Smoothing Multivariate Performance Measures
This work addresses the computational efficiency of training SVMs for multivariate performance measures, which is an incremental improvement for machine learning practitioners dealing with classification tasks.
The paper tackles the optimization problem for multivariate performance measures in SVMs by introducing a smoothing strategy for scores like precision/recall break-even point and ROCArea, combined with Nesterov's accelerated gradient, resulting in faster convergence to an accurate solution without loss of generalization, as shown empirically on public datasets.
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.