  Influence estimation analyzes how changes to the training data can lead to
different model predictions; this analysis can help us better understand these
predictions, the models making those predictions, and the data sets they're
trained on. However, most influence-estimation techniques are designed for deep
learning models with continuous parameters. Gradient-boosted decision trees
(GBDTs) are a powerful and widely-used class of models; however, these models
are black boxes with opaque decision-making processes. In the pursuit of better
understanding GBDT predictions and generally improving these models, we adapt
recent and popular influence-estimation methods designed for deep learning
models to GBDTs. Specifically, we adapt representer-point methods and TracIn,
denoting our new methods TREX and BoostIn, respectively; source code is
available at https://github.com/jjbrophy47/tree_influence. We compare these
methods to LeafInfluence and other baselines using 5 different evaluation
measures on 22 real-world data sets with 4 popular GBDT implementations. These
experiments give us a comprehensive overview of how different approaches to
influence estimation work in GBDT models. We find BoostIn is an efficient
influence-estimation method for GBDTs that performs equally well or better than
existing work while being four orders of magnitude faster. Our evaluation also
suggests the gold-standard approach of leave-one-out (LOO) retraining
consistently identifies the single-most influential training example but
performs poorly at finding the most influential set of training examples for a
given target prediction.
