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

2026-04-20 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Health & Medical Research, Research Methodology & Innovation · Depth: Expert, extended

Summary

Mauri and Dunson introduce Factor Analysis for Multi-view data via spectral Alignment (FAMA), a novel methodology for covariance estimation in high-dimensional multi-view datasets. Traditional approaches often rely on computationally intensive Markov chain Monte Carlo (MCMC) or variational approximations that may underestimate uncertainty. FAMA addresses these limitations by employing spectral decompositions to estimate and align latent factors active across views. It then uses jointly conjugate prior distributions for factor loadings and residual variances, resulting in a posterior that is a simple product of normal-inverse gamma distributions, thus bypassing MCMC. The method demonstrates favorable increasing-dimension asymptotic properties, including posterior contraction and central limit theorems. In simulations, FAMA shows superior performance in accuracy and uncertainty quantification, particularly in unbalanced data scenarios, and is applied to integrate four high-dimensional multi-omics views from cancer cell samples, revealing interpretable biological signals.

Key takeaway

For AI Scientists and Research Scientists working with high-dimensional multi-view data, FAMA provides a robust alternative to traditional MCMC or variational inference methods. Its spectral decomposition and conjugate prior approach offer significantly faster computation and more accurate uncertainty quantification, especially in unbalanced datasets. You should consider FAMA for applications like multi-omics data integration where precise covariance structure inference and reliable credible intervals are critical for drawing valid biological conclusions.

Key insights

FAMA offers a scalable, accurate Bayesian method for multi-view covariance estimation with strong theoretical guarantees.

Principles

• Spectral decomposition aligns latent factors across views.
• Conjugate priors enable efficient posterior computation.
• Asymptotic properties ensure accuracy in high dimensions.

Method

FAMA estimates latent factors via spectral decomposition, then infers loadings and residual variances using surrogate Bayesian regression with conjugate normal-inverse gamma priors, enabling parallel, analytical posterior computation.

In practice

• Integrate diverse multi-omics datasets.
• Quantify uncertainty without MCMC.
• Identify interpretable biological correlations.

Topics

• Multi-view Data Analysis
• Covariance Estimation
• Factor Analysis
• Spectral Decomposition
• Bayesian Computation

Code references

• maurilorenzo/FAMA

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.