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Detection of vaccine adverse events is crucial to the discovery and improvement of problematic vaccines. To achieve it, traditionally formal reporting systems like VAERS support accurate but delayed surveillance, while recently social media have been mined for timely but noisy observations. Utilizing the complementary strengths of these two domains to boost the detection performance looks good but cannot be effectively achieved by existing methods due to significant differences between their data characteristics, including: 1) formal language v.s. informal language, 2) single-message per user v.s. multi-messages per user, and 3) one class v.s. binary class. In this paper, we propose a novel generic framework named Multi-instance Domain Adaptation (MIDA) to maximize the synergy between these two domains in the vaccine adverse event detection task for social media users. Specifically, we propose a generalized Maximum Mean Discrepancy (MMD) criterion to measure the semantic distances between the heterogeneous messages from these two domains in their shared latent semantic space. Then these message-level generalized MMD distances are synthesized by newly proposed mixed instance kernels to user-level distances. We finally minimize the distances between the samples of the partially-matched classes from these two domains. In order to solve the non-convex optimization problem, an efficient Alternating Direction Method of Multipliers (ADMM) based algorithm combined with the Convex-Concave Procedure (CCP) is developed to optimize parameters accurately. Extensive experiments demonstrated that our model outperformed the baselines by a large margin under six metrics. Case studies showed that formal reports and extracted adverse-relevant tweets by MIDA shared a similarity of keyword and description patterns.