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As a widely used weakly supervised learning scheme, modern multiple instance learning (MIL) models achieve competitive performance at the bag level. However, instance-level prediction, which is essential for many important applications, remains largely unsatisfactory. We propose to conduct novel active deep multiple instance learning that samples a small subset of informative instances for annotation, aiming to significantly boost the instance-level prediction. A variance regularized loss function is designed to properly balance the bias and variance of instance-level predictions, aiming to effectively accommodate the highly imbalanced instance distribution in MIL and other fundamental challenges. Instead of directly minimizing the variance regularized loss that is non-convex, we optimize a distributionally robust bag level likelihood as its convex surrogate. The robust bag likelihood provides a good approximation of the variance based MIL loss with a strong theoretical guarantee. It also automatically balances bias and variance, making it effective to identify the potentially positive instances to support active sampling. The robust bag likelihood can be naturally integrated with a deep architecture to support deep model training using mini-batches of positive-negative bag pairs. Finally, a novel P-F sampling function is developed that combines a probability vector and predicted instance scores, obtained by optimizing the robust bag likelihood. By leveraging the key MIL assumption, the sampling function can explore the most challenging bags and effectively detect their positive instances for annotation, which significantly improves the instance-level prediction. Experiments conducted over multiple real-world datasets clearly demonstrate the state-of-the-art instance-level prediction achieved by the proposed model.