How can I offset exposures in a gbm model in R?

Question

I am trying to fit a gradient boosting machine (GBM) to insurance claims. The observations have unequal exposure so I am trying to use an offset equal to the log of exposures. I tried two different ways:

1. Put an offset term in the formula. This resulted in nan for the train and validation deviance for every iteration.

2. Use the offset parameter in the gbm function. This parameter is listed under gbm.more. This results in an error message that there is an unused parameter.

I can't share my company's data but I reproduced the problem using the Insurance data table in the MASS package. See the code and output below.

library(MASS)
library(gbm)

data(Insurance)

# Try using offset in the formula.
fm1 = formula(Claims ~ District + Group + Age + offset(log(Holders)))

fitgbm1 = gbm(fm1, distribution = "poisson",
              data = Insurance,
              n.trees = 10,
              shrinkage = 0.1,
              verbose = TRUE)

# Try using offset in the gbm statement.
fm2 = formula(Claims ~ District + Group + Age)
offset2 = log(Insurance$Holders)

fitgbm2 = gbm(fm2, distribution = "poisson",
              data = Insurance,
              n.trees = 10,
              shrinkage = 0.1,
              offset = offset2,
              verbose = TRUE)

This then outputs:

> source('D:/Rprojects/auto_tutorial/rcode/example_gbm.R')
Iter   TrainDeviance   ValidDeviance   StepSize   Improve
     1     -347.8959             nan     0.1000    0.0904
     2     -348.2181             nan     0.1000    0.0814
     3     -348.3845             nan     0.1000    0.0616
     4     -348.5424             nan     0.1000    0.0333
     5     -348.6732             nan     0.1000    0.0850
     6     -348.7744             nan     0.1000    0.0610
     7     -348.8795             nan     0.1000    0.0633
     8     -348.9132             nan     0.1000   -0.0109
     9     -348.9200             nan     0.1000   -0.0212
    10     -349.0271             nan     0.1000    0.0267

Error in gbm(fm2, distribution = "poisson", data = Insurance, n.trees = 10,  : 
  unused argument (offset = offset2)

My question is what am I doing wrong? Also, is there another way? I noticed a weights parameter in the gbm function. Should I use that?

Answer 1

Your first suggestion works if you specify a training fraction less than 1. The default is 1, which means there is no validation set.

library(MASS)
library(gbm)

data(Insurance)

# Try using offset in the formula.
fm1 = formula(Claims ~ District + Group + Age + offset(log(Holders)))

fitgbm1 = gbm(fm1, distribution = "poisson",
              data = Insurance,
              n.trees = 10,
              shrinkage = 0.1,
              verbose = TRUE,
              train.fraction = .75)

results in

Iter   TrainDeviance   ValidDeviance   StepSize   Improve
     1     -428.8293       -105.1735     0.1000    0.0888
     2     -429.0869       -105.3063     0.1000    0.0708
     3     -429.1805       -105.3941     0.1000    0.0486
     4     -429.3414       -105.4816     0.1000    0.0933
     5     -429.4934       -105.5432     0.1000    0.0566
     6     -429.6714       -105.5188     0.1000    0.1212
     7     -429.8470       -105.5200     0.1000    0.0833
     8     -429.9655       -105.6073     0.1000    0.0482
     9     -430.1367       -105.6003     0.1000    0.0473
    10     -430.2462       -105.6100     0.1000    0.0487