The protein-protein interactions (PPIs) are generally assumed to be mediated by domain-domain interactions (DDIs). Many computational methods have been proposed based on this assumption to predict DDIs from available data of PPIs. However, most of the existing methods are generative methods that consider only PPI data without taking into account non-PPIs. In this paper, we propose a novel discriminative method for predicting DDIs from both PPIs and non-PPIs, which improves the prediction reliability. In particular, the DDI identification is formalized as a feature selection problem, which is equivalent to the parsimonious principle and is able to predict both DDIs and PPIs in a systematic and accurate manner. The numerical results on benchmark dataset demonstrate that formulating DDI prediction as a feature selection problem can predict DDIs from PPIs in a reliable way, which in turn is able to verify and further predict PPIs based on inferred DDIs.