In this paper, a powerful open Multiple Instance Learning (MIL) framework is proposed. Such an open framework is powerful since different sub-methods can be plugged into the framework to generate different specific Multiple Instance Learning algorithms. In our proposed framework, the Multiple Instance Learning problem is first converted to an unconstrained optimization problem by the Minimum Square Error (MSE) criterion, and then the framework can be constructed with an open form of hypothesis and gradient search method. The proposed Multiple Instance Learning framework is applied to the drug activity problems in bioinformatics applications. Specifically, experiments are conducted on the Musk-1 dataset to predict the binding activity of drug molecules. In the experiments, an algorithm with the exponential hypothesis model and the Quasi-Newton method is embedded into our proposed framework. We compare our proposed framework with other existing algorithms and the experimental results show that our proposed framework yields a good accuracy of classification, which demonstrates the feasibility and effectiveness of our framework.