fit2 = lgb.train(params2, ds_Custom, verb=-1)
#print(" ")
fit3 = lgb.train(params3, ds_Custom, verb=-1)
# Predict
pred = predict(fit, data.matrix(db_Test[, FeatureCols, with = FALSE]))
db_Test[, prediction := pmax(0, pred)]
pred2 = predict(fit2, data.matrix(db_Test[, FeatureCols, with = FALSE]))
db_Test[, prediction2 := pmax(0, pred2)]
pred3 = predict(fit3, data.matrix(db_Test[, FeatureCols, with = FALSE]))
db_Test[, prediction3 := pmax(0, pred3)]
print(db_Test[,.(X,prediction,prediction2,prediction3)])
我得到了结果（期望预测2或预测3与预测结果非常相似）：
"X" "prediction" "prediction2" "prediction3"
4.8931646234958 4.89996556839721 0 1.59154656425556
6.07328897031702 6.12313647937047 0 1.81022588429474
2.05728566704078 2.06824004875244 0 0.740577102751491
2.54732526765174 2.50329903656292 0 0.932517774958986
4.07044099941395 4.07047912554207 0 1.39922723582939
2.74639568121359 2.74408567443232 0 1.01628212910587
3.47720295158928 3.49241414141969 0 1.23049599462599
2.92043718858535 2.90464303454649 0 1.0680618051659
4.44415913080697 4.43091665909845 0 1.48607456777287
4.96566318066753 4.97898586895233 0 1.60163901781479
我有什么遗漏吗？是我的计算或编码有误吗？