Network Estimation by Mixing: Adaptivity and More

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suffers from model misspecification or relies on additional model selection procedures that are not well understood in theory and can potentially be unstable in practice. To address this difficulty, we propose a mixing strategy that leverages available arbitrary models to improve their individual performances. The proposed method is computationally efficient and almost tuning-free; thus, it can be used as an off-the-shelf method for network modeling. We show that the proposed method performs equally well as the oracle estimate when the true model is included as individual candidates. More importantly, the method remains robust and outperforms all current estimates even when the models are misspecified. Extensive simulation examples are used to verify the advantage of the proposed mixing method. Evaluation of link prediction performance on 385 real-world networks from six domains also demonstrates the universal competitiveness of the mixing method across multiple domains.