Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Subhabrata Majumdar & George Michailidis

Presenter: Aiying Zhang

April 25th, 2018

Goal:

Build a framework based on Gaussian Graphical Model (GGM) for horizontal and vertical integration of information across multi-omics data.

Horizontal: multi-conditions/subtypes

Vertical： different omics

Omics: genomic, proteomic, metabolomic

Contribution：

Borrow information across multiple similar multi-layer networks to simultaneously perform inference on all model parameters.

Introduction

Dataset D, K groups, M layers
Each layer m has pm variables(nodes)
Model: for each group k=1,...,K

Parameters of interest :
- the precision matrices
- the coefficient matrices

JMMLE

Hypothesis testing

Debiased estimator and asymptotic normality

Proposed by Zhang and Zhang (2014)
A debiasing procedure for lasso estimates for individual coeffcients in high-dimensional linear regression
Method:

Performance

Evaluation

K=5, M=2

Within-layer: non-zero probability
Between-layer: non-zero probability
Non-zero elements independently from the uniform distribution
50 replications in each setting

Performance

Evaluation

Simulation 2: Testing

K=2
Generate the by randomly assigning each element to be non-zero with probability , then drawing values of those elements from Unif{ }.
Generate a matrix of differences D, where takes values -1, 1, 0 w.p. 0.1, 0.1, 0.8, respectively.
Finally, set

Type-1 error set , FDR controlled at

\pi

\pi

(D)_{ij}

(D)_{ij}

\alpha = 0.05

\alpha = 0.05

\beta = 0.2

\beta = 0.2

Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Content

Goal:

Contribution：

Introduction

Introduction

JMMLE

JMMLE

Algorithm

Algorithm

Algorithm

Algorithm

Hypothesis testing

Hypothesis testing

Hypothesis testing

Hypothesis testing

Performance

Evaluation

Performance

Evaluation

Performance

Evaluation

Performance

Evaluation

Performance

Evaluation

Discussion

Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Aiying Zhang

Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

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