In many real-world tasks, a canonical 'big data' problem is created by combining data from several individual groups or domains. Because test data will likely come from a new group of data, we want to utilize the grouped structure of our training data to enforce generalization between groups of data, not just individual samples. This can be viewed as a multiple-domain generalization problem. Specifically, the goal is to encourage generalization between previously seen labeled source data from multiple domains and unlabeled target domain data. To address this challenge, we introduce Domain-Specific Filter Group (DSFG), where each training domain has a unique filter group and each test data point is predicted by a weighted sum over the outputs of different domain filters. A separate neural network learns to estimate the appropriate filter group weights through a meta-learning strategy. Empirically, experiments on three benchmark datasets demonstrate improved performance compared to current state-of-the-art approaches.