arXiv subjects

Yaoming Zhen

Publications and source records attributed to Yaoming Zhen.

7 recordsLinked to original sources

arXiv2026

A Probabilistic Model for Zero-Inflated Count Tensors with Structured Latent Representations

We propose a unified probabilistic framework for modeling high-dimensional count tensors with excess zeros. Such data arise naturally in a variety of applications, including single-cell Hi-C experiments, where observations are represented as a third-order tensor indexed by genomic locus pairs and cells. We develop a zero-inflated Poisson tensor model that captures the underlying latent structure through a low-rank tensor decomposition. For single-cell Hi-C data, the proposed framework further accommodates heterogeneous cell populations through latent cluster structure and exploits the ordered nature of genomic loci via smooth latent representations. We develop a likelihood-based estimation procedure together with a Bayes-optimal classifier for distinguishing structural zeros from technical zeros, enabling principled false-zero detection, imputation, and uncertainty quantification. Theoretically, we establish identifiability of the proposed model and consistency of the proposed estimators. Simulation studies and analyses of single-cell Hi-C data demonstrate improved performance in false-zero detection, latent structure recovery, and clustering.

stat.ME↗

arXiv2025

Probabilistic PCA on tensors

In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to have Tucker structure, yielding a probabilistic multilinear PCA model that enables uncertainty quantification and naturally accommodates multiple, possibly heterogeneous, tensor observations. We develop the associated theory: we establish identifiability of the loadings and noise variance and show that-unlike in matrix PPCA-the maximum likelihood estimator (MLE) exists even from a single tensor sample. We then study two estimators. First, we consider the MLE and propose an expectation maximization (EM) algorithm to compute it. Second, exploiting that Tucker maps correspond to rank-one elements after a Kronecker lifting, we design a computationally efficient estimator for which we provide provable finite-sample guarantees. Together, these results provide a coherent probabilistic framework and practical algorithms for learning from tensor-valued data.

math.ST↗

arXiv2024

Network-based Neighborhood regression

Given the ubiquity of modularity in biological systems, module-level regulation analysis is vital for understanding biological systems across various levels and their dynamics. Current statistical analysis on biological modules predominantly focuses on either detecting the functional modules in biological networks or sub-group regression on the biological features without using the network data. This paper proposes a novel network-based neighborhood regression framework whose regression functions depend on both the global community-level information and local connectivity structures among entities. An efficient community-wise least square optimization approach is developed to uncover the strength of regulation among the network modules while enabling asymptotic inference. With random graph theory, we derive non-asymptotic estimation error bounds for the proposed estimator, achieving exact minimax optimality. Unlike the root-n consistency typical in canonical linear regression, our model exhibits linear consistency in the number of nodes n, highlighting the advantage of incorporating neighborhood information. The effectiveness of the proposed framework is further supported by extensive numerical experiments. Application to whole-exome sequencing and RNA-sequencing Autism datasets demonstrates the usage of the proposed method in identifying the association between the gene modules of genetic variations and the gene modules of genomic differential expressions.

stat.ME↗

arXiv2024

Consistent community detection in multi-layer networks with heterogeneous differential privacy

As network data has become increasingly prevalent, a substantial amount of attention has been paid to the privacy issue in publishing network data. One of the critical challenges for data publishers is to preserve the topological structures of the original network while protecting sensitive information. In this paper, we propose a personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference. It can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable. Theoretically, we establish the consistency of community detection in the privatized multi-layer network and show that better privacy protection of edges can be obtained for a proportion of nodes while allowing other nodes to give up their privacy. Furthermore, the advantage of the proposed personalized edge-flipping mechanism is also supported by its numerical performance on various synthetic networks and a real-life multi-layer network.

stat.ME↗

arXiv2024

Tensorized Hypergraph Neural Networks

Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph connectivity patterns, which ignores important high-order information. To address this issue, we propose a novel adjacency-tensor-based \textbf{T}ensorized \textbf{H}ypergraph \textbf{N}eural \textbf{N}etwork (THNN). THNN is a faithful hypergraph modeling framework through high-order outer product feature message passing and is a natural tensor extension of the adjacency-matrix-based graph neural networks. The proposed THNN is equivalent to a high-order polynomial regression scheme, which enables THNN with the ability to efficiently extract high-order information from uniform hypergraphs. Moreover, in consideration of the exponential complexity of directly processing high-order outer product features, we propose using a partially symmetric CP decomposition approach to reduce model complexity to a linear degree. Additionally, we propose two simple yet effective extensions of our method for non-uniform hypergraphs commonly found in real-world applications. Results from experiments on two widely used {hypergraph datasets for 3-D visual object classification} show the model's promising performance.

cs.AI↗

arXiv2022

Transfer learning for tensor Gaussian graphical models

Tensor Gaussian graphical models (GGMs), interpreting conditional independence structures within tensor data, have important applications in numerous areas. Yet, the available tensor data in one single study is often limited due to high acquisition costs. Although relevant studies can provide additional data, it remains an open question how to pool such heterogeneous data. In this paper, we propose a transfer learning framework for tensor GGMs, which takes full advantage of informative auxiliary domains even when non-informative auxiliary domains are present, benefiting from the carefully designed data-adaptive weights. Our theoretical analysis shows substantial improvement of estimation errors and variable selection consistency on the target domain under much relaxed conditions, by leveraging information from auxiliary domains. Extensive numerical experiments are conducted on both synthetic tensor graphs and a brain functional connectivity network data, which demonstrates the satisfactory performance of the proposed method.

stat.ML↗

arXiv2021

Community Detection in General Hypergraph via Graph Embedding

Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null vertex to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multi-hypergraph in a low-dimensional vector space such that vertices within the same community are close to each other. The resultant optimization task can be efficiently tackled by an alternative updating scheme. The asymptotic consistencies of the proposed method are established in terms of both community detection and hypergraph estimation, which are also supported by numerical experiments on some synthetic and real-life hypergraph networks.

stat.ML↗