arXiv:2608.19127v1 Announce Type: cross
Abstract: A gradient-boosted ensemble predicts by summing one leaf value per tree. Read
those values as coordinates rather than as intermediate results, and every
instance becomes a point in R^M on which the model acts linearly: the score is
the sum of the coordinates.
This small change of view makes contrastive explanation exact. The difference
between two instances is a vector that is identically zero wherever they share
a leaf, so the gap between a rejected applicant and an accepted one is carried
by a handful of coordinates, each traceable to a real split in a real tree.
Nothing is fitted, sampled, or assumed additive in features — the additivity
is already there, in the right space.
We build a recourse method on this representation and evaluate it on five
tabular datasets under repeated cross-validation. Its recommendation
reconstructs the model's own decision to 6.2 x 10^-15, so an auditor can
re-check the arithmetic without the model. On the credit datasets it is
Pareto-non-dominated on effort against realism. And when recommendations are
restricted to changes the subject could actually make — not their age, not a
settled delinquency — it retains 58% of its validity where the strongest
baseline retains 41%, a distinction the standard evaluation cannot see because
it never asks whether a recommendation can be carried out.
Abstract: A gradient-boosted ensemble predicts by summing one leaf value per tree. Read
those values as coordinates rather than as intermediate results, and every
instance becomes a point in R^M on which the model acts linearly: the score is
the sum of the coordinates.
This small change of view makes contrastive explanation exact. The difference
between two instances is a vector that is identically zero wherever they share
a leaf, so the gap between a rejected applicant and an accepted one is carried
by a handful of coordinates, each traceable to a real split in a real tree.
Nothing is fitted, sampled, or assumed additive in features — the additivity
is already there, in the right space.
We build a recourse method on this representation and evaluate it on five
tabular datasets under repeated cross-validation. Its recommendation
reconstructs the model's own decision to 6.2 x 10^-15, so an auditor can
re-check the arithmetic without the model. On the credit datasets it is
Pareto-non-dominated on effort against realism. And when recommendations are
restricted to changes the subject could actually make — not their age, not a
settled delinquency — it retains 58% of its validity where the strongest
baseline retains 41%, a distinction the standard evaluation cannot see because
it never asks whether a recommendation can be carried out.
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