arXiv subjects

Wenqing Su

Publications and source records attributed to Wenqing Su.

6 recordsLinked to original sources

arXiv2026

Multilayer-Dynamic Network Clustering with Application to World Trade Data

The rapid development of global economic integration has made international trade increasingly dynamic and interdependent. The real-world trade data sets, such as the FAO dataset, can be naturally represented as a \emph{multilayer-dynamic network} where countries are treated as nodes, trade flows between countries are represented by edges, and different products correspond to different layers. Therefore, an important problem is how to identify evolving community structures in the multilayer-dynamic trade network. However, most existing methods are designed for static multilayer networks or single-layer dynamic networks, leaving the community detection in multilayer-dynamic networks largely unexplored. Motivated by this problem, we study community detection in multilayer-dynamic networks, allowing the community structure to vary across both layers and time. We propose a novel method, \emph{MuDySC} (Multilayer-Dynamic Spectral Clustering), which smooths the eigenspace projection matrices across adjacent time points and across layers at the same time point. We develop an efficient alternating iterative algorithm for solving the resulting optimization problem and establish its convergence to the global optimum under mild conditions. We further apply MuDySC to the FAO data. The analysis reveals clear asymmetry between export and import community structures and highlights both persistent and shifting trade positions of major countries.

stat.AP↗

arXiv2025

High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression

Continual learning is motivated by the need to adapt to real-world dynamics in tasks and data distribution while mitigating catastrophic forgetting. Despite significant advances in continual learning techniques, the theoretical understanding of their generalization performance lags behind. This paper examines the theoretical properties of continual ridge regression in high-dimensional linear models, where the dimension is proportional to the sample size in each task. Using random matrix theory, we derive exact expressions of the asymptotic prediction risk, thereby enabling the characterization of three evaluation metrics of generalization performance in continual learning: average risk, backward transfer, and forward transfer. Furthermore, we present the theoretical risk curves to illustrate the trends in these evaluation metrics throughout the continual learning process. Our analysis reveals several intriguing phenomena in the risk curves, demonstrating how model specifications influence the generalization performance. Simulation studies are conducted to validate our theoretical findings.

stat.ME↗

arXiv2025

Randomized Spectral Clustering for Large-Scale Multi-Layer Networks

Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized spectral clustering algorithm for community detection of multi-layer networks. We first utilize the random sampling strategy to sparsify the adjacency matrix of each layer. Then we use the random projection strategy to accelerate the eigen-decomposition of the sum-of-squared sparsified adjacency matrices of all layers. The communities are finally obtained via the k-means of the eigenvectors. The algorithm not only has low time complexity but also saves the storage space. Theoretically, we study the misclassification error rate of the proposed algorithm under the multi-layer stochastic block models, which shows that the randomization does not deteriorate the error bound under certain conditions. Numerical studies on multi-layer networks with millions of nodes show the superior efficiency of the proposed algorithm, which achieves clustering results rapidly. A new R package called MLRclust is developed and made available to the public.

stat.CO↗

arXiv2024

Limit Results for Estimation of Connectivity Matrix in Multi-layer Stochastic Block Models

Multi-layer networks arise naturally in various domains including biology, finance and sociology, among others. The multi-layer stochastic block model (multi-layer SBM) is commonly used for community detection in the multi-layer networks. Most of current literature focuses on statistical consistency of community detection methods under multi-layer SBMs. However, the asymptotic distributional properties are also indispensable which play an important role in statistical inference. In this work, we aim to study the estimation and asymptotic properties of the layer-wise scaled connectivity matrices in the multi-layer SBMs. We develop a novel and efficient method to estimate the scaled connectivity matrices. Under the multi-layer SBM and its variant multi-layer degree-corrected SBM, we establish the asymptotic normality of the estimated matrices under mild conditions, which can be used for interval estimation and hypothesis testing. Simulations show the superior performance of proposed method over existing methods in two considered statistical inference tasks. We also apply the method to a real dataset and obtain interpretable results.

math.ST↗

arXiv2024

Spectral co-Clustering in Multi-layer Directed Networks

Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly limited to undirected relations. However, direct relations are more common and may introduce extra information. This study focuses on community detection (or clustering) in multi-layer directed networks. To take into account the asymmetry, a novel spectral-co-clustering-based algorithm is developed to detect co-clusters, which capture the sending patterns and receiving patterns of nodes, respectively. Specifically, the eigendecomposition of the debiased sum of Gram matrices over the layer-wise adjacency matrices is computed, followed by the k-means, where the sum of Gram matrices is used to avoid possible cancellation of clusters caused by direct summation. Theoretical analysis of the algorithm under the multi-layer stochastic co-block model is provided, where the common assumption that the cluster number is coupled with the rank of the model is relaxed. After a systematic analysis of the eigenvectors of the population version algorithm, the misclassification rates are derived, which show that multi-layers would bring benefits to the clustering performance. The experimental results of simulated data corroborate the theoretical predictions, and the analysis of a real-world trade network dataset provides interpretable results.

math.ST↗

arXiv2019

Differentially Private Precision Matrix Estimation

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. The theoretical results and empirical results that show the utility of the proposed methods are also provided.

stat.ML↗