Towards Comprehensive Information-theoretic Multi-view Learning

Information theory has inspired numerous advancements in multi-view learning. Most multi-view methods incorporating information-theoretic principles rely an assumption called multi-view redundancy which states that common information between views is necessary and sufficient for down-stream tasks. This assumption emphasizes the importance of common information for prediction, but inherently ignores the potential of unique information in each view that could be predictive to the task. In this paper, we propose a comprehensive information-theoretic multi-view learning framework named CIML, which discards the assumption of multi-view redundancy. Specifically, CIML considers the potential predictive capabilities of both common and unique information based on information theory. First, the common representation learning maximizes Gacs-Korner common information to extract shared features and then compresses this information to learn task-relevant representations based on the Information Bottleneck (IB). For unique representation learning, IB is employed to achieve the most compressed unique representation for each view while simultaneously minimizing the mutual information between unique and common representations, as well as among different unique representations. Importantly, we theoretically prove that the learned joint representation is predictively sufficient for the downstream task. Extensive experimental results have demonstrated the superiority of our model over several state-of-art methods. The code is released on CIML.