The prediction of drug-target interactions plays a fundamental role in facilitating drug discovery, where the goal is to find prospective drug candidates. With the increase in the number of drug-protein interactions, machine learning techniques, especially deep learning methods, have become applicable for drug-target interaction discovery because they significantly reduce the required experimental workload. In this paper, we present a spontaneous formulation of the drug-target interaction prediction problem as an instance of multi-instance learning. We address the problem in three stages, first organizing given drug and target sequences into instances via a private-public mechanism, then identifying the predicted scores of all instances in the same bag, and finally combining all the predicted scores as the output prediction. A comprehensive evaluation demonstrates that the proposed method outperforms other state-of-the-art methods on three benchmark datasets.