arXiv subjects

Seydou Keita

Publications and source records attributed to Seydou Keita.

4 recordsLinked to original sources

arXiv2024

Hypothesis testing for general network models

The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in literature usually assume that the underlying structure is a known model. In practice, however, the true model is usually unknown, and network learning procedures based on these methods may suffer from model misspecification. To handle this issue, based on the random matrix theory, we first give a spectral property of the normalized adjacency matrix under a mild condition. Further, we establish a general goodness-of-fit test procedure for the unweight and undirected network. We prove that the null distribution of the proposed statistic converges in distribution to the standard normal distribution. Theoretically, this testing procedure is suitable for nearly all popular network models, such as stochastic block models, and latent space models. Further, we apply the proposed method to the degree-corrected mixed membership model and give a sequential estimator of the number of communities. Both simulation studies and real-world data examples indicate that the proposed method works well.

stat.ME↗

arXiv2023

Extreme eigenvalues of principal minors of random matrix with moment conditions

Let $\bm{x}_1,\cdots,\bm{x}_n$ be a random sample of size $n$ from a $p$-dimensional population distribution, where $p=p(n)\rightarrow\infty$. Consider a symmetric matrix $W=X^\top X$ with parameters $n$ and $p$, where $X=(\bm{x}_1,\cdots,\bm{x}_n)^\top$. In this paper, motivated by model selection theory in high-dimensional statistics, we mainly investigate the asymptotic behavior of the eigenvalues of the principal minors of the random matrix $W$. For the Gaussian case, under a simple condition that $m=o(n/\log p)$, we obtain the asymptotic results on maxima and minima of the eigenvalues of all $m\times m$ principal minors of $W$. We also extend our results to general distributions with some moment conditions. Moreover, we gain the asymptotic results of the extreme eigenvalues of the principal minors in the case of the real Wigner matrix. Finally, similar results for the maxima and minima of the eigenvalues of all the principal minors with a size smaller than or equal to $m$ are also given.

math.PR↗

arXiv2022

Two-Sample Test for Stochastic Block Models via Maximum Entry-wise Deviation

The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has been a largely under-explored domain, and too little work has been devoted to it. In this article, based on the maximum entry--wise deviation of the two centered and rescaled adjacency matrices, we propose a novel test statistic to test two samples of stochastic block models. We prove that the null distribution of the proposed test statistic converges in distribution to a Gumbel distribution, and we show the change of the two samples from stochastic block models can be tested via the proposed method. Then, we show that the proposed test has an asymptotic power guarantee against alternative models. One noticeable advantage of the proposed test statistic is that the number of communities can be allowed to grow linearly up to a logarithmic factor. Further, we extend the proposed method to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.

stat.ME↗

arXiv2022

Two-Sample Test for Stochastic Block Models via the Largest Singular Value

The stochastic block model is widely used for detecting community structures in network data. However, the research interest of much literature focuses on the study of one sample of stochastic block models. How to detect the difference of the community structures is a less studied issue for stochastic block models. In this article, we propose a novel test statistic based on the largest singular value of a residual matrix obtained by subtracting the geometric mean of two estimated block mean effects from the sum of two observed adjacency matrices. We prove that the null distribution of the proposed test statistic converges in distribution to the Tracy-Widom distribution with index 1, and we show the difference between the two samples for stochastic block models can be tested via the proposed method. Further, we show that the proposed test has asymptotic power guarantee against alternative models. Both simulation studies and real-world data examples indicate that the proposed method works well.

stat.ME↗