arXiv subjects

Zhenggang Wang

Publications and source records attributed to Zhenggang Wang.

7 recordsLinked to original sources

arXiv2026

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications

Cycle count statistics are fundamental tools in statistics and engineering, with applications in motif counting, channel coding, and statistical inference of network and matrix data. However, how to compute high-order cycle count statistics efficiently is still an open problem. In this paper, we aim to derive Computationally Efficient Equivalent Forms (CEEF) for cycle count statistics of any given order, where we express each cycle count statistic equivalently as a linear combination of finitely many terms. Using the CEEF, we provide a much more efficient way to compute the cycle count statistics. The CEEF problem has no known general solution and requires delicate combinatorial arguments together with extensive calculations. While this task is hard to accomplish by humans alone, it provides an ideal setting in which Artificial Intelligence (AI) can be useful. We solve the problem by combining several theorems we derive with powerful coding skills of modern AI systems. Our results leverage graph-theoretic arguments and yield new formulas for general cases that were previously unknown. We find that, although AI cannot solve the problem independently, it becomes highly effective when guided by humans through theorems we derive as well as a clear derivation strategy, step-by-step instructions, and carefully-written prompts. We consider several statistical applications, including spiked matrix testing, estimation of weak spike eigenvalues, and pairwise network comparison. For each problem, we demonstrate that optimal statistical performance is achieved by using high-order cycle count statistics, and our CEEF formulas make their computation feasible on large-scale data sets.

cs.CL↗

arXiv2026

Alignment and matching tests for high-dimensional tensor signals via tensor contraction

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit long-range dependence, which makes the analysis of the matrix challenging, involved, and distinct from standard random matrix theory. Our approach provides a novel framework for addressing hypothesis testing problems in the context of high-dimensional tensor signals.

stat.ME↗

arXiv2025

Fair Bayesian Data Selection via Generalized Discrepancy Measures

Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs, limited scalability, and poor generalization. To address these challenges, we propose a Bayesian data selection framework that ensures fairness by aligning group-specific posterior distributions of model parameters and sample weights with a shared central distribution. Our framework supports flexible alignment via various distributional discrepancy measures, including Wasserstein distance, maximum mean discrepancy, and $f$-divergence, allowing geometry-aware control without imposing explicit fairness constraints. This data-centric approach mitigates group-specific biases in training data and improves fairness in downstream tasks, with theoretical guarantees. Experiments on benchmark datasets show that our method consistently outperforms existing data selection and model-based fairness methods in both fairness and accuracy.

cs.LG↗

arXiv2023

Two sample test for covariance matrices in ultra-high dimension

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology relies on a data splitting procedure and a comparison of a set of well selected eigenvalues of the sample covariance matrices on the split data sets. Compared to the existing methods, our methodology is adaptive in the sense that (i). it does not require specific assumption (e.g., comparable or balancing, etc.) on the sizes of two samples; (ii). it does not need quantitative or structural assumptions of the population covariance matrices; (iii). it does not need the parametric distributions or the detailed knowledge of the moments of the two populations. Theoretically, we establish the asymptotic distributions of the statistics used in our method and conduct the power analysis. We justify that our method is powerful under very weak alternatives. We conduct extensive numerical simulations and show that our method significantly outperforms the existing ones both in terms of size and power. Analysis of two real data sets is also carried out to demonstrate the usefulness and superior performance of our proposed methodology. An $\texttt{R}$ package $\texttt{UHDtst}$ is developed for easy implementation of our proposed methodology.

stat.ME↗

arXiv2023

Global and local CLTs for linear spectral statistics of general sample covariance matrices when the dimension is much larger than the sample size with applications

In this paper, under the assumption that the dimension is much larger than the sample size, i.e., $p \asymp n^α, α>1,$ we consider the (unnormalized) sample covariance matrices $Q = Σ^{1/2} XX^*Σ^{1/2}$, where $X=(x_{ij})$ is a $p \times n$ random matrix with centered i.i.d entries whose variances are $(pn)^{-1/2}$, and $Σ$ is the deterministic population covariance matrix. We establish two classes of central limit theorems (CLTs) for the linear spectral statistics (LSS) for $Q,$ the global CLTs on the macroscopic scales and the local CLTs on the mesoscopic scales. We prove that the LSS converge to some Gaussian processes whose mean and covariance functions depending on $Σ$, the ratio $p/n$ and the test functions, can be identified explicitly on both macroscopic and mesoscopic scales. We also show that even though the global CLTs depend on the fourth cumulant of $x_{ij},$ the local CLTs do not. Based on these results, we propose two classes of statistics for testing the structures of $Σ,$ the global statistics and the local statistics, and analyze their superior power under general local alternatives. To our best knowledge, the local LSS testing statistics which do not rely on the fourth moment of $x_{ij},$ is used for the first time in hypothesis testing while the literature mostly uses the global statistics and requires the prior knowledge of the fourth cumulant. Numerical simulations also confirm the accuracy and powerfulness of our proposed statistics and illustrate better performance compared to the existing methods in the literature.

math.ST↗

arXiv2021

Central limit theorem for linear spectral statistics of block-Wigner-type matrices

Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with certain block structures, and establish a CLT for the corresponding linear spectral statistics via the large-deviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be block-Wigner-type matrices. Further, we show that for certain estimator of such renormalized adjacency matrices, which will be no longer Wigner-type but share long-range non-decaying weak correlations among the entries, the linear spectral statistics of such estimators will still share the same limiting behavior as those of the block-Wigner-type matrices, thus enabling hypothesis testing about stochastic block model.

math.PR↗

arXiv2009

Structure Profile by a Model of Precipitation

The organizational structure of a network is investigated with a simulated precipitation model which does not make use of prior knowledge about the community structure of the network. The result is presented as a structure profile through which various definitions of communities can be applied for specific applications. The simulated precipitation model performs the grouping of nodes so that nodes belonging to the same 'community' automatically aggregate, thereby revealing regions of the adjacency matrix with denser interconnections. The process is analogous to massive particles precipitating towards the lower potential layer. Without loss of the infrastructure information, a community structure profile of a network can be obtained as the ground state of the Hamiltonian. The method is also applicable to directed and weighted networks.

cond-mat.mtrl-sci↗