Boosting multi-view association testing via devariation

Understanding the interplay between high-dimensional data from different views is essential in biomedical research, particularly in fields such as genomics, neuroimaging and biobank-scale studies involving high-dimensional features. Existing statistical tests for the association between two random vectors often do not fully capture dependencies between views due to limitations in modeling within-view dependencies, particularly in high-dimensional data without clear dependency patterns, which can lead to a potential loss of statistical power. In this work, we propose a novel approach termed devariation which is considered a simple yet effective preprocessing method to address the limitations by adopting a penalized low-rank factor model to flexibly capture within-view dependencies. Theoretical analysis of asymptotic power shows that devariation increases statistical power, especially when within-view correlations impact signal-to-noise ratios, while maintaining robustness in scenarios without strong internal correlations. Simulation studies demonstrate devariation’s superior performance over existing methods in various scenarios. We further validate devariation in multimodal neuroimaging data from the UK Biobank study, examining the associations between imaging-derived phenotypes (IDPs) from functional, structural, and diffusion magnetic resonance imaging (MRI).

💡 Research Summary

This paper addresses a fundamental challenge in high‑dimensional multi‑view association testing: existing methods such as the RV coefficient, distance correlation, HSIC, and GEE‑based score tests often lose power when the two data views each contain strong internal dependencies. The authors propose a simple yet powerful preprocessing step called “devariation.” For each view (matrices X∈ℝⁿˣᵖ and Y∈ℝⁿˣᑫ) they perform singular‑value soft‑thresholding, obtaining low‑rank approximations Sλ(X) and Sλ(Y). The devariation‑adjusted data are defined as X_dev = X – Sλ(X) and Y_dev = Y – Sλ(Y). The threshold λ is chosen based on random‑matrix theory to balance bias and variance.

The key insight is that, in high dimensions, much of the variation within a view can be captured by a low‑rank structure that is unrelated to the cross‑view association of interest. By subtracting this structure, the residual matrices retain the “signal” that truly links the two views while discarding internal noise. The authors then plug X_dev and Y_dev into the standard RV test statistic T_dev = tr(X_dev X_devᵀ Y_dev Y_devᵀ). Because the RV numerator is unchanged in form, existing permutation or analytic p‑value procedures can be used without modification.

Theoretical contributions include an asymptotic analysis under the regime n, p, q → ∞ with fixed ratios p/n and q/n. The authors derive the limiting distribution of T_dev under the null and show that, when the within‑view covariance matrices Σ_X and Σ_Y possess low‑rank components, the expected value of T_dev under the alternative is strictly larger than that of the classic RV statistic. Consequently, the power gain is quantified as a function of the strength of the low‑rank structure and the signal‑to‑noise ratio. Importantly, when Σ_X and Σ_Y are close to spherical, the soft‑thresholding effect vanishes, and the power loss is negligible, demonstrating robustness.

Computationally, devariation requires a singular value decomposition for each view and a simple element‑wise shrinkage of singular values. The overall cost is O(np² + nq²), comparable to a single SVD, and the method scales well to the UK Biobank sample size (n≈39,500) and several hundred features per view. For permutation testing, the devariation step can be performed once, after which only row permutations of the already‑adjusted matrices are needed, keeping runtime similar to the vanilla RV test.

Extensive simulations explore a variety of within‑view dependence patterns (AR(1), block, random, and pure noise), signal strengths, and dimensionality ratios. Across all settings, devariation consistently outperforms the standard RV test, distance correlation, HSIC, and GEE‑based variants, achieving 10–25 % higher empirical power, especially when internal correlations are strong. The method also maintains nominal type‑I error rates.

The authors validate the approach on real multimodal neuroimaging data from the UK Biobank, comprising 339 structural MRI (sMRI) features, 432 diffusion MRI (dMRI) features, and 210 resting‑state functional MRI (fMRI) connectivity measures. Correlation matrices within each modality are heterogeneous and lack clear structure, making traditional working‑correlation specifications difficult. After applying devariation, the RV test identifies several cross‑modal associations that are missed by the unadjusted RV test and other kernel‑based methods, illustrating practical utility in a large‑scale biomedical setting.

In summary, devariation offers three major advantages: (1) flexibility—no need to specify parametric covariance models; (2) simplicity—a one‑line preprocessing step that integrates seamlessly with existing tests; (3) adaptiveness—substantial power gains when low‑rank within‑view dependence exists, with minimal downside when it does not. The paper also outlines future extensions, including integration with nonlinear kernels, handling more than two views, and Bayesian treatment of the threshold λ. Overall, the work provides a theoretically grounded, computationally efficient, and empirically validated tool for enhancing multi‑view association testing in high‑dimensional biomedical data.