In this paper, we investigate the problem of optimization of multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction function, the problem studied in this paper is how to learn effective hyper-predictor for a tuple of data points, so that a complex loss function corresponding to a multivariate performance measure can be minimized. We propose to present the tuple of data points to a tuple of sparse codes via a dictionary, and then apply a linear function to compare a sparse code against a given candidate class label. To learn the dictionary, sparse codes, and parameter of the linear function, we propose a joint optimization problem. In this problem, the both the reconstruction error and sparsity of sparse code, and the upper bound of the complex loss function are minimized. Moreover, the upper bound of the loss function is approximated by the sparse codes and the linear function parameter. To optimize this problem, we develop an iterative algorithm based on descent gradient methods to learn the sparse codes and hyper-predictor parameter alternately. Experiment results on some benchmark data sets show the advantage of the proposed methods over other state-of-the-art algorithms.
@cite_19: This paper presents a Support Vector Method for optimizing multivariate nonlinear performance measures like the F 1 -score. Taking a multivariate prediction approach, we give an algorithm with which such multivariate SVMs can be trained in polynomial time for large classes of potentially non-linear performance measures, in particular ROCArea and all measures that can be computed from the contingency table. The conventional classification SVM arises as a special case of our method.
Joachims @cite_19 proposed a SVM method to optimize multivariate nonlinear performance measures, including F-score, AUC etc. This method takes a multivariate predictor, and gives an algorithm to train the a multivariate SVM in polynomial time for large classes so that the potentially non-linear performance measures can be optimized. Moreover, the translational SVM with hinge loss function can be treated as a special case of this method.