33 research outputs found
Error-Correcting Tournaments
We present a family of pairwise tournaments reducing -class classification
to binary classification. These reductions are provably robust against a
constant fraction of binary errors. The results improve on the PECOC
construction \cite{SECOC} with an exponential improvement in computation, from
to , and the removal of a square root in the regret
dependence, matching the best possible computation and regret up to a constant.Comment: Minor wording improvement
Maximum Margin Multiclass Nearest Neighbors
We develop a general framework for margin-based multicategory classification
in metric spaces. The basic work-horse is a margin-regularized version of the
nearest-neighbor classifier. We prove generalization bounds that match the
state of the art in sample size and significantly improve the dependence on
the number of classes . Our point of departure is a nearly Bayes-optimal
finite-sample risk bound independent of . Although -free, this bound is
unregularized and non-adaptive, which motivates our main result: Rademacher and
scale-sensitive margin bounds with a logarithmic dependence on . As the best
previous risk estimates in this setting were of order , our bound is
exponentially sharper. From the algorithmic standpoint, in doubling metric
spaces our classifier may be trained on examples in time and
evaluated on new points in time