Supplementary Material - Optimizing Average Precision using Weakly Supervised Data
نویسندگان
چکیده
Briefly, the algorithm starts by specifying no constraints (step 1 of Algorithm 1: W is initialized to the null set). At each iteration, it adds a single constraint, which corresponds to the most violated ranking (step 4 of Algorithm 1: solving problem (1)). Intuitively, problem (1) finds a ranking that differs significantly from the ground-truth ranking in terms of AP but has a high score. Having added the most violated constraint, the cutting plane algorithm updates the parameters by solving a convex quadratic program (step 3 of Algorithm 1). The algorithm stops once no constraint can be found that is violated by more than the desired precision . The feasibility of the cutting plane algorithm relies on solving problem (1) efficiently. For fixed values of HP and HN (which is indeed the case for supervised AP-SVM), this can be achieved using the algorithm described in the following appendix.
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