In this work, we propose a novel Weakly Supervised Learning (WSL) framework dedicated to learn discriminative part detectors from images annotated with a global label. Our WSL method encompasses three main contributions. Firstly, we introduce a new structured output latent variable model, Minimum mAximum lateNt sTRucturAl SVM (MANTRA), which prediction relies on a pair of latent variables: $h^+$ (resp. $h^-$) provides positive (resp. negative) evidence for a given output $y$. Secondly, we instantiate MANTRA for two different visual recognition tasks: multi-class classification and ranking. For ranking, we propose efficient solutions to exactly solve the inference and the loss-augmented problems. Finally, extensive experiments highlight the relevance of the proposed method: MANTRA outperforms state-of-the art results on five different datasets.