報告人：劉一鳴 副教授
報告題目：Identify the source of spikes: factor or mixture?
報告時間：2025年11月18日（周二）11:00-12:00
報告地點：云龍校區6號樓304會議室
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
劉一鳴，暨南大學經濟學院副教授。目前主要研究方向：機器學習、隨機矩陣、經驗似然及其相關應用等。主持國自然科學基金，廣東省自然科學面上基金等項目。至今已在IEEE Transactions on Information Theory, Bernoulli, Statistica Sinica, Scandinavian Journal of Statistics等雜志發表論文15篇。
報告摘要：
We consider the problem of identifying the pattern of latent variables in high-dimensional linear latent variable models, which can also be interpreted as determining the source of spiked singular values in the data matrix. Specifically, we test whether the latent variables are continuous or categorical, a distinction which is crucial for data interpretation but challenging when the dimensionality is comparable to the sample size. To address this inference problem, we analyze the asymptotic behavior of empirical measures associated with singular vectors corresponding to large spiked singular values. Leveraging these insights, we propose a novel test statistic based on the eigenvector quantile differences and establish its theoretical performance under the null hypothesis. Simulation studies and real data analyses for breast cancer and glioblastoma gene expression datasets demonstrate the effectiveness and practical utility of our method.