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Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration

Raphiel J. Murden, Ganzhong Tian, Deqiang Qiu, Benajmin B. Risk

Abstract

Collecting multiple types of data on the same set of subjects is common in modern scientific applications including, genomics, metabolomics, and neuroimaging. Joint and Individual Variance Explained (JIVE) seeks a low-rank approximation of the joint variation between two or more sets of features captured on common subjects and isolates this variation from that unique to eachset of features. We develop an expectation-maximization (EM) algorithm to estimate a probabilistic model for the JIVE framework. The model extends probabilistic principal components analysis to multiple data sets. Our maximum likelihood approach simultaneously estimates joint and individual components, which can lead to greater accuracy compared to other methods. We apply ProJIVE to measures of brain morphometry and cognition in Alzheimer's disease. ProJIVE learns biologically meaningful courses of variation, and the joint morphometry and cognition subject scores are strongly related to more expensive existing biomarkers. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Code to reproduce the analysis is available on our GitHub page.

Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration

Abstract

Collecting multiple types of data on the same set of subjects is common in modern scientific applications including, genomics, metabolomics, and neuroimaging. Joint and Individual Variance Explained (JIVE) seeks a low-rank approximation of the joint variation between two or more sets of features captured on common subjects and isolates this variation from that unique to eachset of features. We develop an expectation-maximization (EM) algorithm to estimate a probabilistic model for the JIVE framework. The model extends probabilistic principal components analysis to multiple data sets. Our maximum likelihood approach simultaneously estimates joint and individual components, which can lead to greater accuracy compared to other methods. We apply ProJIVE to measures of brain morphometry and cognition in Alzheimer's disease. ProJIVE learns biologically meaningful courses of variation, and the joint morphometry and cognition subject scores are strongly related to more expensive existing biomarkers. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Code to reproduce the analysis is available on our GitHub page.
Paper Structure (23 sections, 1 theorem, 10 equations, 8 figures)

This paper contains 23 sections, 1 theorem, 10 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. The original JIVE decomposition
  4. Probabilistic JIVE
  5. Connections between ProJIVE and previous models
  6. Model identifiability
  7. Expectation-Maximization algorithm for ProJIVE
  8. Simulation study
  9. Simulation design
  10. Simulation results
  11. Joint Analysis of Brain Morphometry and Cognition in ADNI Data
  12. Cognition
  13. Brain morphometry
  14. Dimension reduction, preprocessing, and summary
  15. Joint subspace
  16. ...and 8 more sections

Key Result

Theorem 1

Suppose $K=2$ and let $f_\Phi$ define the multivariate normal density according to the parameters $\{ \mathbf{W}_{J1}, \mathbf{W}_{J2}, \mathbf{W}_{I1}, \mathbf{W}_{I2}, \; \sigma_1^2, \; \sigma_2^2 \}$ and the assumptions in eqn:jive.ml.mod. Let $f_{\Phi^*}$ denote the multivariate normal density w

Figures (8)

  • Figure 1:
  • Figure 2:
  • Figure 3:
  • Figure 4:
  • Figure 5:
  • ...and 3 more figures

Theorems & Definitions (1)

  • Theorem 1