Inferring network structure in non-normal and mixed discrete-continuous genomic data

TL;DR

This paper introduces a unified Bayesian framework using Gaussian scale mixtures to infer dependence structures in high-dimensional genomic data, accommodating non-normal, mixed discrete-continuous data, and overcoming limitations of traditional models.

Contribution

It proposes a novel approach that handles non-normal and mixed data types for genomic dependence inference, improving upon existing Gaussian and Ising models.

Findings

Effective in simulations compared to alternative methods

Successfully applied to real cancer genomics data

Improves inference accuracy in complex data scenarios

Abstract

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach.