arXiv subjects

Runbing Zheng

Publications and source records attributed to Runbing Zheng.

6 recordsLinked to original sources

arXiv2025

A functional tensor model for dynamic multilayer networks with common invariant subspaces and the RKHS estimation

Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However, exploration of analytical methods for these complex data structures remains limited. We propose a functional tensor-based model for dynamic multilayer networks, with the key feature of capturing the shared structure among common vertices across all layers, while simultaneously accommodating smoothly varying temporal dynamics and layer-specific heterogeneity. The proposed model and its embeddings can be applied to various downstream network inference tasks, including dimensionality reduction, vertex community detection, analysis of network evolution periodicity, visualization of dynamic network evolution patterns, and evaluation of inter-layer similarity. We provide an estimation algorithm based on functional tensor Tucker decomposition and the reproducing kernel Hilbert space framework, with an effective initialization strategy to improve computational efficiency. The estimation procedure can be extended to address more generalized functional tensor problems, as well as to handle missing data or unaligned observations. We validate our method on simulated data and two real-world cases: the dynamic Citi Bike trip network and an international food trade dynamic multilayer network, with each layer corresponding to a different product.

stat.ME↗

arXiv2025

Detection and estimation of vertex-wise latent position shifts across networks

Pairwise network comparison is essential for various applications, including neuroscience, disease research, and dynamic network analysis. While existing literature primarily focuses on comparing entire network structures, we address a vertex-wise comparison problem where two random networks share the same set of vertices but allow for structural variations in some vertices, enabling a more detailed and flexible analysis of network differences. In our framework, some vertices retain their latent positions between networks, while others undergo shifts. To identify the shifted and unshifted vertices and estimate their latent position shifts, we propose a method that first derives vertex embeddings in a low-rank Euclidean space for each network, then aligns these estimated vertex latent positions into a common space to resolve potential non-identifiability, and finally tests whether each vertex is shifted or not and estimates the vertex shifts. Our theoretical results establish the test statistic for the algorithms, guide parameter selection, and provide performance guarantees. Simulation studies and real data applications, including a case-control study in disease research and dynamic network analysis, demonstrate that the proposed algorithms are both computationally efficient and effective in extracting meaningful insights from network comparisons.

stat.ME↗

arXiv2024

Dynamic networks clustering via mirror distance

The classification of different patterns of network evolution, for example in brain connectomes or social networks, is a key problem in network inference and modern data science. Building on the notion of a network's Euclidean mirror, which captures its evolution as a curve in Euclidean space, we develop the Dynamic Network Clustering through Mirror Distance (DNCMD), an algorithm for clustering dynamic networks based on a distance measure between their associated mirrors. We provide theoretical guarantees for DNCMD to achieve exact recovery of distinct evolutionary patterns for latent position random networks both when underlying vertex features change deterministically and when they follow a stochastic process. We validate our theoretical results through numerical simulations and demonstrate the application of DNCMD to understand edge functions in Drosophila larval connectome data, as well as to analyze temporal patterns in dynamic trade networks.

stat.ME↗

arXiv2024

Chain-linked multiple matrix integration via embedding alignment

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where only a few noisy submatrices representing (overlapping) parts of the full matrix are available. We propose the Chain-linked Multiple Matrix Integration (CMMI) procedure to efficiently combine the information that can be extracted from these individual noisy submatrices. CMMI begins by deriving entity embeddings for each observed submatrix, then aligns these embeddings using overlapping entities between pairs of submatrices, and finally aggregates them to reconstruct the entire matrix of interest. We establish, under mild regularity conditions, entrywise error bounds and normal approximations for the CMMI estimates. Simulation studies and real data applications show that CMMI is computationally efficient and effective in recovering the full matrix, even when overlaps between the observed submatrices are minimal.

stat.ME↗

arXiv2022

Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA

Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces $U^{(i)}$ consist of a shared subspace $U_c$ and individual subspaces $U_s^{(i)}$. We consider a distributed estimation procedure that first obtains $\hat U^{(i)}$ as the leading singular vectors for each observed noisy matrix, then computes the leading left singular vectors of the concatenated matrix $[\hat U^{(1)}|\hat U^{(2)}|\dots|\hat U^{(m)}]$ as $\hat U_c$, and finally computes the leading singular vectors of the projection of each $\hat U^{(i)}$ onto the orthogonal complement of $\hat U_c$ as $\hat U_s^{(i)}$. In this paper, we provide a framework for deriving limit results for such distributed estimation procedures, including expansions of estimation errors in both common and individual subspaces and their asymptotically normal approximations. We apply this framework specifically to (1) parameter estimation for multiple heterogeneous random graphs with shared subspaces, and (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structures. Leveraging these results, we also consider a two-sample test for the null hypothesis that a pair of random graphs have the same edge probabilities, and present a test statistic whose limiting distribution converges to a central (resp., non-central) $\chi^2$ distribution under the null (resp., local alternative) hypothesis.

math.ST↗

arXiv2022

Vertex nomination between graphs via spectral embedding and quadratic programming

Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the list. An important variant of this problem is vertex nomination in the multi-graphs setting. Given two graphs $G_1, G_2$ with common vertices and a vertex of interest $x \in G_1$, we wish to rank the vertices of $G_2$ such that the vertices most similar to $x$ are ranked at the top of the list. The current paper addresses this problem and proposes a method that first applies adjacency spectral graph embedding to embed the graphs into a common Euclidean space, and then solves a penalized linear assignment problem to obtain the nomination lists. Since the spectral embedding of the graphs are only unique up to orthogonal transformations, we present two approaches to eliminate this potential non-identifiability. One approach is based on orthogonal Procrustes and is applicable when there are enough vertices with known correspondence between the two graphs. Another approach uses adaptive point set registration and is applicable when there are few or no vertices with known correspondence. We show that our nomination scheme leads to accurate nomination under a generative model for pairs of random graphs that are approximately low-rank and possibly with pairwise edge correlations. We illustrate our algorithm's performance through simulation studies on synthetic data as well as analysis of a high-school friendship network and analysis of transition rates between web pages on the Bing search engine.

cs.SI↗