Record linkage is the process of identifying records that refer to the same entities from different data sources. While most research efforts are concerned with linking individual records, new approaches have recently been proposed to link groups of records across databases. Group record linkage aims to determine if two groups of records in two databases refer to the same entity or not. One application where group record linkage is of high importance is the linking of census data that contain household information across time. In this paper we propose a novel method to group record linkage based on multiple instance learning. Our method treats group links as bags and individual record links as instances. We extend multiple instance learning from bag to instance classification to reconstruct bags from candidate instances. The classified bag and instance samples lead to a significant reduction in multiple group links, thereby improving the overall quality of linked data. We evaluate our method with both synthetic data and real historical census data.