Bo Zhang

Social network platforms today generate vast amounts of data, including network structures and a large number of user-defined tags, which reflect users' interests. The dimensionality of these personalized tags can be ultra-high, posing challenges for model analysis in targeted preference analysis. Traditional categorical feature screening methods overlook the network structure, which can lead to incorrect feature set and suboptimal prediction accuracy. This study focuses on feature screening for network-involved preference analysis based on ultra-high-dimensional categorical tags. We introduce the concepts of self-related features and network-related features, defined as those directly related to the response and those related to the network structure, respectively. We then propose a pseudo-likelihood ratio feature screening procedure that identifies both types of features. Theoretical properties of this procedure under different scenarios are thoroughly investigated. Extensive simulations and real data analysis on Sina Weibo validate our findings.

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development in matrix completion, the potential relationship between observed data and missing indicators has largely been overlooked. To address this gap, we propose a joint modeling framework for the observed data and missing indicators within the context of a generalized factor model and derive the asymptotic limit distribution of the estimators. Furthermore, to tackle the rank estimation problem for model specification, we employ matrix nonconvex penalty regularization and establish nonasymptotic probability guarantees for the Oracle property. The theoretical results are validated through extensive simulation studies and real-world data analysis, demonstrating the effectiveness of the proposed method.

This paper proposes a distributed pseudo-likelihood method (DPL) to conveniently identify the community structure of large-scale networks. Specifically, we first propose a block-wise splitting method to divide large-scale network data into several subnetworks and distribute them among multiple workers. For simplicity, we assume the classical stochastic block model. Then, the DPL algorithm is iteratively implemented for the distributed optimization of the sum of the local pseudo-likelihood functions. At each iteration, the worker updates its local community labels and communicates with the master. The master then broadcasts the combined estimator to each worker for the new iterative steps. Based on the distributed system, DPL significantly reduces the computational complexity of the traditional pseudo-likelihood method using a single machine. Furthermore, to ensure statistical accuracy, we theoretically discuss the requirements of the worker sample size. Moreover, we extend the DPL method to estimate degree-corrected stochastic block models. The superior performance of the proposed distributed algorithm is demonstrated through extensive numerical studies and real data analysis.

Volatility modeling is a challenging topic in high-frequency financial data analysis. In this paper, we propose a novel Bayesian framework for modeling and forecasting spot volatility by assuming a latent GARCH structure is embedded into the volatility process at a series of unobserved “anchor” time points, which can well describe the evolving volatility of financial assets in high frequency. We introduce an ideal approximation of latent anchors, which shares similar posterior distribution with true latent anchors. Furthermore, we develop an efficient two-stage inference framework with its corresponding two-stage MCMC sampling algorithm. The simulation study and real data analysis both show our method outperforms the existing alternatives in explanation of latent anchors and the estimation and forecasting of volatility.