  The work in ICML'09 showed that the derivatives of the classical multi-class
logistic regression loss function could be re-written in terms of a pre-chosen
"base class" and applied the new derivatives in the popular boosting framework.
In order to make use of the new derivatives, one must have a strategy to
identify/choose the base class at each boosting iteration. The idea of
"adaptive base class boost" (ABC-Boost) in ICML'09, adopted a computationally
expensive "exhaustive search" strategy for the base class at each iteration. It
has been well demonstrated that ABC-Boost, when integrated with trees, can
achieve substantial improvements in many multi-class classification tasks.
Furthermore, the work in UAI'10 derived the explicit second-order tree split
gain formula which typically improved the classification accuracy considerably,
compared with using only the fist-order information for tree-splitting, for
both multi-class and binary-class classification tasks. In this paper, we
develop a unified framework for effectively selecting the base class by
introducing a series of ideas to improve the computational efficiency of
ABC-Boost. Our framework has parameters $(s,g,w)$. At each boosting iteration,
we only search for the "$s$-worst classes" (instead of all classes) to
determine the base class. We also allow a "gap" $g$ when conducting the search.
That is, we only search for the base class at every $g+1$ iterations. We
furthermore allow a "warm up" stage by only starting the search after $w$
boosting iterations. The parameters $s$, $g$, $w$, can be viewed as tunable
parameters and certain combinations of $(s,g,w)$ may even lead to better test
accuracy than the "exhaustive search" strategy. Overall, our proposed framework
provides a robust and reliable scheme for implementing ABC-Boost in practice.
