The centrality in a network is often used to measure nodes' importance and model network effects on a certain outcome. Empirical studies widely adopt a two-stage procedure, which first estimates the centrality from the observed noisy network and then infers the network effect from the estimated centrality, even though it lacks theoretical understanding. We propose a unified modeling framework to study the properties of centrality estimation and inference and the subsequent network regression analysis with noisy network observations. Furthermore, we propose a supervised centrality estimation methodology, which aims to simultaneously estimate both centrality and network effect. We showcase the advantages of our method compared with the two-stage method both theoretically and numerically via extensive simulations and a case study in predicting currency risk premiums from the global trade network. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Bayesian computation often scales poorly with increasing data size, motivating developments such as divide-and-conquer approaches for scalable inference. These methods partition the data into subsets, perform parallel inference on each subset, and aggregate the results into a single posterior. Appealing theoretical properties and practical performance have been demonstrated for independent data; however, methods for dependent data remain challenging. Existing methods rely on ad hoc approximations with limited theoretical guarantees that lead to potentially poor accuracy in practice. Here, we focus on time-series data and propose a simple, scalable divide-and-conquer method for dependent time series, with theoretically rigorous accuracy guarantees. Simulation studies and real-data examples are used to empirically verify the effectiveness of our approach. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Transfer learning is a critical technique that enables the application of knowledge gained from existing tasks or domains to improve performance on a new one, reducing the need for extensive data and training in each new context. Many existing transfer learning methods rely on leveraging information from source populations closely resembling the target population. However, this approach often overlooks valuable knowledge that may be present in different yet potentially related auxiliary samples. When dealing with a limited amount of target data and multiple source data, we introduce a novel approach, Guided Adversarial Robust Transfer (GART) learning, that breaks free from strict similarity constraints. GART is designed to optimize the most adversarial loss with respect to a collection of source mixture distributions that guarantee excellent prediction performances for the target data. We establish the closed form of the population GART and show that the GART estimator achieves a faster convergence rate than the model fitted with the target data. Our simulation studies suggest that GART outperforms existing transfer learning methods, attaining higher robustness and accuracy. We highlight GART's predictiveness and robustness by applying it to form genetic prediction models of high-density lipoprotein cholesterol using multi-institutional biobank-linked electronic health records data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
