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Table 1 Summary of notations

From: Fast and robust group-wise eQTL mapping using sparse graphical models

Symbols

Description

K

Number of SNPs

N

Number of genes

D

Number of samples

x

The random variables of K SNPs

z

The random variables of N genes

s

The latent variables to model confounding

 

factors

y

The latent variables to model group-wise

 

associaiton

\(\mathbf {X}\in {\mathbb {R}}^{K \times D}\)

The SNP matrix data

M

Number of latent variables y

H

Number of latent variables s

\(\mathbf {Z} \in {\mathbb {R}}^{N \times D}\)

The gene expression matrix data

\(\textbf {A} \in \mathbb {R}^{M\times K}\)

The coefficient matrix between x and y

\(\textbf {B} \in \mathbb {R}^{N\times M}\)

The coefficient matrix between y and z

\(\textbf {C} \in \mathbb {R}^{N\times K}\)

The coefficient matrix between x and y

\(\textbf {W} \in \mathbb {R}^{N\times H}\)

The coefficient matrix of confounding factors

\(\mathbf {\boldsymbol {\mu }_{\textbf {A}}}\in \mathbb {R}^{M\times 1}\), \(\boldsymbol {\mu }_{\textbf {B}}\in \mathbb {R}^{N\times 1}\)

The translation factor vectors