For simplicity, we have no special handling for ties;
instead, we break ties randomly. This is slightly
inaccurate for individual groups, but should have
only a small effect on the overall measure.
gbm.conc
computes the concordance index:
Fraction of all pairs (i,j) with i<j, x[i] != x[j], such that x[j] < x[i]
If obs
is binary, then
gbm.roc.area(obs, pred) = gbm.conc(obs[order(-pred)])
.
gbm.conc
is more general as it allows non-binary targets,
but is significantly slower.