Reconstruction of molecular network evolution from cross‐sectional omics data

Abstract

Cross-sectional studies may shed light on the evolution of a disease like cancer through the comparison of patient traits among disease stages. This problem is especially challenging when a gene-gene interaction network needs to be reconstructed from omics data, and, in addition, the patients of each stage need not form a homogeneous group. Here, the problem is operationalized as the estimation of stage-wise mixtures of Gaussian graphical models (GGMs) from high-dimensional data. These mixtures are fitted by a (fused) ridge penalized EM algorithm. The fused ridge penalty shrinks GGMs of contiguous stages. The (fused) ridge penalty parameters are chosen through cross-validation. The proposed estimation procedures are shown to be consistent and their performance in other respects is studied in simulation. The down-stream exploitation of the fitted GGMs is outlined. In a data illustration the methodology is employed to identify gene-gene interaction network changes in the transition from normal to cancer prostate tissue.

Updating of the Gaussian graphical model through targeted penalized estimation

“…, p − 1}, and zero otherwise. The precision matrix is estimated from the K data sets in accordance with updating scheme (1) where the penalty parameter λ k is chosen through leave-oneout cross-validation (LOOCV). Updating is initiated with three different targets: a zero target T r = 0 pp , a diagonal target T r = I pp , and a perfect T r = Ω.…”

Analysis of Twitter data with the Bayesian fused graphical lasso

“…The influence of the proposed component membership priors, as specified in (15), on the cluster assignment was assessed. The clustering approaches were compared for BSM only, as the clustering in both the BSM and BFM procedures is carried out for each period separately.…”

“…For the assessment two different scenarios were considered: a) no additional information on the samples is available: BSM-CRP, and b) external evidence on the samples' similarity is available: BSM-DICRP. In scenario a) the priors (15) were equivalent to those of CRP as S ¼ 0. In scenario b) priors (15) were used with a non-zero similarity matrix.…”

“…In scenario a) the priors (15) were equivalent to those of CRP as S ¼ 0. In scenario b) priors (15) were used with a non-zero similarity matrix. For the data in each stage, the similarity matrix S was generated based on the true clustering of the data points, where s ij = 1 if data point i lies in the same cluster as data point j, and s ij = 0 otherwise.…”

“…However, they lack the flexibility to account for heterogeneity within each data set. In [15] the problem of learning the evolution of an interaction network, modeled as a GGM, from cross-sectional, high-dimensional data in the face of heterogeneity was addressed through fused ridge penalized estimation of a combination of mixtures of GGMs. Here we consider this problem from a Bayesian perspective.…”