Uncertainty in Artificial Intelligence
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Smoothing Multivariate Performance Measures
Xinhua Zhang, Ankan Saha, S. Vishwanatan
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.
Pages: 814-821
PS Link:
PDF Link: /papers/11/p814-zhang.pdf
AUTHOR = "Xinhua Zhang and Ankan Saha and S. Vishwanatan",
TITLE = "Smoothing Multivariate Performance Measures",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "814--821"

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