arXiv subjects

Huan Qing

Publications and source records attributed to Huan Qing.

3 recordsLinked to original sources

arXiv2026

Directed mixed membership stochastic blockmodel

Mixed membership modeling for undirected networks has been extensively explored in network science over the past few years. Despite the substantial progress made for undirected cases, handling mixed membership structures in directed networks continues to pose substantial difficulties. To address this gap, we introduce the Directed Mixed Membership Stochastic Blockmodel (DiMMSB), a novel framework tailored for directed networks with overlapping communities. A key feature of DiMMSB is its ability to treat the row and column nodes of the adjacency matrix as distinct entities, each potentially following its own community organization. Building on this model, we develop DiSP, an efficient spectral procedure to estimate mixed memberships for both sets of nodes. Through delicate analysis, we derive node-specific error bounds of DiSP under mild sparsity conditions. Simulation results support the theoretical results, demonstrating that DiSP achieves lower error rates and faster computation than its competitor. Moreover, applications to real data highlight DiSP's effectiveness in uncovering asymmetric structural patterns.

stat.ML↗

arXiv2026

Latent class analysis by regularized spectral clustering

The latent class model is a highly effective tool in the analysis of categorical data from social, psychological, and behavioral sciences, where populations often share hidden common characteristics. In this article, we introduce two new algorithms for estimating the parameters of a latent class model for ordered categorical data with polytomous responses. These algorithms are based on a newly defined regularized Laplacian matrix derived from the response matrix. We provide theoretical convergence rates for our algorithms by considering a sparsity parameter and demonstrate that under a mild condition on data's sparsity, our algorithms yield consistent latent class analysis. Furthermore, we introduce a metric to assess the strength of latent class analysis and develop procedures based on this metric to determine the optimal number of latent classes for real-world ordered categorical data. Extensive simulation experiments demonstrate the efficiency and accuracy of our algorithms, and we demonstrate their practical application to real-world ordered categorical data with promising results.

cs.LG↗

arXiv2026

A Subsampled Davis-Kahan Bound for Large-Scale Eigenspace Estimation

The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symmetric matrix and its perturbation. However, when the matrix dimension is large, computing leading eigenvectors is computationally expensive, limiting the practical use of spectral methods in modern large-scale applications. This paper addresses this problem by proposing an independent Bernoulli sampling scheme and proves that the leading left singular vectors of the subsampled matrix faithfully approximate the target subspace of a low-rank symmetric matrix. Our main result is a subsampled Davis-Kahan bound that gives an explicit error bound depending directly on the sampling probability. The bound reveals the trade-off: the computational cost scales linearly with the sampling probability, while the statistical error scales as the inverse square root of the sampling probability. Our result thus extends the Davis-Kahan theorem to the subsampled setting, enabling scalable spectral analysis of large-scale symmetric matrices.

stat.ML↗