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Finding Groups of Cross-Correlated Features in Bi-View Data

Miheer Dewaskar, John Palowitch, Mark He, Michael I. Love, Andrew B. Nobel

TL;DR

This work addresses the challenge of discovering groups of cross-correlated features across two data modalities without relying on explicit generative models. It introduces BSP, an iterative testing framework that defines stable bimodules via permutation-based p-values that account for intra-type correlations, with an analytic Gamma-based p-value approximation and a half-permutation scheme to tune the false-discovery parameter. BSP is shown to reliably recover bimodules with strong aggregate cross-correlation and controlled edge-level false discoveries in simulations, outperforming or complementing existing methods such as CONDOR, sCCA, and MatrixEQTL. Applied to GTEx thyroid eQTL data, BSP identifies thousands of SNP-gene bimodules, revealing biologically meaningful subnetworks and providing network-level insights beyond standard eQTL analyses. The approach offers practical tools for exploratory multi-view analysis, including post-processing to handle overlap, essential-edge networks for interpretation, and GO enrichment validation, with broad applicability to genomics and other bi-modal domains.

Abstract

Datasets in which measurements of two (or more) types are obtained from a common set of samples arise in many scientific applications. A common problem in the exploratory analysis of such data is to identify groups of features of different data types that are strongly associated. A bimodule is a pair (A,B) of feature sets from two data types such that the aggregate cross-correlation between the features in A and those in B is large. A bimodule (A,B) is stable if A coincides with the set of features that have significant aggregate correlation with the features in B, and vice-versa. This paper proposes an iterative-testing based bimodule search procedure (BSP) to identify stable bimodules. Compared to existing methods for detecting cross-correlated features, BSP was the best at recovering true bimodules with sufficient signal, while limiting the false discoveries. In addition, we applied BSP to the problem of expression quantitative trait loci (eQTL) analysis using data from the GTEx consortium. BSP identified several thousand SNP-gene bimodules. While many of the individual SNP-gene pairs appearing in the discovered bimodules were identified by standard eQTL methods, the discovered bimodules revealed genomic subnetworks that appeared to be biologically meaningful and worthy of further scientific investigation.

Finding Groups of Cross-Correlated Features in Bi-View Data

TL;DR

This work addresses the challenge of discovering groups of cross-correlated features across two data modalities without relying on explicit generative models. It introduces BSP, an iterative testing framework that defines stable bimodules via permutation-based p-values that account for intra-type correlations, with an analytic Gamma-based p-value approximation and a half-permutation scheme to tune the false-discovery parameter. BSP is shown to reliably recover bimodules with strong aggregate cross-correlation and controlled edge-level false discoveries in simulations, outperforming or complementing existing methods such as CONDOR, sCCA, and MatrixEQTL. Applied to GTEx thyroid eQTL data, BSP identifies thousands of SNP-gene bimodules, revealing biologically meaningful subnetworks and providing network-level insights beyond standard eQTL analyses. The approach offers practical tools for exploratory multi-view analysis, including post-processing to handle overlap, essential-edge networks for interpretation, and GO enrichment validation, with broad applicability to genomics and other bi-modal domains.

Abstract

Datasets in which measurements of two (or more) types are obtained from a common set of samples arise in many scientific applications. A common problem in the exploratory analysis of such data is to identify groups of features of different data types that are strongly associated. A bimodule is a pair (A,B) of feature sets from two data types such that the aggregate cross-correlation between the features in A and those in B is large. A bimodule (A,B) is stable if A coincides with the set of features that have significant aggregate correlation with the features in B, and vice-versa. This paper proposes an iterative-testing based bimodule search procedure (BSP) to identify stable bimodules. Compared to existing methods for detecting cross-correlated features, BSP was the best at recovering true bimodules with sufficient signal, while limiting the false discoveries. In addition, we applied BSP to the problem of expression quantitative trait loci (eQTL) analysis using data from the GTEx consortium. BSP identified several thousand SNP-gene bimodules. While many of the individual SNP-gene pairs appearing in the discovered bimodules were identified by standard eQTL methods, the discovered bimodules revealed genomic subnetworks that appeared to be biologically meaningful and worthy of further scientific investigation.

Paper Structure

This paper contains 61 sections, 1 theorem, 20 equations, 13 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Existing Work
  3. Our Contributions
  4. Organization of the Paper
  5. Stable Bimodules and the Bimodule Search Procedure
  6. Notation
  7. Permutation P-values
  8. Stable Bimodules
  9. The Bimodule Search Procedure (BSP)
  10. Approximation of Permutation P-Values
  11. Post-Processing of Bimodules to Address Overlap
  12. Network-Based Assessment of Minimality
  13. Choice of $\alpha$ Using Half-Permutation Based Edge-Error Estimates
  14. Half-Permutation
  15. Estimating the Edge-Error Using Half-Permutations
  16. ...and 46 more sections

Key Result

Lemma 1

Fix $\rho, \eta \in [0,1]$, $a, b \in \mathbb{N}$, and $d \in \{1, 2 \ldots a\}$ so that $\delta \doteq 1 + \rho(d-1) \geq \eta^2 d$. Suppose $\hbox{$\bf X$}$ is an $a$-dimensional random column vector with covariance matrix $\mathop{\mathrm{Cov}}\nolimits(\hbox{$\bf X$}) = \rho U_a + (1-\rho) I_a$, where $\boldsymbol{\epsilon}$ is another $b$-dimensional random vector independent of $\hbox{$\bf X

Figures (13)

  • Figure 1: Illustration of a bimodule $(A,B)$ (shaded) arising in two numeric data matrices $X$ and $Y$ matched by samples (rows). The columns of $A$ and $B$ need not be contiguous.
  • Figure 2: Recovery of target bimodules under the equality based metric Jaccard and the inclusion based metric recall. Left: dependence of cross-correlation strength and intra-correlation parameter of target bimodules on BSP Jaccard. Right: the averaged recovery curves for target bimodules under CONDOR, BSP, and MatrixEQTL as a function of their cross-correlation strength.
  • Figure 3: The sizes of bimodules detected by BSP, CONDOR and sCCA, and sizes of bimodules detected by BSP under the 5 permuted datasets.
  • Figure 4: BSP is able to detect weak signals. Correlations corresponding to SNP-gene pairs that appear as essential edges (Section \ref{['sec:connectivity']}) in one or more BSP bimodules with mean size ($\sqrt{|A||B|}$) above 10. Local pairs to the left of the blue line (cis-analysis threshold) and distal pairs to the left red line (trans-analysis threshold) show importance at the network level but were not discovered by standard eQTL analyses.
  • Figure 5: Two examples of SNP-gene essential edge networks from bimodules discovered by BSP, mapped onto the genome. The edges in these networks were obtained by thresholding the cross-correlation matrix for the bimodule at the connectivity threshold (Section \ref{['sec:connectivity']}). Comparing such networks to known gene regulatory networks may aid in identifying new SNP-gene interactions.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Lemma 1
  • proof