Smoothing Multivariate Performance Measures
Abstract
A Support Vector Method for multivariate performance measures was recently introduced by Joachims (2005). The underlying optimization problem is currently solved using cutting plane methods such as SVM-Perf and BMRM. One can show that these algorithms converge to an eta accurate solution in O(1/Lambda*e) iterations, where lambda is the trade-off parameter between the regularizer and the loss function. We present a smoothing strategy for multivariate performance scores, in particular precision/recall break-even point and ROCArea. When combined with Nesterov's accelerated gradient algorithm our smoothing strategy yields an optimization algorithm which converges to an eta accurate solution in O(min{1/e,1/sqrt(lambda*e)}) iterations. Furthermore, the cost per iteration of our scheme is the same as that of SVM-Perf and BMRM. Empirical evaluation on a number of publicly available datasets shows that our method converges significantly faster than cutting plane methods without sacrificing generalization ability.
Cite
@article{arxiv.1202.3776,
title = {Smoothing Multivariate Performance Measures},
author = {Xinhua Zhang and Ankan Saha and S. V. N. Vishwanatan},
journal= {arXiv preprint arXiv:1202.3776},
year = {2012}
}