GBrank: what is the final model?

Question

A colleague and I cannot reach a consensus in what the GBrank model (after training) should look like.

Introduction

The method starts by performing the typical conversion from pairwise to a pointwise dataset, where the target variable z represents now a score which should be higher, z_i > z_j when i is preferred over j. The authors then suggest using Gradient Boosting Trees, and "punish" cases where that model is predicting z_j > z_j and i is preferred over j. The "punishment" is performed by switching the scores and also incrementing or decrementing by τ.

Disagreement

Where we disagree is whether Gradient Boosting Rank is itself an ensembler. That is, is the model we are training g_k or is it h_k?

Reference Material

• The original article: http://www.cc.gatech.edu/~zha/papers/fp086-zheng.pdf

Answer 1

h is used in the whole paper to denote the hypothesis you are working with, g is just a domain specific regression model used to construct h, thus GBRank is h_k. In particular, it is a boosting method, thus it has to be an ensemble, trained by building a strong learner from set of weak learners (from definition of boosting posed by Kearns and Valiant in late '80) - h is an ensemble (due to recurrent definition), g is not (as it is just a regressor trained on some transformed dataset).