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 SVMPerf and BMRM. One can show that these algorithms converge to an eta accurate solution in O(1/Lambda*e) iterations, where lambda is the tradeoff parameter between the regularizer and the loss function. We present a smoothing strategy for multivariate performance scores, in particular precision/recall breakeven 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 SVMPerf 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 arXiv:
 arXiv:1202.3776
 Bibcode:
 2012arXiv1202.3776Z
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning