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相关任务间的经验贝叶斯谱部分汇聚AI 解读

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected…

通过自适应谱收缩实现过拟合高维矩阵分解AI 解读

Factor models are popular approaches for analyzing high-dimensional data to extract low-rank signals and estimate covariances. They decompose the covariance matrix as the sum of low-rank and diagonal components. A key issue is how to choose the latent dimension $k$, which is particularly challenging when the factor model only holds approximately and in low signal-to-noise scenarios. Bayesian overfitted factor models specify an upper bound on $k$ and rely on structured…

高维多视图数据协方差结构的推断AI 解读

This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo (MCMC) sampling or variational approximations that underestimate uncertainty and lack theoretical guarantees. Our proposed methodology employs spectral decompositions to estimate and align latent factors that are…

用于组学数据的通路引导贝叶斯因子模型AI 解读

Interpreting RNA-sequencing data requires identifying coordinated gene expression patterns that correspond to biological pathways. Standard factor models provide useful dimension reduction but typically ignore existing pathway knowledge or incorporate it through restrictive assumptions, limiting interpretability, and reproducibility. Here, we develop Bayesian Analysis with gene-Sets Informed Latent space (BASIL), a scalable framework for analyzing transcriptomic data that…

谱分解辅助的多研究因子分析AI 解读

This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii) study-specific low-rank components, and (iii) a diagonal term capturing idiosyncratic variability. Our proposed methodology estimates the latent factors via spectral decompositions, with a novel approach for separating shared and specific factors, and…