# Inference on covariance structure in high-dimensional multi-view data

arXiv: https://arxiv.org/abs/2509.02772 · HTML: https://mlsanity.com/paper/2509.02772/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 60 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Cooperative learning for multiview analysis](https://mlsanity.com/paper/2112.12337/) (2021)
- [Group Factor Analysis](https://mlsanity.com/paper/1411.5799/) (2014)
- [sJIVE: Supervised Joint and Individual Variation Explained](https://mlsanity.com/paper/2102.13278/) (2021)
- [Decoupling shrinkage and selection in Bayesian linear models: a posterior summary perspective](https://mlsanity.com/paper/1408.0464/) (2014)
- [Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications](https://mlsanity.com/paper/1712.08966/) (2017)
- [Hierarchical nuclear norm penalization for multi-view data](https://mlsanity.com/paper/2206.12891/) (2022)
- [Estimating shared subspace with AJIVE: the power and limitation of multiple data matrices](https://mlsanity.com/paper/2501.09336/) (2025)
- [Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices](https://mlsanity.com/paper/2411.17054/) (2024)
- [Bayesian Factor Analysis for Inference on Interactions](https://mlsanity.com/paper/1904.11603/) (2019)
- [Determining the Number of Factors in High-dimensional Generalized Latent Factor Models](https://mlsanity.com/paper/2010.02326/) (2020)
- [Are Latent Factor Regression and Sparse Regression Adequate?](https://mlsanity.com/paper/2203.01219/) (2022)
- [Compressive Bayesian non-negative matrix factorization for mutational signatures analysis](https://mlsanity.com/paper/2404.10974/) (2024)
- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Bayesian Clustering via Fusing of Localized Densities](https://mlsanity.com/paper/2304.00074/) (2023)
- [Spectral decomposition-assisted multi-study factor analysis](https://mlsanity.com/paper/2502.14600/) (2025)
- [Encoding Domain Knowledge in Multi-view Latent Variable Models: A Bayesian Approach with Structured Sparsity](https://mlsanity.com/paper/2204.06242/) (2022)
- [Blessing of dimension in Bayesian inference on covariance matrices](https://mlsanity.com/paper/2404.03805/) (2024)
- [A Latent Variable Approach to Learning High-dimensional Multivariate longitudinal Data](https://mlsanity.com/paper/2405.15053/) (2024)
- [Bayesian Factor-adjusted Sparse Regression](https://mlsanity.com/paper/1903.09741/) (2019)
- [Factor pre-training in Bayesian multivariate logistic models](https://mlsanity.com/paper/2409.17441/) (2024)
- [A Bayesian decision-theoretic approach to sparse estimation](https://mlsanity.com/paper/2502.00126/) (2025)

## Built on by (most cited first, 1 of 1)

- [Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage](https://mlsanity.com/paper/2606.19540/) (2026)

## Abstract (arXiv)

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 active in at least one view. Conditionally on these factors, we choose jointly conjugate prior distributions for factor loadings and residual variances. The resulting posterior is a simple product of normal-inverse gamma distributions for each variable, bypassing MCMC and facilitating posterior computation. We prove favorable increasing-dimension asymptotic properties, including posterior contraction and central limit theorems for point estimators. We show excellent performance in simulations, including accurate uncertainty quantification, and apply the methodology to integrate four high-dimensional views from a multi-omics dataset of cancer cell samples.