  We present a simple unified framework for multi-class cost-sensitive
boosting. The minimum-risk class is estimated directly, rather than via an
approximation of the posterior distribution. Our method jointly optimizes
binary weak learners and their corresponding output vectors, requiring classes
to share features at each iteration. By training in a cost-sensitive manner,
weak learners are invested in separating classes whose discrimination is
important, at the expense of less relevant classification boundaries.
Additional contributions are a family of loss functions along with proof that
our algorithm is Boostable in the theoretical sense, as well as an efficient
procedure for growing decision trees for use as weak learners. We evaluate our
method on a variety of datasets: a collection of synthetic planar data, common
UCI datasets, MNIST digits, SUN scenes, and CUB-200 birds. Results show
state-of-the-art performance across all datasets against several strong
baselines, including non-boosting multi-class approaches.
